%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SCT147+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:55:32 AM UTC 2026
% Result : Theorem 33.54s 33.89s
% Output : Proof 33.64s
% 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__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____,
file('theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_A_061_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_096,axiom,
! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i))) ),
file('theBenchmark.p',fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_A_061_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_096) ).
fof(fact_iff,axiom,
! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i))) ),
file('theBenchmark.p',fact_iff) ).
fof(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096,axiom,
! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____))) ),
file('theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) ).
fof(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096,axiom,
! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____))) ),
file('theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) ).
fof(fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096,axiom,
! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
file('theBenchmark.p',fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096) ).
fof(fact_equalityCE,axiom,
! [V_ca_2,T_a,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_equalityCE) ).
fof(fact_in__mkbot,axiom,
! [V_z_2,V_L_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2)))
<=> ( ( V_x_2 != V_z_2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) )
& ( V_x_2 = V_z_2
=> V_x_2 != V_y_2 )
& V_y_2 != V_z_2 ) ),
file('theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [V_z_2,V_L_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2)))
<=> ( ( V_y_2 != V_z_2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) )
& ( V_y_2 = V_z_2
=> V_x_2 != V_y_2 )
& V_x_2 != V_z_2 ) ),
file('theBenchmark.p',fact_in__mktop) ).
fof(fact__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
file('theBenchmark.p',fact__096P_H_A_058_AProf_096) ).
fof(fact_in__rel__def,axiom,
! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ),
file('theBenchmark.p',fact_in__rel__def) ).
fof(fact_same__fstI,axiom,
! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2))) ) ),
file('theBenchmark.p',fact_same__fstI) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [V_r_2,T_a] :
( c_Nitpick_Orefl_H(T_a,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ),
file('theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_ab,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) ),
file('theBenchmark.p',fact_ab) ).
fof(fact_ac,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)))) ),
file('theBenchmark.p',fact_ac) ).
fof(fact_bc,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)))) ),
file('theBenchmark.p',fact_bc) ).
fof(fact__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(fact_split__paired__All,axiom,
! [T_b,T_a,V_Pa_2] :
( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ),
file('theBenchmark.p',fact_split__paired__All) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('theBenchmark.p',fact_u) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('theBenchmark.p',fact_assms_I3_J) ).
fof(fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
file('theBenchmark.p',fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096) ).
fof(fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)),c_Arrow__Order__Mirabelle_OProf)),
file('theBenchmark.p',fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096) ).
fof(fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)),c_Arrow__Order__Mirabelle_OProf)),
file('theBenchmark.p',fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096) ).
fof(fact_eq__mem__trans,axiom,
! [V_A_2,T_a,V_ba_2,V_aa_2] :
( V_aa_2 = V_ba_2
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eq__mem__trans) ).
fof(fact_eqelem__imp__iff,axiom,
! [V_A_2,T_a,V_y_2,V_x_2] :
( V_x_2 = V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eqelem__imp__iff) ).
fof(fact_eqset__imp__iff,axiom,
! [V_x_2,T_a,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_eqset__imp__iff) ).
fof(fact_mem__def,axiom,
! [V_A_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_mem__def) ).
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_ba_2,V_aa_2,T_b,T_a] :
( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2)
<=> ( V_ba_2 = V_b_H_2
& V_aa_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_Pair__eq) ).
fof(fact__C1_C,axiom,
! [V_P_Ha_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
( V_aa_2 != V_ba_2
=> ( V_a_H_2 != V_b_H_2
=> ( V_aa_2 != V_b_H_2
=> ( V_ba_2 != V_a_H_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_Ha_2),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_Ha_2))) ) ) ) ) ) ) ) ),
file('theBenchmark.p',fact__C1_C) ).
fof(fact__C2_C,axiom,
! [V_P_Ha_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
( V_aa_2 != V_ba_2
=> ( V_a_H_2 != V_b_H_2
=> ( V_aa_2 != V_b_H_2
=> ( V_ba_2 != V_a_H_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_Ha_2),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_Ha_2))) ) ) ) ) ) ) ) ),
file('theBenchmark.p',fact__C2_C) ).
fof(fact_pred__equals__eq2,axiom,
! [V_S_2,V_R_2,T_b,T_a] :
( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)
<=> V_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_prod_Orecs,axiom,
! [V_ba_2,V_aa_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2),
file('theBenchmark.p',fact_prod_Orecs) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('theBenchmark.p',fact_assms_I1_J) ).
fof(fact_in__lex__prod,axiom,
! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_H_2)),V_s_2))
& V_aa_2 = V_a_H_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_in__lex__prod) ).
fof(fact_dictator__def,axiom,
! [V_i_2,V_Fa_2] :
( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
=> hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2) ) ),
file('theBenchmark.p',fact_dictator__def) ).
fof(fact_in__below,axiom,
! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
( V_aa_2 != V_ba_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_aa_2),V_ba_2)))
<=> ( ( V_y_2 != V_aa_2
=> ( ( V_x_2 != V_aa_2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) )
& ( V_x_2 = V_aa_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2))
| V_y_2 = V_ba_2 ) ) ) )
& ( V_y_2 = V_aa_2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2)) )
& V_x_2 != V_y_2 ) ) ) ),
file('theBenchmark.p',fact_in__below) ).
fof(fact_internal__split__conv,axiom,
! [V_ba_2,V_aa_2,V_ca_2,T_a,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_a,V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_ca_2,V_aa_2),V_ba_2),
file('theBenchmark.p',fact_internal__split__conv) ).
fof(fact_const__Lin__Prof,axiom,
! [V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,V_L_2)),c_Arrow__Order__Mirabelle_OProf)) ),
file('theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_pred__equals__eq,axiom,
! [V_S_2,V_R_2,T_a] :
( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)
<=> V_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_below__Lin,axiom,
! [V_L_2,V_y_2,V_x_2] :
( V_x_2 != V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('theBenchmark.p',fact_below__Lin) ).
fof(fact_mktop__Lin,axiom,
! [V_x_2,V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mkbot__Lin,axiom,
! [V_x_2,V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_eq__mem,axiom,
! [V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_eq__mem) ).
fof(fact_notin__Lin__iff,axiom,
! [V_y_2,V_x_2,V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> ( V_x_2 != V_y_2
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2)) ) ) ),
file('theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [V_ba_2,V_aa_2,V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2)) ) ),
file('theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_PiE,axiom,
! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_PiE) ).
fof(fact_in__above,axiom,
! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
( V_aa_2 != V_ba_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_aa_2,V_ba_2)))
<=> ( ( V_x_2 != V_ba_2
=> ( ( V_y_2 != V_ba_2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) )
& ( V_y_2 = V_ba_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2))
| V_x_2 = V_aa_2 ) ) ) )
& ( V_x_2 = V_ba_2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2)) )
& V_x_2 != V_y_2 ) ) ) ),
file('theBenchmark.p',fact_in__above) ).
fof(fact_dictatorI,axiom,
! [V_i_2,V_Fa_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
=> ! [B_a,B_b] :
( B_a != B_b
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ),
file('theBenchmark.p',fact_dictatorI) ).
fof(fact_funcset__mem,axiom,
! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2)) ) ),
file('theBenchmark.p',fact_funcset__mem) ).
fof(fact_Pi__mem,axiom,
! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) ) ),
file('theBenchmark.p',fact_Pi__mem) ).
fof(fact_funcset__id,axiom,
! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2)))),
file('theBenchmark.p',fact_funcset__id) ).
fof(fact_above__Lin,axiom,
! [V_L_2,V_y_2,V_x_2] :
( V_x_2 != V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('theBenchmark.p',fact_above__Lin) ).
fof(fact_unanimity__def,axiom,
! [V_Fa_2] :
( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
=> ! [B_a,B_b] :
( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) ),
file('theBenchmark.p',fact_unanimity__def) ).
fof(fact_IIA__def,axiom,
! [V_Fa_2] :
( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf))
=> ! [B_a,B_b] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa))) ) ) ) ) ),
file('theBenchmark.p',fact_IIA__def) ).
fof(fact_complete__Lin,axiom,
! [V_ba_2,V_aa_2] :
( V_aa_2 != V_ba_2
=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('theBenchmark.p',fact_complete__Lin) ).
fof(fact_Pi__I,axiom,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ),
file('theBenchmark.p',fact_Pi__I) ).
fof(fact_funcsetI,axiom,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) ),
file('theBenchmark.p',fact_funcsetI) ).
fof(fact_curry__def,axiom,
! [V_y_2,V_x_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,T_a,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),
file('theBenchmark.p',fact_curry__def) ).
fof(fact_Pi__I_H,axiom,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ),
file('theBenchmark.p',fact_Pi__I_H) ).
fof(fact_Pi__cong,axiom,
! [V_B_2,T_b,V_g_2,V_f_2,V_A_2,T_a] :
( ! [B_w] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_w),V_A_2))
=> hAPP(V_f_2,B_w) = hAPP(V_g_2,B_w) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ) ),
file('theBenchmark.p',fact_Pi__cong) ).
fof(fact_funcset__compose,axiom,
! [V_C_2,V_g_2,T_c,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_c)),V_g_2),c_FuncSet_OPi(T_b,T_c,V_B_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b,V_C_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_c)),c_FuncSet_Ocompose(T_a,T_b,T_c,V_A_2,V_g_2,V_f_2)),c_FuncSet_OPi(T_a,T_c,V_A_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a,V_C_2)))) ) ),
file('theBenchmark.p',fact_funcset__compose) ).
fof(fact_compose__assoc,axiom,
! [V_D_2,V_h_2,T_d,V_C_2,V_g_2,T_c,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_c)),V_g_2),c_FuncSet_OPi(T_b,T_c,V_B_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b,V_C_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,T_d)),V_h_2),c_FuncSet_OPi(T_c,T_d,V_C_2,c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c,V_D_2))))
=> c_FuncSet_Ocompose(T_a,T_c,T_d,V_A_2,V_h_2,c_FuncSet_Ocompose(T_a,T_b,T_c,V_A_2,V_g_2,V_f_2)) = c_FuncSet_Ocompose(T_a,T_b,T_d,V_A_2,c_FuncSet_Ocompose(T_b,T_c,T_d,V_B_2,V_h_2,V_g_2),V_f_2) ) ) ),
file('theBenchmark.p',fact_compose__assoc) ).
fof(fact_acc__downward,axiom,
! [V_aa_2,V_r_2,V_ba_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downward) ).
fof(fact_acc_Osimps,axiom,
! [V_r_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_aa_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_acc_Osimps) ).
fof(fact_curryI,axiom,
! [V_ba_2,V_aa_2,T_b,T_a,V_f_2] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2)) ),
file('theBenchmark.p',fact_curryI) ).
fof(fact_compose__eq,axiom,
! [V_f_2,V_g_2,T_b,T_c,V_A_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hAPP(c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2),V_x_2) = hAPP(V_g_2,hAPP(V_f_2,V_x_2)) ),
file('theBenchmark.p',fact_compose__eq) ).
fof(fact_curryD,axiom,
! [V_ba_2,V_aa_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))) ),
file('theBenchmark.p',fact_curryD) ).
fof(fact_curryE,axiom,
! [V_ba_2,V_aa_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))) ),
file('theBenchmark.p',fact_curryE) ).
fof(fact_curry__conv,axiom,
! [V_ba_2,V_aa_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,T_a,V_f_2),V_aa_2),V_ba_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)),
file('theBenchmark.p',fact_curry__conv) ).
fof(fact_accp__acc__eq,axiom,
! [V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
file('theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_acc_OaccI,axiom,
! [V_r_2,V_x_2,T_a] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
file('theBenchmark.p',fact_acc_OaccI) ).
fof(fact_not__acc__down,axiom,
! [V_R_2,V_x_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
=> ~ ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ),
file('theBenchmark.p',fact_not__acc__down) ).
fof(fact_compose__extensional,axiom,
! [V_g_2,V_f_2,V_A_2,T_c,T_b,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_f_2,V_g_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2))),
file('theBenchmark.p',fact_compose__extensional) ).
fof(fact_acc__downwards,axiom,
! [V_ba_2,V_r_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards) ).
fof(fact_acc__downwards__aux,axiom,
! [V_r_2,V_aa_2,V_ba_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_wfrec__rel_Oequations,axiom,
! [V_a2_2,V_a1_2,V_Fa_2,V_R_2,T_b,T_a] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2),hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2)))
<=> ? [B_g] :
( ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_a1_2)),V_R_2))
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(B_g,B_z))) )
& hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2) = hAPP(hAPP(V_Fa_2,B_g),V_a1_2) ) ),
file('theBenchmark.p',fact_wfrec__rel_Oequations) ).
fof(fact_tfl__cut__apply,axiom,
! [T_b,V_aa_2,V_x_2,T_a,B_f,B_R] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),B_R))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),B_f),B_R),V_aa_2),V_x_2) = hAPP(B_f,V_x_2) ),
file('theBenchmark.p',fact_tfl__cut__apply) ).
fof(fact_cuts__eq,axiom,
! [V_g_2,V_x_2,V_r_2,V_f_2,T_b,T_a] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2) = hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_g_2),V_r_2),V_x_2)
<=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2))
=> hAPP(V_f_2,B_y) = hAPP(V_g_2,B_y) ) ),
file('theBenchmark.p',fact_cuts__eq) ).
fof(fact_accp__downward,axiom,
! [V_aa_2,V_ba_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) ) ),
file('theBenchmark.p',fact_accp__downward) ).
fof(fact_accp_Oequations,axiom,
! [V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp_Osimps,axiom,
! [V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Osimps) ).
fof(fact_cut__apply,axiom,
! [V_f_2,T_b,V_r_2,V_aa_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),V_r_2))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_aa_2),V_x_2) = hAPP(V_f_2,V_x_2) ),
file('theBenchmark.p',fact_cut__apply) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [V_r_2,V_aa_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))),
file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_r__into__rtrancl,axiom,
! [V_r_2,V_p_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
file('theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_rtrancl__trans,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_Id__compose,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
=> c_FuncSet_Ocompose(T_a,T_b,T_b,V_A_2,c_FuncSet_Orestrict(T_b,T_b,c_COMBI(T_b),V_B_2),V_f_2) = V_f_2 ) ),
file('theBenchmark.p',fact_Id__compose) ).
fof(fact_compose__Id,axiom,
! [V_B_2,V_A_2,V_g_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
=> c_FuncSet_Ocompose(T_a,T_a,T_b,V_A_2,V_g_2,c_FuncSet_Orestrict(T_a,T_a,c_COMBI(T_a),V_A_2)) = V_g_2 ) ),
file('theBenchmark.p',fact_compose__Id) ).
fof(fact_adm__lemma,axiom,
! [V_Fa_2,V_R_2,T_b,T_a] : c_Recdef_Oadm__wf(T_a,T_b,V_R_2,hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(T_a,T_a),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),c_COMBS(T_a,T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),hAPP(c_COMBB(tc_fun(T_a,T_b),tc_fun(T_a,T_b),T_a),V_Fa_2)),hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_fun(T_a,T_b))),c_Recdef_Ocut(T_a,T_b)),V_R_2)))),c_COMBI(T_a))),
file('theBenchmark.p',fact_adm__lemma) ).
fof(fact_compose__def,axiom,
! [V_f_2,V_g_2,V_A_2,T_b,T_c,T_a] : c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2) = c_FuncSet_Orestrict(T_a,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_a),V_g_2),V_f_2),V_A_2),
file('theBenchmark.p',fact_compose__def) ).
fof(fact_extensional__restrict,axiom,
! [V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
=> c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2) = V_f_2 ),
file('theBenchmark.p',fact_extensional__restrict) ).
fof(fact_restrict__extensional,axiom,
! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2))),
file('theBenchmark.p',fact_restrict__extensional) ).
fof(fact_rtrancl__idemp,axiom,
! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
file('theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_restrictI,axiom,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ),
file('theBenchmark.p',fact_restrictI) ).
fof(fact_restrict__in__funcset,axiom,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) ),
file('theBenchmark.p',fact_restrict__in__funcset) ).
fof(fact_single__valued__confluent,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ),
file('theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_adm__wf__def,axiom,
! [V_Fa_2,V_R_2,T_b,T_a] :
( c_Recdef_Oadm__wf(T_a,T_b,V_R_2,V_Fa_2)
<=> ! [B_f,B_g,B_x] :
( ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),B_x)),V_R_2))
=> hAPP(B_f,B_z) = hAPP(B_g,B_z) )
=> hAPP(hAPP(V_Fa_2,B_f),B_x) = hAPP(hAPP(V_Fa_2,B_g),B_x) ) ),
file('theBenchmark.p',fact_adm__wf__def) ).
fof(fact_cut__def,axiom,
! [V_f_2,T_b,V_r_2,V_x_2,V_y_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2),V_y_2) = c_HOL_Oundefined(T_b) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2),V_y_2) = hAPP(V_f_2,V_y_2) ) ),
file('theBenchmark.p',fact_cut__def) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [V_y_2,V_R_2,V_x_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_a,V_R_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_converse__rtranclE2,axiom,
! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))
=> ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_2)
=> ~ ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) ) ) ),
file('theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
=> ( ! [B_a,B_b,B_aa,B_ba] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
=> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ),
file('theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_restrict__def,axiom,
! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = c_HOL_Oundefined(T_b) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ),
file('theBenchmark.p',fact_restrict__def) ).
fof(fact_restrict__apply,axiom,
! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = c_HOL_Oundefined(T_b) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ),
file('theBenchmark.p',fact_restrict__apply) ).
fof(fact_extensional__arb,axiom,
! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hAPP(V_f_2,V_x_2) = c_HOL_Oundefined(T_b) ) ),
file('theBenchmark.p',fact_extensional__arb) ).
fof(fact_DomainI,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))) ),
file('theBenchmark.p',fact_DomainI) ).
fof(fact_Domain__iff,axiom,
! [V_r_2,T_b,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2)) ),
file('theBenchmark.p',fact_Domain__iff) ).
fof(fact_single__valuedD,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_b,T_a] :
( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2))
=> B_y = B_z ) ) ),
file('theBenchmark.p',fact_single__valued__def) ).
fof(fact_DomainP__Domain__eq,axiom,
! [V_x_2,V_r_2,T_b,T_a] :
( c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2)
<=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_b,V_r_2))) ),
file('theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_rtrancl__induct2,axiom,
! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
=> ( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))
=> ! [B_aa,B_ba] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
=> hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ),
file('theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_extensional__funcset__arb,axiom,
! [V_x_2,V_T_2,V_S_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2))
=> hAPP(V_f_2,V_x_2) = c_HOL_Oundefined(T_b) ) ),
file('theBenchmark.p',fact_extensional__funcset__arb) ).
fof(fact_DomainP_Ointros,axiom,
! [T_b,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
=> c_Predicate_ODomainP(T_a,T_b,V_r_2,V_aa_2) ),
file('theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_extensional__funcset__mem,axiom,
! [V_x_2,V_T_2,V_S_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_T_2)) ) ),
file('theBenchmark.p',fact_extensional__funcset__mem) ).
fof(fact_irrefl__def,axiom,
! [V_r_2,T_a] :
( c_Relation_Oirrefl(T_a,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ),
file('theBenchmark.p',fact_irrefl__def) ).
fof(fact_DomainE,axiom,
! [V_r_2,T_b,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2)))
=> ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2)) ),
file('theBenchmark.p',fact_DomainE) ).
fof(fact_RangeI,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Relation_ORange(T_a,T_b,V_r_2))) ),
file('theBenchmark.p',fact_RangeI) ).
fof(fact_Id__on__iff,axiom,
! [V_A_2,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Id__on__iff) ).
fof(fact_Id__on__eqI,axiom,
! [V_A_2,T_a,V_ba_2,V_aa_2] :
( V_aa_2 = V_ba_2
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Relation_OId__on(T_a,V_A_2))) ) ),
file('theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_wfrec__rel_Osimps,axiom,
! [V_a2_2,V_a1_2,V_Fa_2,V_R_2,T_b,T_a] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2),V_a2_2))
<=> ? [B_g] :
( ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_a1_2)),V_R_2))
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(B_g,B_z))) )
& V_a2_2 = hAPP(hAPP(V_Fa_2,B_g),V_a1_2) ) ),
file('theBenchmark.p',fact_wfrec__rel_Osimps) ).
fof(fact_wfrec__rel_Ointros,axiom,
! [V_g_2,V_Fa_2,T_b,V_R_2,V_x_2,T_a] :
( ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2))
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(V_g_2,B_z))) )
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2),hAPP(hAPP(V_Fa_2,V_g_2),V_x_2))) ),
file('theBenchmark.p',fact_wfrec__rel_Ointros) ).
fof(fact_Range__Id__on,axiom,
! [V_A_2,T_a] : c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Range__Id__on) ).
fof(fact_Domain__Id__on,axiom,
! [V_A_2,T_a] : c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_single__valued__Id__on,axiom,
! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),
file('theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_Range__iff,axiom,
! [V_r_2,T_b,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ORange(T_b,T_a,V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_aa_2)),V_r_2)) ),
file('theBenchmark.p',fact_Range__iff) ).
fof(fact_RangeP__Range__eq,axiom,
! [V_x_2,V_r_2,T_b,T_a] :
( c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2)
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Relation_ORange(T_a,T_b,V_r_2))) ),
file('theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_Id__onE,axiom,
! [V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ),
file('theBenchmark.p',fact_Id__onE) ).
fof(fact_RangeE,axiom,
! [V_r_2,T_b,V_ba_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Relation_ORange(T_b,T_a,V_r_2)))
=> ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_ba_2)),V_r_2)) ),
file('theBenchmark.p',fact_RangeE) ).
fof(fact_extensionalityI,axiom,
! [V_g_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
=> V_f_2 = V_g_2 ) ) ),
file('theBenchmark.p',fact_extensionalityI) ).
fof(fact_single__valuedI,axiom,
! [V_r_2,T_b,T_a] :
( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2))
=> B_y = B_z ) )
=> c_Relation_Osingle__valued(T_a,T_b,V_r_2) ),
file('theBenchmark.p',fact_single__valuedI) ).
fof(fact_extensional__funcset__def,axiom,
! [V_T_2,V_S_2,T_b,T_a] : c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_S_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_T_2)),c_FuncSet_Oextensional(T_a,T_b,V_S_2)),
file('theBenchmark.p',fact_extensional__funcset__def) ).
fof(fact_rtranclE,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( V_aa_2 != V_ba_2
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_y)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_ba_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_rtranclE) ).
fof(fact_inf1I,axiom,
! [T_a,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(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_RangeP_Ointros,axiom,
! [T_b,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
=> c_Predicate_ORangeP(T_a,T_b,V_r_2,V_ba_2) ),
file('theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_IntI,axiom,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) ) ),
file('theBenchmark.p',fact_IntI) ).
fof(fact_IntE,axiom,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_IntE) ).
fof(fact_RangeP_Oequations,axiom,
! [V_a2_2,V_r_2,T_b,T_a] :
( c_Predicate_ORangeP(T_a,T_b,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_Int__absorb,axiom,
! [V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),
file('theBenchmark.p',fact_Int__commute) ).
fof(fact_Int__left__absorb,axiom,
! [V_B_2,V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),
file('theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_Int__left__commute,axiom,
! [V_C_2,V_B_2,V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)),
file('theBenchmark.p',fact_Int__left__commute) ).
fof(fact_Int__assoc,axiom,
! [V_C_2,V_B_2,V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),
file('theBenchmark.p',fact_Int__assoc) ).
fof(fact_inf1D1,axiom,
! [V_x_2,V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))
=> hBOOL(hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_inf1D2) ).
fof(fact_Int__iff,axiom,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ),
file('theBenchmark.p',fact_IntD1) ).
fof(fact_IntD2,axiom,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ),
file('theBenchmark.p',fact_IntD2) ).
fof(fact_inf__Int__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_a] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2))) ),
file('theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_inf__fun__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_inf__fun__def) ).
fof(fact_inf__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_inf__apply) ).
fof(fact_rtrancl__induct,axiom,
! [V_Pa_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(V_Pa_2,V_aa_2))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_y)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_z)),V_r_2))
=> ( hBOOL(hAPP(V_Pa_2,B_y))
=> hBOOL(hAPP(V_Pa_2,B_z)) ) ) )
=> hBOOL(hAPP(V_Pa_2,V_ba_2)) ) ) ),
file('theBenchmark.p',fact_rtrancl__induct) ).
fof(fact_converse__rtrancl__induct,axiom,
! [V_Pa_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(V_Pa_2,V_ba_2))
=> ( ! [B_y,B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_z)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(V_Pa_2,B_z))
=> hBOOL(hAPP(V_Pa_2,B_y)) ) ) )
=> hBOOL(hAPP(V_Pa_2,V_aa_2)) ) ) ),
file('theBenchmark.p',fact_converse__rtrancl__induct) ).
fof(fact_converse__rtranclE,axiom,
! [V_r_2,V_z_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( V_x_2 != V_z_2
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ),
file('theBenchmark.p',fact_converse__rtranclE) ).
fof(fact_total__on__def,axiom,
! [V_r_2,V_A_2,T_a] :
( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
=> ( B_x != B_xa
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2)) ) ) ) ) ),
file('theBenchmark.p',fact_total__on__def) ).
fof(fact_inf__Int__eq2,axiom,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2))) ),
file('theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_inf_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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)
=> 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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b) = 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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = 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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = 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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) = 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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = 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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = 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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)) ),
file('theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,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)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) ),
file('theBenchmark.p',fact_inf__assoc) ).
fof(fact_in__inv__image,axiom,
! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),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),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_refl__onD,axiom,
! [V_aa_2,V_r_2,V_A_2,T_a] :
( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_refl__onD) ).
fof(fact_refl__onD2,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD2) ).
fof(fact_refl__onD1,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD1) ).
fof(fact_trancl__into__rtrancl,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
file('theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_rtranclp__rtrancl__eq,axiom,
! [V_xa_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2),V_xa_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_xa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
file('theBenchmark.p',fact_rtranclp__rtrancl__eq) ).
fof(fact_rtranclp_Ortrancl__refl,axiom,
! [V_aa_2,V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_aa_2)),
file('theBenchmark.p',fact_rtranclp_Ortrancl__refl) ).
fof(fact_r__into__rtranclp,axiom,
! [T_a,V_y_2,V_x_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_r__into__rtranclp) ).
fof(fact_inf2I,axiom,
! [T_b,T_a,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(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_inf2I) ).
fof(fact_inf2E,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,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_trancl_Or__into__trancl,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
file('theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_inf2D1,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,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_rtranclp__r__diff__Id,axiom,
! [V_r_2,T_a] : c_Transitive__Closure_Ortranclp(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_r_2,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(T_a,V_r_2),
file('theBenchmark.p',fact_rtranclp__r__diff__Id) ).
fof(fact_rtranclp__idemp,axiom,
! [V_r_2,T_a] : c_Transitive__Closure_Ortranclp(T_a,c_Transitive__Closure_Ortranclp(T_a,V_r_2)) = c_Transitive__Closure_Ortranclp(T_a,V_r_2),
file('theBenchmark.p',fact_rtranclp__idemp) ).
fof(fact_rtranclp_Oequations_I1_J,axiom,
! [V_aa_2,V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_aa_2)),
file('theBenchmark.p',fact_rtranclp_Oequations_I1_J) ).
fof(fact_rtranclp_Oequations_I2_J,axiom,
! [V_a3_2,V_a1_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),V_a3_2))
<=> ( ? [B_b] :
( hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),B_b)) )
| V_a3_2 = V_a1_2 ) ),
file('theBenchmark.p',fact_rtranclp_Oequations_I2_J) ).
fof(fact_converse__rtranclp__into__rtranclp,axiom,
! [V_ca_2,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_converse__rtranclp__into__rtranclp) ).
fof(fact_rtranclp_Ortrancl__into__rtrancl,axiom,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_rtranclp_Ortrancl__into__rtrancl) ).
fof(fact_rtranclp__trans,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_z_2)) ) ),
file('theBenchmark.p',fact_rtranclp__trans) ).
fof(fact_r__into__trancl_H,axiom,
! [V_r_2,V_p_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
file('theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_trancl__domain,axiom,
! [V_r_2,T_a] : c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ODomain(T_a,T_a,V_r_2),
file('theBenchmark.p',fact_trancl__domain) ).
fof(fact_trancl__range,axiom,
! [V_r_2,T_a] : c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ORange(T_a,T_a,V_r_2),
file('theBenchmark.p',fact_trancl__range) ).
fof(fact_accp__downwards,axiom,
! [V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_aa_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2)) ) ),
file('theBenchmark.p',fact_accp__downwards) ).
fof(fact_accp__downwards__aux,axiom,
! [V_aa_2,V_ba_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_aa_2))
=> ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2)) ) ),
file('theBenchmark.p',fact_accp__downwards__aux) ).
fof(fact_refl__on__Int,axiom,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
=> ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
=> c_Relation_Orefl__on(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)) ) ),
file('theBenchmark.p',fact_refl__on__Int) ).
fof(fact_refl__on__Id__on,axiom,
! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)),
file('theBenchmark.p',fact_refl__on__Id__on) ).
fof(fact_r__r__into__trancl,axiom,
! [V_ca_2,V_R_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_R_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ),
file('theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_trancl__into__trancl2,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_trancl__trans,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__trans) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [V_R_2,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,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_rtrancl__into__trancl2,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_rtranclD,axiom,
! [V_R_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
& V_aa_2 != V_ba_2 )
| V_aa_2 = V_ba_2 ) ),
file('theBenchmark.p',fact_rtranclD) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_tranclD2,axiom,
! [V_R_2,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ),
file('theBenchmark.p',fact_tranclD2) ).
fof(fact_tranclD,axiom,
! [V_R_2,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) ) ),
file('theBenchmark.p',fact_tranclD) ).
fof(fact_acyclic__def,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_Oacyclic(T_a,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
file('theBenchmark.p',fact_acyclic__def) ).
fof(fact_irrefl__trancl__rD,axiom,
! [V_y_2,V_x_2,V_r_2,T_a] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
=> V_x_2 != V_y_2 ) ),
file('theBenchmark.p',fact_irrefl__trancl__rD) ).
fof(fact_converse__tranclE,axiom,
! [V_r_2,V_z_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),V_r_2))
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ),
file('theBenchmark.p',fact_converse__tranclE) ).
fof(fact_acyclicI,axiom,
! [V_r_2,T_a] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> c_Wellfounded_Oacyclic(T_a,V_r_2) ),
file('theBenchmark.p',fact_acyclicI) ).
fof(fact_acyclic__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_a] :
( c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2),V_r_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
& c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__insert) ).
fof(fact_tranclE,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
=> ~ ! [B_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_c)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_c),V_ba_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_tranclE) ).
fof(fact_tranclp__trancl__eq,axiom,
! [V_xa_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2),V_xa_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_xa_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
file('theBenchmark.p',fact_tranclp__trancl__eq) ).
fof(fact_tranclp_Or__into__trancl,axiom,
! [T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2)) ),
file('theBenchmark.p',fact_tranclp_Or__into__trancl) ).
fof(fact_insertE,axiom,
! [V_A_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2)))
=> ( V_aa_2 != V_ba_2
=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ),
file('theBenchmark.p',fact_insertE) ).
fof(fact_insertCI,axiom,
! [V_ba_2,V_B_2,V_aa_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2))
=> V_aa_2 = V_ba_2 )
=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ),
file('theBenchmark.p',fact_insertCI) ).
fof(fact_insert__inter__insert,axiom,
! [V_B_2,V_A_2,V_aa_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)),
file('theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_insert__absorb2,axiom,
! [V_A_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2),
file('theBenchmark.p',fact_insert__absorb2) ).
fof(fact_insert__commute,axiom,
! [V_A_2,V_y_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)),
file('theBenchmark.p',fact_insert__commute) ).
fof(fact_insert__code,axiom,
! [V_x_2,V_A_2,V_y_2,T_a] :
( hBOOL(hAPP(c_Set_Oinsert(T_a,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_tranclp_Oequations_I1_J,axiom,
! [V_a2_2,V_a1_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),V_a2_2))
<=> ( ? [B_b] :
( hBOOL(hAPP(hAPP(V_r_2,B_b),V_a2_2))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),B_b)) )
| hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ),
file('theBenchmark.p',fact_tranclp_Oequations_I1_J) ).
fof(fact_tranclp_Oequations_I2_J,axiom,
! [V_a3_2,V_a1_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),V_a3_2))
<=> ( ? [B_b] :
( hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),B_b)) )
| hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a3_2)) ) ),
file('theBenchmark.p',fact_tranclp_Oequations_I2_J) ).
fof(fact_tranclp__into__tranclp2,axiom,
! [V_ca_2,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_ba_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_tranclp__into__tranclp2) ).
fof(fact_tranclp_Otrancl__into__trancl,axiom,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_tranclp_Otrancl__into__trancl) ).
fof(fact_tranclp__trans,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_x_2),V_z_2)) ) ),
file('theBenchmark.p',fact_tranclp__trans) ).
fof(fact_insert__absorb,axiom,
! [V_A_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2 ),
file('theBenchmark.p',fact_insert__absorb) ).
fof(fact_insertI2,axiom,
! [V_ba_2,V_B_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ),
file('theBenchmark.p',fact_insertI2) ).
fof(fact_insert__ident,axiom,
! [V_B_2,V_A_2,V_x_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
=> ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2)
<=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_insert__ident) ).
fof(fact_insert__iff,axiom,
! [V_A_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
| V_aa_2 = V_ba_2 ) ),
file('theBenchmark.p',fact_insert__iff) ).
fof(fact_insertI1,axiom,
! [V_B_2,V_aa_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))),
file('theBenchmark.p',fact_insertI1) ).
fof(fact_Range__insert,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_a,T_b] : c_Relation_ORange(T_b,T_a,c_Set_Oinsert(tc_prod(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_aa_2),V_ba_2),V_r_2)) = c_Set_Oinsert(T_a,V_ba_2,c_Relation_ORange(T_b,T_a,V_r_2)),
file('theBenchmark.p',fact_Range__insert) ).
fof(fact_Domain__insert,axiom,
! [V_r_2,V_ba_2,V_aa_2,T_b,T_a] : c_Relation_ODomain(T_a,T_b,c_Set_Oinsert(tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2),V_r_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2)),
file('theBenchmark.p',fact_Domain__insert) ).
fof(fact_rtranclp__into__tranclp2,axiom,
! [V_ca_2,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_rtranclp__into__tranclp2) ).
fof(fact_rtranclpD,axiom,
! [V_ba_2,V_aa_2,V_R_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_R_2),V_aa_2),V_ba_2))
=> ( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_R_2),V_aa_2),V_ba_2))
& V_aa_2 != V_ba_2 )
| V_aa_2 = V_ba_2 ) ),
file('theBenchmark.p',fact_rtranclpD) ).
fof(fact_tranclp__into__rtranclp,axiom,
! [V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ba_2)) ),
file('theBenchmark.p',fact_tranclp__into__rtranclp) ).
fof(fact_rtranclp__into__tranclp1,axiom,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_rtranclp__into__tranclp1) ).
fof(fact_tranclp__rtranclp__tranclp,axiom,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_tranclp__rtranclp__tranclp) ).
fof(fact_rtranclp__tranclp__tranclp,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_x_2),V_z_2)) ) ),
file('theBenchmark.p',fact_rtranclp__tranclp__tranclp) ).
fof(fact_Int__insert__left__if1,axiom,
! [V_B_2,V_C_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) ),
file('theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_Int__insert__right__if1,axiom,
! [V_B_2,V_A_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) ),
file('theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_Int__insert__left__if0,axiom,
! [V_B_2,V_C_2,V_aa_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) ),
file('theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_Int__insert__right__if0,axiom,
! [V_B_2,V_A_2,V_aa_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
file('theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_Int__insert__left,axiom,
! [V_B_2,V_C_2,V_aa_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) ) ),
file('theBenchmark.p',fact_Int__insert__left) ).
fof(fact_Int__insert__right,axiom,
! [V_B_2,V_A_2,V_aa_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) ) ),
file('theBenchmark.p',fact_Int__insert__right) ).
fof(fact_extensional__funcset__restrict__domain,axiom,
! [V_T_2,V_f_2,T_b,V_S_2,V_x_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional__funcset(T_a,T_b,c_Set_Oinsert(T_a,V_x_2,V_S_2),V_T_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,c_HOL_Oundefined(T_b))),c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2))) ) ),
file('theBenchmark.p',fact_extensional__funcset__restrict__domain) ).
fof(fact_extensional__funcset__extend__domainI,axiom,
! [V_x_2,V_S_2,V_f_2,T_b,V_T_2,V_y_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_f_2),c_FuncSet_Oextensional__funcset(T_b,T_a,V_S_2,V_T_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2)),c_FuncSet_Oextensional__funcset(T_b,T_a,c_Set_Oinsert(T_b,V_x_2,V_S_2),V_T_2))) ) ),
file('theBenchmark.p',fact_extensional__funcset__extend__domainI) ).
fof(fact_wf__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_a] :
( c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2),V_r_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
& c_Wellfounded_Owf(T_a,V_r_2) ) ),
file('theBenchmark.p',fact_wf__insert) ).
fof(fact_acyclic__impl__antisym__rtrancl,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_Oacyclic(T_a,V_r_2)
=> c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ),
file('theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
fof(fact_wf__inv__image,axiom,
! [V_f_2,T_b,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_wf__inv__image) ).
fof(fact_wf__lex__prod,axiom,
! [V_rb_2,T_b,V_ra_2,T_a] :
( c_Wellfounded_Owf(T_a,V_ra_2)
=> ( c_Wellfounded_Owf(T_b,V_rb_2)
=> c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ),
file('theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_wf__trancl,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ),
file('theBenchmark.p',fact_wf__trancl) ).
fof(fact_wf__Int2,axiom,
! [V_r_H_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_H_2,V_r_2)) ),
file('theBenchmark.p',fact_wf__Int2) ).
fof(fact_wf__Int1,axiom,
! [V_r_H_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_r_H_2)) ),
file('theBenchmark.p',fact_wf__Int1) ).
fof(fact_wf__acyclic,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> c_Wellfounded_Oacyclic(T_a,V_r_2) ),
file('theBenchmark.p',fact_wf__acyclic) ).
fof(fact_wf__irrefl,axiom,
! [V_aa_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),V_r_2)) ),
file('theBenchmark.p',fact_wf__irrefl) ).
fof(fact_wf__asym,axiom,
! [V_x_2,V_aa_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_x_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__asym) ).
fof(fact_wf__not__sym,axiom,
! [V_x_2,V_aa_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_x_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__not__sym) ).
fof(fact_wf__not__refl,axiom,
! [V_aa_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),V_r_2)) ),
file('theBenchmark.p',fact_wf__not__refl) ).
fof(fact_wf__acc__iff,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ),
file('theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_acc__wfD,axiom,
! [V_x_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
file('theBenchmark.p',fact_acc__wfD) ).
fof(fact_antisym__Id__on,axiom,
! [V_A_2,T_a] : c_Relation_Oantisym(T_a,c_Relation_OId__on(T_a,V_A_2)),
file('theBenchmark.p',fact_antisym__Id__on) ).
fof(fact_antisymD,axiom,
! [V_ba_2,V_aa_2,V_r_2,T_a] :
( c_Relation_Oantisym(T_a,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),V_r_2))
=> V_aa_2 = V_ba_2 ) ) ),
file('theBenchmark.p',fact_antisymD) ).
fof(fact_antisym__def,axiom,
! [V_r_2,T_a] :
( c_Relation_Oantisym(T_a,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
=> B_x = B_y ) ) ),
file('theBenchmark.p',fact_antisym__def) ).
fof(fact_fun__upd__triv,axiom,
! [V_x_2,V_f_2,T_b,T_a] : c_Fun_Ofun__upd(T_a,T_b,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_wf__measure,axiom,
! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)),
file('theBenchmark.p',fact_wf__measure) ).
fof(fact_tfl__wfrec,axiom,
! [T_b,T_a,B_M,B_R] :
( c_Wellfounded_Owf(T_a,B_R)
=> ! [B_x] : hAPP(c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_x) = hAPP(hAPP(B_M,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),c_Recdef_Owfrec(T_a,T_b,B_R,B_M)),B_R),B_x)),B_x) ),
file('theBenchmark.p',fact_tfl__wfrec) ).
fof(fact_wfrec,axiom,
! [V_aa_2,V_H_2,T_b,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> hAPP(c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_aa_2) = hAPP(hAPP(V_H_2,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2)),V_r_2),V_aa_2)),V_aa_2) ),
file('theBenchmark.p',fact_wfrec) ).
fof(fact_fun__upd__idem,axiom,
! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
( hAPP(V_f_2,V_x_2) = V_y_2
=> c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2) = V_f_2 ),
file('theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_fun__upd__other,axiom,
! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
( V_z_2 != V_x_2
=> hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ),
file('theBenchmark.p',fact_fun__upd__other) ).
fof(fact_fun__upd__twist,axiom,
! [V_d_2,V_ba_2,V_m_2,T_b,T_a,V_ca_2,V_aa_2] :
( V_aa_2 != V_ca_2
=> c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_aa_2,V_ba_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_ca_2,V_d_2),V_aa_2,V_ba_2) ),
file('theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_fun__upd__apply,axiom,
! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
( ( V_z_2 != V_x_2
=> hAPP(c_Fun_Ofun__upd(T_a,T_b,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_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) ),
file('theBenchmark.p',fact_fun__upd__apply) ).
fof(fact_fun__upd__same,axiom,
! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2,
file('theBenchmark.p',fact_fun__upd__same) ).
fof(fact_fun__upd__upd,axiom,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_z_2),
file('theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_fun__upd__idem__iff,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
( c_Fun_Ofun__upd(T_a,T_b,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__def,axiom,
! [V_ba_2,V_f_2,T_b,T_a,V_aa_2,V_x_2] :
( ( V_x_2 != V_aa_2
=> hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_aa_2,V_ba_2),V_x_2) = hAPP(V_f_2,V_x_2) )
& ( V_x_2 = V_aa_2
=> hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_aa_2,V_ba_2),V_x_2) = V_ba_2 ) ),
file('theBenchmark.p',fact_fun__upd__def) ).
fof(fact_def__wfrec,axiom,
! [V_aa_2,V_H_2,V_r_2,T_b,T_a,V_f_2] :
( V_f_2 = c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2)
=> ( c_Wellfounded_Owf(T_a,V_r_2)
=> hAPP(V_f_2,V_aa_2) = hAPP(hAPP(V_H_2,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_aa_2)),V_aa_2) ) ),
file('theBenchmark.p',fact_def__wfrec) ).
fof(fact_wfrec__def,axiom,
! [V_x_2,V_Fa_2,V_R_2,T_a,T_b] : hAPP(c_Recdef_Owfrec(T_b,T_a,V_R_2,V_Fa_2),V_x_2) = c_HOL_OThe(T_a,c_Recdef_Owfrec__rel(T_b,T_a,V_R_2,hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(T_b,T_b),tc_fun(T_b,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_a)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_a)),tc_fun(T_b,T_a)),c_COMBS(T_b,T_b,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_a)),tc_fun(T_b,tc_fun(T_b,T_a)),tc_fun(T_b,T_a)),hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(T_b,T_a),T_b),V_Fa_2)),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,T_a))),c_Recdef_Ocut(T_b,T_a)),V_R_2)))),c_COMBI(T_b)),V_x_2)),
file('theBenchmark.p',fact_wfrec__def) ).
fof(fact_wf__same__fst,axiom,
! [T_a,V_R_2,T_b,V_Pa_2] :
( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
=> c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__same__fst) ).
fof(fact_wfrec__unique,axiom,
! [V_x_2,V_Fa_2,V_R_2,T_b,T_a] :
( c_Recdef_Oadm__wf(T_a,T_b,V_R_2,V_Fa_2)
=> ( c_Wellfounded_Owf(T_a,V_R_2)
=> ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2),B_y))
=> B_y = B_x )
& hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2),B_x)) ) ) ),
file('theBenchmark.p',fact_wfrec__unique) ).
fof(fact_Nitpick_Owfrec_H__def,axiom,
! [V_x_2,V_Fa_2,T_b,V_R_2,T_a] :
( ( ~ c_Wellfounded_Owf(T_a,V_R_2)
=> c_Nitpick_Owfrec_H(T_a,T_b,V_R_2,V_Fa_2,V_x_2) = c_HOL_OThe(T_b,c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(T_a,T_a),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),c_COMBS(T_a,T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),hAPP(c_COMBB(tc_fun(T_a,T_b),tc_fun(T_a,T_b),T_a),V_Fa_2)),hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_fun(T_a,T_b))),c_Recdef_Ocut(T_a,T_b)),V_R_2)))),c_COMBI(T_a)),V_x_2)) )
& ( c_Wellfounded_Owf(T_a,V_R_2)
=> c_Nitpick_Owfrec_H(T_a,T_b,V_R_2,V_Fa_2,V_x_2) = c_Nitpick_Owf__wfrec_H(T_a,T_b,V_R_2,V_Fa_2,V_x_2) ) ),
file('theBenchmark.p',fact_Nitpick_Owfrec_H__def) ).
fof(fact_the__sym__eq__trivial,axiom,
! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(fact_the__eq__trivial,axiom,
! [V_aa_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_aa_2)) = V_aa_2,
file('theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_Nitpick_Owf__wfrec_H__def,axiom,
! [V_x_2,V_Fa_2,V_R_2,T_a,T_b] : c_Nitpick_Owf__wfrec_H(T_b,T_a,V_R_2,V_Fa_2,V_x_2) = hAPP(hAPP(V_Fa_2,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_b,T_a),c_Nitpick_Owf__wfrec(T_b,T_a,V_R_2,V_Fa_2)),V_R_2),V_x_2)),V_x_2),
file('theBenchmark.p',fact_Nitpick_Owf__wfrec_H__def) ).
fof(fact_wfP__wf__eq,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2))
<=> c_Wellfounded_Owf(T_a,V_r_2) ),
file('theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_wf__eq__minimal,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
<=> ! [B_Q] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
=> ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) )
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) ) ) ),
file('theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_wfP__empty,axiom,
! [T_a] : c_Wellfounded_OwfP(T_a,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,c_COMBK(tc_HOL_Obool,T_a,c_fFalse))),
file('theBenchmark.p',fact_wfP__empty) ).
fof(fact_accp__wfPD,axiom,
! [V_x_2,V_r_2,T_a] :
( c_Wellfounded_OwfP(T_a,V_r_2)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ),
file('theBenchmark.p',fact_accp__wfPD) ).
fof(fact_wfP__accp__iff,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_OwfP(T_a,V_r_2)
<=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ),
file('theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_wfP__trancl,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_OwfP(T_a,V_r_2)
=> c_Wellfounded_OwfP(T_a,c_Transitive__Closure_Otranclp(T_a,V_r_2)) ),
file('theBenchmark.p',fact_wfP__trancl) ).
fof(fact_wf__in__rel,axiom,
! [V_R_2,T_a] :
( c_Wellfounded_Owf(T_a,V_R_2)
=> c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ),
file('theBenchmark.p',fact_wf__in__rel) ).
fof(fact_the__inv__into__def,axiom,
! [V_x_2,V_f_2,V_A_2,T_b,T_a] : c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2,V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))),
file('theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_acc__wfI,axiom,
! [V_r_2,T_a] :
( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2)))
=> c_Wellfounded_Owf(T_a,V_r_2) ),
file('theBenchmark.p',fact_acc__wfI) ).
fof(fact_antisymI,axiom,
! [V_r_2,T_a] :
( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
=> B_x = B_y ) )
=> c_Relation_Oantisym(T_a,V_r_2) ),
file('theBenchmark.p',fact_antisymI) ).
fof(fact_in__measure,axiom,
! [V_f_2,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)))
<=> 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_override__on__def,axiom,
! [V_g_2,V_f_2,T_b,V_A_2,V_aa_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_f_2,V_aa_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_g_2,V_aa_2) ) ),
file('theBenchmark.p',fact_override__on__def) ).
fof(fact_measure__def,axiom,
! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_measure__def) ).
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_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))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ),
file('theBenchmark.p',fact_less__than__iff) ).
fof(fact_less__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_x)
=> c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x) ) ),
file('theBenchmark.p',fact_less__infI1) ).
fof(fact_less__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_x)
=> c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x) ) ),
file('theBenchmark.p',fact_less__infI2) ).
fof(fact_override__on__apply__notin,axiom,
! [V_g_2,V_f_2,T_b,V_A_2,V_aa_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_f_2,V_aa_2) ),
file('theBenchmark.p',fact_override__on__apply__notin) ).
fof(fact_override__on__apply__in,axiom,
! [V_g_2,V_f_2,T_b,V_A_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
=> c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_g_2,V_aa_2) ),
file('theBenchmark.p',fact_override__on__apply__in) ).
fof(fact_mlex__less,axiom,
! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
( 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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ),
file('theBenchmark.p',fact_mlex__less) ).
fof(fact_mlex__prod__def,axiom,
! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))),
file('theBenchmark.p',fact_mlex__prod__def) ).
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_psubsetD,axiom,
! [V_ca_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubsetD) ).
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_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)))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_less__eq) ).
fof(fact_wf__mlex,axiom,
! [V_f_2,V_R_2,T_a] :
( c_Wellfounded_Owf(T_a,V_R_2)
=> c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__mlex) ).
fof(fact_pair__leqI1,axiom,
! [V_t_2,V_s_2,V_ba_2,V_aa_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_ba_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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__leq)) ),
file('theBenchmark.p',fact_pair__leqI1) ).
fof(fact_pair__lessI1,axiom,
! [V_t_2,V_s_2,V_ba_2,V_aa_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_ba_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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__less)) ),
file('theBenchmark.p',fact_pair__lessI1) ).
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)))
<=> 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_psubset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
=> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) ) ),
file('theBenchmark.p',fact_psubset__trans) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_pair__lessI2,axiom,
! [V_t_2,V_s_2,V_ba_2,V_aa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_aa_2,V_ba_2)
=> ( 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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__less)) ) ),
file('theBenchmark.p',fact_pair__lessI2) ).
fof(fact_pair__leqI2,axiom,
! [V_t_2,V_s_2,V_ba_2,V_aa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_aa_2,V_ba_2)
=> ( 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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__leq)) ) ),
file('theBenchmark.p',fact_pair__leqI2) ).
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_inf__sup__ord_I1_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,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)
=> c_Orderings_Oord__class_Oless__eq(T_a,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)
=> c_Orderings_Oord__class_Oless__eq(T_a,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)
=> c_Orderings_Oord__class_Oless__eq(T_a,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_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,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_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2))
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2)
& c_Orderings_Oord__class_Oless__eq(T_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x)
=> c_Orderings_Oord__class_Oless__eq(T_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x)
=> c_Orderings_Oord__class_Oless__eq(T_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> 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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> 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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))
=> ~ ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
=> ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) ) ) ),
file('theBenchmark.p',fact_le__infE) ).
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__leq,axiom,
! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
( 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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ),
file('theBenchmark.p',fact_mlex__leq) ).
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),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_YS_2))),c_FunDef_Omin__weak)) ) ) ),
file('theBenchmark.p',fact_wmin__insertI) ).
fof(fact_wmax__insertI,axiom,
! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ),
file('theBenchmark.p',fact_wmax__insertI) ).
fof(fact_smin__insertI,axiom,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),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_subsetD,axiom,
! [V_ca_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subsetD) ).
fof(fact_subset__psubset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
=> c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
=> c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
<=> ( V_A_2 = V_B_2
| c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
<=> ( V_A_2 != V_B_2
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ),
file('theBenchmark.p',fact_psubset__eq) ).
fof(fact_pred__subset__eq,axiom,
! [V_S_2,V_R_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2) ),
file('theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_pred__subset__eq2,axiom,
! [V_S_2,V_R_2,T_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2) ),
file('theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_set__mp,axiom,
! [V_x_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__mp) ).
fof(fact_set__rev__mp,axiom,
! [V_B_2,V_A_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__rev__mp) ).
fof(fact_in__mono,axiom,
! [V_x_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__mono) ).
fof(fact_wf__subset,axiom,
! [V_p_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_p_2,V_r_2)
=> c_Wellfounded_Owf(T_a,V_p_2) ) ),
file('theBenchmark.p',fact_wf__subset) ).
fof(fact_Domain__mono,axiom,
! [V_s_2,V_r_2,T_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_r_2),c_Relation_ODomain(T_a,T_b,V_s_2)) ),
file('theBenchmark.p',fact_Domain__mono) ).
fof(fact_acc__subset,axiom,
! [V_R2_2,V_R1_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2)) ),
file('theBenchmark.p',fact_acc__subset) ).
fof(fact_Pi__anti__mono,axiom,
! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2,V_A_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2)) ),
file('theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_accp__subset,axiom,
! [V_R2_2,V_R1_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_R1_2,V_R2_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oaccp(T_a,V_R2_2),c_Wellfounded_Oaccp(T_a,V_R1_2)) ),
file('theBenchmark.p',fact_accp__subset) ).
fof(fact_rtrancl__mono,axiom,
! [V_s_2,V_r_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)) ),
file('theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_rtrancl__subset,axiom,
! [V_S_2,V_R_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2))
=> c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ),
file('theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [V_s_2,V_r_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)) ),
file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_rtranclp__mono,axiom,
! [V_s_2,V_r_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_r_2,V_s_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(T_a,V_r_2),c_Transitive__Closure_Ortranclp(T_a,V_s_2)) ),
file('theBenchmark.p',fact_rtranclp__mono) ).
fof(fact_rtranclp__subset,axiom,
! [V_S_2,V_R_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_R_2,V_S_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_S_2,c_Transitive__Closure_Ortranclp(T_a,V_R_2))
=> c_Transitive__Closure_Ortranclp(T_a,V_S_2) = c_Transitive__Closure_Ortranclp(T_a,V_R_2) ) ),
file('theBenchmark.p',fact_rtranclp__subset) ).
fof(fact_Int__lower1,axiom,
! [V_B_2,V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)) ) ),
file('theBenchmark.p',fact_Int__mono) ).
fof(fact_single__valued__subset,axiom,
! [V_s_2,V_r_2,T_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2)
=> ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
=> c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ),
file('theBenchmark.p',fact_single__valued__subset) ).
fof(fact_acyclic__subset,axiom,
! [V_r_2,V_s_2,T_a] :
( c_Wellfounded_Oacyclic(T_a,V_s_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)
=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__subset) ).
fof(fact_antisym__subset,axiom,
! [V_s_2,V_r_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)
=> ( c_Relation_Oantisym(T_a,V_s_2)
=> c_Relation_Oantisym(T_a,V_r_2) ) ),
file('theBenchmark.p',fact_antisym__subset) ).
fof(fact_insert__mono,axiom,
! [V_aa_2,V_D_2,V_C_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2),c_Set_Oinsert(T_a,V_aa_2,V_D_2)) ),
file('theBenchmark.p',fact_insert__mono) ).
fof(fact_subset__insertI2,axiom,
! [V_ba_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_ba_2,V_B_2)) ),
file('theBenchmark.p',fact_subset__insertI2) ).
fof(fact_subset__insertI,axiom,
! [V_aa_2,V_B_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)),
file('theBenchmark.p',fact_subset__insertI) ).
fof(fact_wfP__subset,axiom,
! [V_p_2,V_r_2,T_a] :
( c_Wellfounded_OwfP(T_a,V_r_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_p_2,V_r_2)
=> c_Wellfounded_OwfP(T_a,V_p_2) ) ),
file('theBenchmark.p',fact_wfP__subset) ).
fof(fact_subset__insert,axiom,
! [V_B_2,V_A_2,V_x_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
& hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_insert__subset) ).
fof(fact_trancl__mono,axiom,
! [V_s_2,V_r_2,V_p_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ),
file('theBenchmark.p',fact_trancl__mono) ).
fof(fact_extensional__subset,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_B_2))) ) ),
file('theBenchmark.p',fact_extensional__subset) ).
fof(fact_Domain__Int__subset,axiom,
! [V_B_2,V_A_2,T_b,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2))),
file('theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_Range__Int__subset,axiom,
! [V_B_2,V_A_2,T_b,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2))),
file('theBenchmark.p',fact_Range__Int__subset) ).
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)),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_order__refl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__refl) ).
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_equalityI,axiom,
! [V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_equalityI) ).
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_rev__predicate2D,axiom,
! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_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_Pa_2,T_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2,V_Q_2)
=> ( hBOOL(hAPP(hAPP(V_Pa_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_predicate1D,axiom,
! [V_x_2,V_Q_2,V_Pa_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2)
=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
file('theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [V_Q_2,T_a,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2)
=> hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
file('theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_equalityE,axiom,
! [T_a,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) ) ),
file('theBenchmark.p',fact_subset__trans) ).
fof(fact_equalityD2,axiom,
! [T_a,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) ),
file('theBenchmark.p',fact_equalityD2) ).
fof(fact_equalityD1,axiom,
! [T_a,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
file('theBenchmark.p',fact_equalityD1) ).
fof(fact_set__eq__subset,axiom,
! [T_a,V_B_2,V_A_2] :
( V_A_2 = V_B_2
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ),
file('theBenchmark.p',fact_set__eq__subset) ).
fof(fact_subset__refl,axiom,
! [V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2),
file('theBenchmark.p',fact_subset__refl) ).
fof(fact_le__fun__def,axiom,
! [V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_linorder__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__linear) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_x_2 = V_y_2
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__eq__refl,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( V_x = V_y
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__eq__refl) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_ord__eq__le__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__le__trans) ).
fof(fact_xt1_I3_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I3_J) ).
fof(fact_ord__le__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__le__eq__trans) ).
fof(fact_xt1_I4_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I4_J) ).
fof(fact_order__antisym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_order__antisym) ).
fof(fact_order__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I5_J,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_le__funE,axiom,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_linorder__le__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_order__less__irrefl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__neq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x_2 != V_y_2
<=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ),
file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__neqE) ).
fof(fact_less__imp__neq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_x != V_y ) ),
file('theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__not__sym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__imp__not__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_x != V_y ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_y != V_x ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__asym_H,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ),
file('theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_xt1_I9_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_ord__eq__less__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__less__trans) ).
fof(fact_xt1_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I1_J) ).
fof(fact_ord__less__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__less__eq__trans) ).
fof(fact_xt1_I2_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I2_J) ).
fof(fact_order__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_order__less__asym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__asym) ).
fof(fact_linorder__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( V_x != V_y
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__cases) ).
fof(fact_less__fun__def,axiom,
! [V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__le__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_leI,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_not__leE) ).
fof(fact_linorder__antisym__conv1,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_order__neq__le__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_order__less__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_a != V_b
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_a != V_b
=> c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__less__le__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I7_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_xt1_I8_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_nat__less__le,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
<=> ( V_m_2 != V_n_2
& 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
<=> ( V_m_2 = V_n_2
| 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_nat__less__cases,axiom,
! [V_Pa_2,V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
=> ( ( V_m_2 = V_n_2
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
fof(fact_less__not__refl3,axiom,
! [V_t,V_s] :
( 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] :
( 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] : ~ 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
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> 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
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| 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] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__not__refl) ).
fof(fact_le__antisym,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_le__antisym) ).
fof(fact_le__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ),
file('theBenchmark.p',fact_le__trans) ).
fof(fact_eq__imp__le,axiom,
! [V_n,V_m] :
( V_m = V_n
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_eq__imp__le) ).
fof(fact_nat__le__linear,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_nat__le__linear) ).
fof(fact_le__refl,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_le__refl) ).
fof(fact_less__or__eq__imp__le,axiom,
! [V_n,V_m] :
( ( V_m = V_n
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_le__neq__implies__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( V_m != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_less__imp__le__nat,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__imp__le__nat) ).
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_rp__inv__image__rp,axiom,
! [V_f_2,T_b,V_Pa_2,T_a] :
( c_FunDef_Oreduction__pair(T_a,V_Pa_2)
=> c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_Pa_2),V_f_2)) ),
file('theBenchmark.p',fact_rp__inv__image__rp) ).
fof(fact_min__ext__wf,axiom,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
=> c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ),
file('theBenchmark.p',fact_min__ext__wf) ).
fof(fact_reduction__pairI,axiom,
! [V_S_2,V_R_2,T_a] :
( c_Wellfounded_Owf(T_a,V_R_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)
=> c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
file('theBenchmark.p',fact_reduction__pairI) ).
fof(fact_rp__inv__image__def,axiom,
! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(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_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),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)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))),
file('theBenchmark.p',fact_rp__inv__image__def) ).
fof(fact_rel__compI,axiom,
! [V_s_2,V_ca_2,T_c,V_r_2,V_ba_2,V_aa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_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_ba_2),V_ca_2)),V_s_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_aa_2),V_ca_2)),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2))) ) ),
file('theBenchmark.p',fact_rel__compI) ).
fof(fact_split__eta,axiom,
! [V_f_2,T_c,T_b,T_a] : c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2,
file('theBenchmark.p',fact_split__eta) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [V_ba_2,V_aa_2,V_f1_2,T_a,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2),
file('theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_split__conv,axiom,
! [V_ba_2,V_aa_2,V_f_2,T_a,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f_2,V_aa_2),V_ba_2),
file('theBenchmark.p',fact_split__conv) ).
fof(fact_trancl__unfold__right,axiom,
! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2),
file('theBenchmark.p',fact_trancl__unfold__right) ).
fof(fact_trancl__unfold__left,axiom,
! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
file('theBenchmark.p',fact_trancl__unfold__left) ).
fof(fact_r__comp__rtrancl__eq,axiom,
! [V_r_2,T_a] : c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2),
file('theBenchmark.p',fact_r__comp__rtrancl__eq) ).
fof(fact_rtrancl__idemp__self__comp,axiom,
! [V_R_2,T_a] : c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
file('theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
fof(fact_single__valued__rel__comp,axiom,
! [V_s_2,T_c,V_r_2,T_b,T_a] :
( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
=> ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
=> c_Relation_Osingle__valued(T_a,T_c,c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)) ) ),
file('theBenchmark.p',fact_single__valued__rel__comp) ).
fof(fact_split__weak__cong,axiom,
! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] :
( V_p_2 = V_q_2
=> hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,V_ca_2),V_p_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,V_ca_2),V_q_2) ),
file('theBenchmark.p',fact_split__weak__cong) ).
fof(fact_split__twice,axiom,
! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c),V_g_2),V_p_2)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f_2))),V_g_2)),V_p_2),
file('theBenchmark.p',fact_split__twice) ).
fof(fact_O__assoc,axiom,
! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : c_Relation_Orel__comp(T_a,T_c,T_b,c_Relation_Orel__comp(T_a,T_d,T_c,V_R_2,V_S_2),V_T_2) = c_Relation_Orel__comp(T_a,T_d,T_b,V_R_2,c_Relation_Orel__comp(T_d,T_c,T_b,V_S_2,V_T_2)),
file('theBenchmark.p',fact_O__assoc) ).
fof(fact_split__curry,axiom,
! [V_f_2,T_c,T_b,T_a] : c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,c_Product__Type_Ocurry(T_a,T_b,T_c,V_f_2)) = V_f_2,
file('theBenchmark.p',fact_split__curry) ).
fof(fact_curry__split,axiom,
! [V_f_2,T_c,T_b,T_a] : c_Product__Type_Ocurry(T_a,T_b,T_c,c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,V_f_2)) = V_f_2,
file('theBenchmark.p',fact_curry__split) ).
fof(fact_wf__comp__self,axiom,
! [V_R_2,T_a] :
( c_Wellfounded_Owf(T_a,V_R_2)
<=> c_Wellfounded_Owf(T_a,c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__comp__self) ).
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__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__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_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_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__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__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
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__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
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__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
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_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
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(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_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_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_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_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_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_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__fNot__1,axiom,
! [V_Pa_2] :
( ~ hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(c_fNot,V_Pa_2)) ),
file('theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [V_Pa_2] :
( hBOOL(hAPP(c_fNot,V_Pa_2))
| ~ ~ hBOOL(V_Pa_2) ),
file('theBenchmark.p',help_c__fNot__2) ).
fof(help_c__fconj__1,axiom,
! [V_Q_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
| ~ hBOOL(V_Q_2)
| ~ hBOOL(V_Pa_2) ),
file('theBenchmark.p',help_c__fconj__1) ).
fof(help_c__fconj__2,axiom,
! [V_Q_2,V_Pa_2] :
( hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [V_Q_2,V_Pa_2] :
( hBOOL(V_Q_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fconj__3) ).
fof(conj_0,conjecture,
! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i))) ),
file('theBenchmark.p',conj_0) ).
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]) ).
fof(f_1_4,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(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,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_4]) ).
fof(f_2_1,plain,
v_a____ != v_b____,
inference(fof_nnf,[status(thm)],[fact__096a_A_126_061_Ab_096]) ).
fof(f_2_2,plain,
v_a____ != v_b____,
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
v_a____ != v_b____,
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [B_i] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(fof_nnf,[status(thm)],[fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_A_061_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_096]) ).
fof(f_3_2,plain,
! [U_3] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_3)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_3))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_3)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_5)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_5))) )
& ! [U_4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_4)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_5)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_5))) )
& ! [U_4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_4)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(definitional_conversion,[status(esa)],[f_3_3]) ).
cnf(f_3_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_4)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_5)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_5))) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [B_i] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i))) ) ),
inference(fof_nnf,[status(thm)],[fact_iff]) ).
fof(f_4_2,plain,
! [U_6] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_6))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_6))) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_8] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_8))) )
& ! [U_7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_7))) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_8] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_8))) )
& ! [U_7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_7))) ) ),
inference(definitional_conversion,[status(esa)],[f_4_3]) ).
cnf(f_4_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_7))) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_8))) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [B_i] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i))) ) ),
inference(fof_nnf,[status(thm)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096]) ).
fof(f_5_2,plain,
! [U_9] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_9)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_9)),v_c____),v_b____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_9)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_9))) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_11] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_11)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_11)),v_c____),v_b____))) )
& ! [U_10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_10)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_10))) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_11] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_11)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_11)),v_c____),v_b____))) )
& ! [U_10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_10)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_10))) ) ),
inference(definitional_conversion,[status(esa)],[f_5_3]) ).
cnf(f_5_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_10)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_10))) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,U_11)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_11)),v_c____),v_b____))) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [B_i] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____))) ) ),
inference(fof_nnf,[status(thm)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096]) ).
fof(f_6_2,plain,
! [U_12] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_12)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_12)),v_c____),v_b____)),v_b____),v_a____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_12)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_12)),v_c____),v_b____))) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_14] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_14)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_14)),v_c____),v_b____)),v_b____),v_a____))) )
& ! [U_13] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_13)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_13)),v_c____),v_b____))) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_14] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_14)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_14)),v_c____),v_b____)),v_b____),v_a____))) )
& ! [U_13] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_13)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_13)),v_c____),v_b____))) ) ),
inference(definitional_conversion,[status(esa)],[f_6_3]) ).
cnf(f_6_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_13)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_13)),v_c____),v_b____))) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_14)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_14)),v_c____),v_b____)),v_b____),v_a____))) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [B_i] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____))) ) ),
inference(fof_nnf,[status(thm)],[fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096]) ).
fof(f_7_2,plain,
! [U_15] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_15)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_15)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_15)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_15)),v_c____),v_b____)),v_b____),v_a____))) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_17] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_17)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_17)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) )
& ! [U_16] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_16)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_16)),v_c____),v_b____)),v_b____),v_a____))) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_17] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_17)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_17)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) )
& ! [U_16] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_16)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_16)),v_c____),v_b____)),v_b____),v_a____))) ) ),
inference(definitional_conversion,[status(esa)],[f_7_3]) ).
cnf(f_7_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_16)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_16)),v_c____),v_b____)),v_b____),v_a____))) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_17)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_17)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
! [V_ca_2,T_a,V_B_2,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
| ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).
fof(f_8_2,plain,
! [U_21,U_20,U_19,U_18] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_19))
& ~ hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_18)) )
| ( hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_19))
& hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_18)) )
| U_18 != U_19 ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_19,U_20,U_18,U_21] :
( ~ hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_19))
| ~ sP1(U_19,U_20,U_18,U_21) )
& ! [U_19,U_20,U_18,U_21] :
( ~ hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_18))
| ~ sP1(U_19,U_20,U_18,U_21) )
& ! [U_19,U_20,U_18,U_21] :
( hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_19))
| ~ sP0(U_19,U_20,U_18,U_21) )
& ! [U_19,U_20,U_18,U_21] :
( hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_18))
| ~ sP0(U_19,U_20,U_18,U_21) )
& ! [U_19,U_20,U_18,U_21] :
( sP1(U_19,U_20,U_18,U_21)
| sP0(U_19,U_20,U_18,U_21)
| U_18 != U_19 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP1(U_19,U_20,U_18,U_21)
| sP0(U_19,U_20,U_18,U_21)
| U_18 != U_19 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_18))
| ~ sP0(U_19,U_20,U_18,U_21) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_19))
| ~ sP0(U_19,U_20,U_18,U_21) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_18))
| ~ sP1(U_19,U_20,U_18,U_21) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_20),U_21),U_19))
| ~ sP1(U_19,U_20,U_18,U_21) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [V_z_2,V_L_2,V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
& V_x_2 != V_z_2 )
| ( V_x_2 = V_y_2
& V_x_2 = V_z_2 )
| V_y_2 = V_z_2 )
& ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
| V_x_2 = V_z_2 )
& ( V_x_2 != V_y_2
| V_x_2 != V_z_2 )
& V_y_2 != V_z_2 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__mkbot]) ).
fof(f_9_2,plain,
! [U_25,U_24,U_23,U_22] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_22),U_23)),c_Arrow__Order__Mirabelle_Omkbot(U_24,U_25)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_22),U_23)),U_24))
& U_22 != U_25 )
| ( U_22 = U_23
& U_22 = U_25 )
| U_23 = U_25 )
& ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_22),U_23)),U_24))
| U_22 = U_25 )
& ( U_22 != U_23
| U_22 != U_25 )
& U_23 != U_25 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_22),U_23)),c_Arrow__Order__Mirabelle_Omkbot(U_24,U_25))) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_33,U_31,U_29,U_27] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_27),U_29)),c_Arrow__Order__Mirabelle_Omkbot(U_31,U_33)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_27),U_29)),U_31))
& U_27 != U_33 )
| ( U_27 = U_29
& U_27 = U_33 )
| U_29 = U_33 )
& ! [U_32,U_30,U_28,U_26] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_26),U_28)),U_30))
| U_26 = U_32 )
& ( U_26 != U_28
| U_26 != U_32 )
& U_28 != U_32 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_26),U_28)),c_Arrow__Order__Mirabelle_Omkbot(U_30,U_32))) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_29,U_27,U_33,U_31] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_27),U_29)),U_31))
| ~ sP4(U_29,U_27,U_33,U_31) )
& ! [U_29,U_27,U_33,U_31] :
( U_27 != U_33
| ~ sP4(U_29,U_27,U_33,U_31) )
& ! [U_29,U_27,U_33] :
( U_27 = U_29
| ~ sP3(U_29,U_27,U_33) )
& ! [U_29,U_27,U_33] :
( U_27 = U_33
| ~ sP3(U_29,U_27,U_33) )
& ! [U_32,U_26,U_28,U_30] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_26),U_28)),U_30))
| U_26 = U_32
| ~ sP2(U_32,U_26,U_28,U_30) )
& ! [U_32,U_26,U_28,U_30] :
( U_26 != U_28
| U_26 != U_32
| ~ sP2(U_32,U_26,U_28,U_30) )
& ! [U_32,U_26,U_28,U_30] :
( U_28 != U_32
| ~ sP2(U_32,U_26,U_28,U_30) )
& ! [U_29,U_27,U_33,U_31] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_27),U_29)),c_Arrow__Order__Mirabelle_Omkbot(U_31,U_33)))
| sP4(U_29,U_27,U_33,U_31)
| sP3(U_29,U_27,U_33)
| U_29 = U_33 )
& ! [U_32,U_26,U_28,U_30] :
( sP2(U_32,U_26,U_28,U_30)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_26),U_28)),c_Arrow__Order__Mirabelle_Omkbot(U_30,U_32))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3,sP4])],[f_9_3]) ).
cnf(f_9_5,plain,
( sP2(U_32,U_26,U_28,U_30)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_26),U_28)),c_Arrow__Order__Mirabelle_Omkbot(U_30,U_32))) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_27),U_29)),c_Arrow__Order__Mirabelle_Omkbot(U_31,U_33)))
| sP4(U_29,U_27,U_33,U_31)
| sP3(U_29,U_27,U_33)
| U_29 = U_33 ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_7,plain,
( U_28 != U_32
| ~ sP2(U_32,U_26,U_28,U_30) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_8,plain,
( U_26 != U_28
| U_26 != U_32
| ~ sP2(U_32,U_26,U_28,U_30) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_26),U_28)),U_30))
| U_26 = U_32
| ~ sP2(U_32,U_26,U_28,U_30) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_10,plain,
( U_27 = U_33
| ~ sP3(U_29,U_27,U_33) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_11,plain,
( U_27 = U_29
| ~ sP3(U_29,U_27,U_33) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_12,plain,
( U_27 != U_33
| ~ sP4(U_29,U_27,U_33,U_31) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_27),U_29)),U_31))
| ~ sP4(U_29,U_27,U_33,U_31) ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
! [V_z_2,V_L_2,V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
& V_y_2 != V_z_2 )
| ( V_x_2 = V_y_2
& V_y_2 = V_z_2 )
| V_x_2 = V_z_2 )
& ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
| V_y_2 = V_z_2 )
& ( V_x_2 != V_y_2
| V_y_2 != V_z_2 )
& V_x_2 != V_z_2 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__mktop]) ).
fof(f_10_2,plain,
! [U_37,U_36,U_35,U_34] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_34),U_35)),c_Arrow__Order__Mirabelle_Omktop(U_36,U_37)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_34),U_35)),U_36))
& U_35 != U_37 )
| ( U_34 = U_35
& U_35 = U_37 )
| U_34 = U_37 )
& ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_34),U_35)),U_36))
| U_35 = U_37 )
& ( U_34 != U_35
| U_35 != U_37 )
& U_34 != U_37 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_34),U_35)),c_Arrow__Order__Mirabelle_Omktop(U_36,U_37))) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_45,U_43,U_41,U_39] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_39),U_41)),c_Arrow__Order__Mirabelle_Omktop(U_43,U_45)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_39),U_41)),U_43))
& U_41 != U_45 )
| ( U_39 = U_41
& U_41 = U_45 )
| U_39 = U_45 )
& ! [U_44,U_42,U_40,U_38] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_38),U_40)),U_42))
| U_40 = U_44 )
& ( U_38 != U_40
| U_40 != U_44 )
& U_38 != U_44 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_38),U_40)),c_Arrow__Order__Mirabelle_Omktop(U_42,U_44))) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_45,U_39,U_43,U_41] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_39),U_41)),U_43))
| ~ sP7(U_45,U_39,U_43,U_41) )
& ! [U_45,U_39,U_43,U_41] :
( U_41 != U_45
| ~ sP7(U_45,U_39,U_43,U_41) )
& ! [U_45,U_39,U_41] :
( U_39 = U_41
| ~ sP6(U_45,U_39,U_41) )
& ! [U_45,U_39,U_41] :
( U_41 = U_45
| ~ sP6(U_45,U_39,U_41) )
& ! [U_42,U_38,U_40,U_44] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_38),U_40)),U_42))
| U_40 = U_44
| ~ sP5(U_42,U_38,U_40,U_44) )
& ! [U_42,U_38,U_40,U_44] :
( U_38 != U_40
| U_40 != U_44
| ~ sP5(U_42,U_38,U_40,U_44) )
& ! [U_42,U_38,U_40,U_44] :
( U_38 != U_44
| ~ sP5(U_42,U_38,U_40,U_44) )
& ! [U_45,U_39,U_43,U_41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_39),U_41)),c_Arrow__Order__Mirabelle_Omktop(U_43,U_45)))
| sP7(U_45,U_39,U_43,U_41)
| sP6(U_45,U_39,U_41)
| U_39 = U_45 )
& ! [U_42,U_38,U_40,U_44] :
( sP5(U_42,U_38,U_40,U_44)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_38),U_40)),c_Arrow__Order__Mirabelle_Omktop(U_42,U_44))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6,sP7])],[f_10_3]) ).
cnf(f_10_5,plain,
( sP5(U_42,U_38,U_40,U_44)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_38),U_40)),c_Arrow__Order__Mirabelle_Omktop(U_42,U_44))) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_39),U_41)),c_Arrow__Order__Mirabelle_Omktop(U_43,U_45)))
| sP7(U_45,U_39,U_43,U_41)
| sP6(U_45,U_39,U_41)
| U_39 = U_45 ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_7,plain,
( U_38 != U_44
| ~ sP5(U_42,U_38,U_40,U_44) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_8,plain,
( U_38 != U_40
| U_40 != U_44
| ~ sP5(U_42,U_38,U_40,U_44) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_38),U_40)),U_42))
| U_40 = U_44
| ~ sP5(U_42,U_38,U_40,U_44) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_10,plain,
( U_41 = U_45
| ~ sP6(U_45,U_39,U_41) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_11,plain,
( U_39 = U_41
| ~ sP6(U_45,U_39,U_41) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_12,plain,
( U_41 != U_45
| ~ sP7(U_45,U_39,U_43,U_41) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_39),U_41)),U_43))
| ~ sP7(U_45,U_39,U_43,U_41) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
inference(fof_nnf,[status(thm)],[fact__096P_H_A_058_AProf_096]) ).
fof(f_11_2,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_in__rel__def]) ).
fof(f_12_2,plain,
! [U_50,U_49,U_48,U_47,U_46] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_46,U_47,U_48),U_49),U_50))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_46,U_47)),hAPP(hAPP(c_Product__Type_OPair(U_46,U_47),U_49),U_50)),U_48)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_46,U_47)),hAPP(hAPP(c_Product__Type_OPair(U_46,U_47),U_49),U_50)),U_48))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_46,U_47,U_48),U_49),U_50)) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_60,U_58,U_56,U_54,U_52] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_52,U_54,U_56),U_58),U_60))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_52,U_54)),hAPP(hAPP(c_Product__Type_OPair(U_52,U_54),U_58),U_60)),U_56)) )
& ! [U_59,U_57,U_55,U_53,U_51] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_51,U_53)),hAPP(hAPP(c_Product__Type_OPair(U_51,U_53),U_57),U_59)),U_55))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_51,U_53,U_55),U_57),U_59)) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_52,U_54,U_56,U_58,U_60] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_52,U_54,U_56),U_58),U_60))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_52,U_54)),hAPP(hAPP(c_Product__Type_OPair(U_52,U_54),U_58),U_60)),U_56)) )
& ! [U_55,U_57,U_51,U_53,U_59] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_51,U_53)),hAPP(hAPP(c_Product__Type_OPair(U_51,U_53),U_57),U_59)),U_55))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_51,U_53,U_55),U_57),U_59)) ) ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_51,U_53)),hAPP(hAPP(c_Product__Type_OPair(U_51,U_53),U_57),U_59)),U_55))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_51,U_53,U_55),U_57),U_59)) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_52,U_54,U_56),U_58),U_60))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_52,U_54)),hAPP(hAPP(c_Product__Type_OPair(U_52,U_54),U_58),U_60)),U_56)) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_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_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).
fof(f_13_2,plain,
! [U_67,U_66,U_65,U_64,U_63,U_62,U_61] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_67,U_63),tc_prod(U_67,U_63))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_67,U_63),tc_prod(U_67,U_63)),hAPP(hAPP(c_Product__Type_OPair(U_67,U_63),U_62),U_64)),hAPP(hAPP(c_Product__Type_OPair(U_67,U_63),U_62),U_65))),c_Recdef_Osame__fst(U_67,U_63,U_61,U_66)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_63,U_63)),hAPP(hAPP(c_Product__Type_OPair(U_63,U_63),U_64),U_65)),hAPP(U_66,U_62)))
| ~ hBOOL(hAPP(U_61,U_62)) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_62,U_61,U_63,U_64,U_65,U_66,U_67] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_67,U_63),tc_prod(U_67,U_63))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_67,U_63),tc_prod(U_67,U_63)),hAPP(hAPP(c_Product__Type_OPair(U_67,U_63),U_62),U_64)),hAPP(hAPP(c_Product__Type_OPair(U_67,U_63),U_62),U_65))),c_Recdef_Osame__fst(U_67,U_63,U_61,U_66)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_63,U_63)),hAPP(hAPP(c_Product__Type_OPair(U_63,U_63),U_64),U_65)),hAPP(U_66,U_62)))
| ~ hBOOL(hAPP(U_61,U_62)) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_67,U_63),tc_prod(U_67,U_63))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_67,U_63),tc_prod(U_67,U_63)),hAPP(hAPP(c_Product__Type_OPair(U_67,U_63),U_62),U_64)),hAPP(hAPP(c_Product__Type_OPair(U_67,U_63),U_62),U_65))),c_Recdef_Osame__fst(U_67,U_63,U_61,U_66)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_63,U_63)),hAPP(hAPP(c_Product__Type_OPair(U_63,U_63),U_64),U_65)),hAPP(U_66,U_62)))
| ~ hBOOL(hAPP(U_61,U_62)) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [V_r_2,T_a] :
( ( c_Nitpick_Orefl_H(T_a,V_r_2)
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
& ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
| ~ c_Nitpick_Orefl_H(T_a,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def]) ).
fof(f_14_2,plain,
! [U_71,U_70] :
( ( c_Nitpick_Orefl_H(U_70,U_71)
| ? [U_69] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_70,U_70)),hAPP(hAPP(c_Product__Type_OPair(U_70,U_70),U_69),U_69)),U_71)) )
& ( ! [U_68] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_70,U_70)),hAPP(hAPP(c_Product__Type_OPair(U_70,U_70),U_68),U_68)),U_71))
| ~ c_Nitpick_Orefl_H(U_70,U_71) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_75,U_73] :
( c_Nitpick_Orefl_H(U_73,U_75)
| ? [U_69] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_73,U_73)),hAPP(hAPP(c_Product__Type_OPair(U_73,U_73),U_69),U_69)),U_75)) )
& ! [U_74,U_72] :
( ! [U_68] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_72,U_72)),hAPP(hAPP(c_Product__Type_OPair(U_72,U_72),U_68),U_68)),U_74))
| ~ c_Nitpick_Orefl_H(U_72,U_74) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_75,U_73] :
( c_Nitpick_Orefl_H(U_73,U_75)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_73,U_73)),hAPP(hAPP(c_Product__Type_OPair(U_73,U_73),sK2(U_75,U_73)),sK2(U_75,U_73))),U_75)) )
& ! [U_74,U_72] :
( ! [U_68] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_72,U_72)),hAPP(hAPP(c_Product__Type_OPair(U_72,U_72),U_68),U_68)),U_74))
| ~ c_Nitpick_Orefl_H(U_72,U_74) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_69,sK2(U_75,U_73))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_73,U_75] :
( c_Nitpick_Orefl_H(U_73,U_75)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_73,U_73)),hAPP(hAPP(c_Product__Type_OPair(U_73,U_73),sK2(U_75,U_73)),sK2(U_75,U_73))),U_75)) )
& ! [U_74,U_72,U_68] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_72,U_72)),hAPP(hAPP(c_Product__Type_OPair(U_72,U_72),U_68),U_68)),U_74))
| ~ c_Nitpick_Orefl_H(U_72,U_74) ) ),
inference(definitional_conversion,[status(esa)],[f_14_4]) ).
cnf(f_14_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_72,U_72)),hAPP(hAPP(c_Product__Type_OPair(U_72,U_72),U_68),U_68)),U_74))
| ~ c_Nitpick_Orefl_H(U_72,U_74) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( c_Nitpick_Orefl_H(U_73,U_75)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_73,U_73)),hAPP(hAPP(c_Product__Type_OPair(U_73,U_73),sK2(U_75,U_73)),sK2(U_75,U_73))),U_75)) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_1,plain,
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____))) ) ),
inference(fof_nnf,[status(thm)],[fact_ab]) ).
fof(f_15_2,plain,
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____))) ) ),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____))) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) ) ),
inference(fof_nnf,[status(thm)],[fact_ac]) ).
fof(f_16_2,plain,
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) ) ),
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)))) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)))) ) ),
inference(fof_nnf,[status(thm)],[fact_bc]) ).
fof(f_17_2,plain,
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)))) ) ),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)))) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)))) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(fof_nnf,[status(thm)],[fact__096P_A_058_AProf_096]) ).
fof(f_18_2,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [T_b,T_a,V_Pa_2] :
( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
| ? [B_a,B_b] : ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) )
& ( ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)))
| ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).
fof(f_19_2,plain,
! [U_84,U_83,U_82] :
( ( ! [U_81] : hBOOL(hAPP(U_82,U_81))
| ? [U_80,U_79] : ~ hBOOL(hAPP(U_82,hAPP(hAPP(c_Product__Type_OPair(U_83,U_84),U_80),U_79))) )
& ( ! [U_78,U_77] : hBOOL(hAPP(U_82,hAPP(hAPP(c_Product__Type_OPair(U_83,U_84),U_78),U_77)))
| ? [U_76] : ~ hBOOL(hAPP(U_82,U_76)) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_90,U_88,U_86] :
( ! [U_81] : hBOOL(hAPP(U_86,U_81))
| ? [U_80,U_79] : ~ hBOOL(hAPP(U_86,hAPP(hAPP(c_Product__Type_OPair(U_88,U_90),U_80),U_79))) )
& ! [U_89,U_87,U_85] :
( ! [U_78,U_77] : hBOOL(hAPP(U_85,hAPP(hAPP(c_Product__Type_OPair(U_87,U_89),U_78),U_77)))
| ? [U_76] : ~ hBOOL(hAPP(U_85,U_76)) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_90,U_88,U_86] :
( ! [U_81] : hBOOL(hAPP(U_86,U_81))
| ? [U_80,U_79] : ~ hBOOL(hAPP(U_86,hAPP(hAPP(c_Product__Type_OPair(U_88,U_90),U_80),U_79))) )
& ! [U_89,U_87,U_85] :
( ! [U_78,U_77] : hBOOL(hAPP(U_85,hAPP(hAPP(c_Product__Type_OPair(U_87,U_89),U_78),U_77)))
| ~ hBOOL(hAPP(U_85,sK3(U_89,U_87,U_85))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_76,sK3(U_89,U_87,U_85))],[f_19_3]) ).
fof(f_19_5,plain,
( ! [U_90,U_88,U_86] :
( ! [U_81] : hBOOL(hAPP(U_86,U_81))
| ? [U_79] : ~ hBOOL(hAPP(U_86,hAPP(hAPP(c_Product__Type_OPair(U_88,U_90),sK4(U_90,U_88,U_86)),U_79))) )
& ! [U_89,U_87,U_85] :
( ! [U_78,U_77] : hBOOL(hAPP(U_85,hAPP(hAPP(c_Product__Type_OPair(U_87,U_89),U_78),U_77)))
| ~ hBOOL(hAPP(U_85,sK3(U_89,U_87,U_85))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_80,sK4(U_90,U_88,U_86))],[f_19_4]) ).
fof(f_19_6,plain,
( ! [U_90,U_88,U_86] :
( ! [U_81] : hBOOL(hAPP(U_86,U_81))
| ~ hBOOL(hAPP(U_86,hAPP(hAPP(c_Product__Type_OPair(U_88,U_90),sK4(U_90,U_88,U_86)),sK5(U_90,U_88,U_86)))) )
& ! [U_89,U_87,U_85] :
( ! [U_78,U_77] : hBOOL(hAPP(U_85,hAPP(hAPP(c_Product__Type_OPair(U_87,U_89),U_78),U_77)))
| ~ hBOOL(hAPP(U_85,sK3(U_89,U_87,U_85))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_79,sK5(U_90,U_88,U_86))],[f_19_5]) ).
fof(f_19_7,plain,
( ! [U_86,U_81,U_88,U_90] :
( hBOOL(hAPP(U_86,U_81))
| ~ hBOOL(hAPP(U_86,hAPP(hAPP(c_Product__Type_OPair(U_88,U_90),sK4(U_90,U_88,U_86)),sK5(U_90,U_88,U_86)))) )
& ! [U_85,U_87,U_77,U_78,U_89] :
( hBOOL(hAPP(U_85,hAPP(hAPP(c_Product__Type_OPair(U_87,U_89),U_78),U_77)))
| ~ hBOOL(hAPP(U_85,sK3(U_89,U_87,U_85))) ) ),
inference(definitional_conversion,[status(esa)],[f_19_6]) ).
cnf(f_19_8,plain,
( hBOOL(hAPP(U_85,hAPP(hAPP(c_Product__Type_OPair(U_87,U_89),U_78),U_77)))
| ~ hBOOL(hAPP(U_85,sK3(U_89,U_87,U_85))) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_9,plain,
( hBOOL(hAPP(U_86,U_81))
| ~ hBOOL(hAPP(U_86,hAPP(hAPP(c_Product__Type_OPair(U_88,U_90),sK4(U_90,U_88,U_86)),sK5(U_90,U_88,U_86)))) ),
inference(clausify,[status(thm)],[f_19_7]) ).
fof(f_20_1,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(fof_nnf,[status(thm)],[fact_u]) ).
fof(f_20_2,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(fof_nnf,[status(thm)],[fact_assms_I3_J]) ).
fof(f_21_2,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
inference(fof_nnf,[status(thm)],[fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096]) ).
fof(f_22_2,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
inference(definitional_conversion,[status(esa)],[f_22_1]) ).
cnf(f_22_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)),c_Arrow__Order__Mirabelle_OProf)),
inference(fof_nnf,[status(thm)],[fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096]) ).
fof(f_23_2,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)),c_Arrow__Order__Mirabelle_OProf)),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_c____)),c_Arrow__Order__Mirabelle_OProf)),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)),c_Arrow__Order__Mirabelle_OProf)),
inference(fof_nnf,[status(thm)],[fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096]) ).
fof(f_24_2,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)),c_Arrow__Order__Mirabelle_OProf)),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____)),c_Arrow__Order__Mirabelle_OProf)),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [V_A_2,T_a,V_ba_2,V_aa_2] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2))
| V_aa_2 != V_ba_2 ),
inference(fof_nnf,[status(thm)],[fact_eq__mem__trans]) ).
fof(f_25_2,plain,
! [U_94,U_93,U_92,U_91] :
( hBOOL(hAPP(hAPP(c_member(U_93),U_91),U_94))
| ~ hBOOL(hAPP(hAPP(c_member(U_93),U_92),U_94))
| U_91 != U_92 ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_91,U_94,U_92,U_93] :
( hBOOL(hAPP(hAPP(c_member(U_93),U_91),U_94))
| ~ hBOOL(hAPP(hAPP(c_member(U_93),U_92),U_94))
| U_91 != U_92 ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_93),U_91),U_94))
| ~ hBOOL(hAPP(hAPP(c_member(U_93),U_92),U_94))
| U_91 != U_92 ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [V_A_2,T_a,V_y_2,V_x_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
| V_x_2 != V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_eqelem__imp__iff]) ).
fof(f_26_2,plain,
! [U_98,U_97,U_96,U_95] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_97),U_95),U_98))
| ~ hBOOL(hAPP(hAPP(c_member(U_97),U_96),U_98)) )
& ( hBOOL(hAPP(hAPP(c_member(U_97),U_96),U_98))
| ~ hBOOL(hAPP(hAPP(c_member(U_97),U_95),U_98)) ) )
| U_95 != U_96 ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_96,U_97,U_95,U_98] :
( hBOOL(hAPP(hAPP(c_member(U_97),U_95),U_98))
| ~ hBOOL(hAPP(hAPP(c_member(U_97),U_96),U_98))
| ~ sP8(U_96,U_97,U_95,U_98) )
& ! [U_96,U_97,U_95,U_98] :
( hBOOL(hAPP(hAPP(c_member(U_97),U_96),U_98))
| ~ hBOOL(hAPP(hAPP(c_member(U_97),U_95),U_98))
| ~ sP8(U_96,U_97,U_95,U_98) )
& ! [U_96,U_97,U_95,U_98] :
( sP8(U_96,U_97,U_95,U_98)
| U_95 != U_96 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_26_2]) ).
cnf(f_26_4,plain,
( sP8(U_96,U_97,U_95,U_98)
| U_95 != U_96 ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_97),U_96),U_98))
| ~ hBOOL(hAPP(hAPP(c_member(U_97),U_95),U_98))
| ~ sP8(U_96,U_97,U_95,U_98) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_97),U_95),U_98))
| ~ hBOOL(hAPP(hAPP(c_member(U_97),U_96),U_98))
| ~ sP8(U_96,U_97,U_95,U_98) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [V_x_2,T_a,V_B_2,V_A_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_eqset__imp__iff]) ).
fof(f_27_2,plain,
! [U_102,U_101,U_100,U_99] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_99))
| ~ hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_100)) )
& ( hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_100))
| ~ hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_99)) ) )
| U_99 != U_100 ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_99,U_100,U_102,U_101] :
( hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_99))
| ~ hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_100))
| ~ sP9(U_99,U_100,U_102,U_101) )
& ! [U_99,U_100,U_102,U_101] :
( hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_100))
| ~ hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_99))
| ~ sP9(U_99,U_100,U_102,U_101) )
& ! [U_99,U_100,U_102,U_101] :
( sP9(U_99,U_100,U_102,U_101)
| U_99 != U_100 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP9(U_99,U_100,U_102,U_101)
| U_99 != U_100 ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_100))
| ~ hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_99))
| ~ sP9(U_99,U_100,U_102,U_101) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_99))
| ~ hBOOL(hAPP(hAPP(c_member(U_101),U_102),U_100))
| ~ sP9(U_99,U_100,U_102,U_101) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [V_A_2,V_x_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),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_a),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__def]) ).
fof(f_28_2,plain,
! [U_105,U_104,U_103] :
( ( hBOOL(hAPP(hAPP(c_member(U_103),U_104),U_105))
| ~ hBOOL(hAPP(U_105,U_104)) )
& ( hBOOL(hAPP(U_105,U_104))
| ~ hBOOL(hAPP(hAPP(c_member(U_103),U_104),U_105)) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_111,U_109] :
( ! [U_107] : hBOOL(hAPP(hAPP(c_member(U_107),U_109),U_111))
| ~ hBOOL(hAPP(U_111,U_109)) )
& ! [U_110,U_108] :
( ! [U_106] : ~ hBOOL(hAPP(hAPP(c_member(U_106),U_108),U_110))
| hBOOL(hAPP(U_110,U_108)) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_107,U_111,U_109] :
( hBOOL(hAPP(hAPP(c_member(U_107),U_109),U_111))
| ~ hBOOL(hAPP(U_111,U_109)) )
& ! [U_106,U_108,U_110] :
( ~ hBOOL(hAPP(hAPP(c_member(U_106),U_108),U_110))
| hBOOL(hAPP(U_110,U_108)) ) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_106),U_108),U_110))
| hBOOL(hAPP(U_110,U_108)) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_107),U_109),U_111))
| ~ hBOOL(hAPP(U_111,U_109)) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_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_29_2,plain,
! [U_117,U_116,U_115,U_114,U_113,U_112] :
( ( U_115 = U_117
& U_114 = U_116 )
| hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_114),U_115) != hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_116),U_117) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_117,U_116,U_115,U_114] :
( ! [U_113,U_112] : hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_114),U_115) != hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_116),U_117)
| ( U_115 = U_117
& U_114 = U_116 ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_114,U_115,U_116,U_117] :
( U_115 = U_117
| ~ sP10(U_114,U_115,U_116,U_117) )
& ! [U_114,U_115,U_116,U_117] :
( U_114 = U_116
| ~ sP10(U_114,U_115,U_116,U_117) )
& ! [U_112,U_113,U_114,U_115,U_116,U_117] :
( hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_114),U_115) != hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_116),U_117)
| sP10(U_114,U_115,U_116,U_117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_29_3]) ).
cnf(f_29_5,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_114),U_115) != hAPP(hAPP(c_Product__Type_OPair(U_112,U_113),U_116),U_117)
| sP10(U_114,U_115,U_116,U_117) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( U_114 = U_116
| ~ sP10(U_114,U_115,U_116,U_117) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_7,plain,
( U_115 = U_117
| ~ sP10(U_114,U_115,U_116,U_117) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] :
( ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2)
| V_ba_2 != V_b_H_2
| V_aa_2 != V_a_H_2 )
& ( ( V_ba_2 = V_b_H_2
& V_aa_2 = V_a_H_2 )
| hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2) != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Pair__eq]) ).
fof(f_30_2,plain,
! [U_123,U_122,U_121,U_120,U_119,U_118] :
( ( hAPP(hAPP(c_Product__Type_OPair(U_118,U_119),U_120),U_121) = hAPP(hAPP(c_Product__Type_OPair(U_118,U_119),U_122),U_123)
| U_121 != U_123
| U_120 != U_122 )
& ( ( U_121 = U_123
& U_120 = U_122 )
| hAPP(hAPP(c_Product__Type_OPair(U_118,U_119),U_120),U_121) != hAPP(hAPP(c_Product__Type_OPair(U_118,U_119),U_122),U_123) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_135,U_133,U_131,U_129] :
( ! [U_127,U_125] : hAPP(hAPP(c_Product__Type_OPair(U_125,U_127),U_129),U_131) = hAPP(hAPP(c_Product__Type_OPair(U_125,U_127),U_133),U_135)
| U_131 != U_135
| U_129 != U_133 )
& ! [U_134,U_132,U_130,U_128] :
( ! [U_126,U_124] : hAPP(hAPP(c_Product__Type_OPair(U_124,U_126),U_128),U_130) != hAPP(hAPP(c_Product__Type_OPair(U_124,U_126),U_132),U_134)
| ( U_130 = U_134
& U_128 = U_132 ) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_132,U_130,U_134,U_128] :
( U_130 = U_134
| ~ sP11(U_132,U_130,U_134,U_128) )
& ! [U_132,U_130,U_134,U_128] :
( U_128 = U_132
| ~ sP11(U_132,U_130,U_134,U_128) )
& ! [U_129,U_131,U_125,U_127,U_133,U_135] :
( hAPP(hAPP(c_Product__Type_OPair(U_125,U_127),U_129),U_131) = hAPP(hAPP(c_Product__Type_OPair(U_125,U_127),U_133),U_135)
| U_131 != U_135
| U_129 != U_133 )
& ! [U_132,U_124,U_126,U_130,U_134,U_128] :
( hAPP(hAPP(c_Product__Type_OPair(U_124,U_126),U_128),U_130) != hAPP(hAPP(c_Product__Type_OPair(U_124,U_126),U_132),U_134)
| sP11(U_132,U_130,U_134,U_128) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_30_3]) ).
cnf(f_30_5,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_124,U_126),U_128),U_130) != hAPP(hAPP(c_Product__Type_OPair(U_124,U_126),U_132),U_134)
| sP11(U_132,U_130,U_134,U_128) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_125,U_127),U_129),U_131) = hAPP(hAPP(c_Product__Type_OPair(U_125,U_127),U_133),U_135)
| U_131 != U_135
| U_129 != U_133 ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_7,plain,
( U_128 = U_132
| ~ sP11(U_132,U_130,U_134,U_128) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_8,plain,
( U_130 = U_134
| ~ sP11(U_132,U_130,U_134,U_128) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [V_P_Ha_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_Ha_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
| ? [B_i] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_Ha_2),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
| V_ba_2 = V_a_H_2
| V_aa_2 = V_b_H_2
| V_a_H_2 = V_b_H_2
| V_aa_2 = V_ba_2 ),
inference(fof_nnf,[status(thm)],[fact__C1_C]) ).
fof(f_31_2,plain,
! [U_142,U_141,U_140,U_139,U_138,U_137] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(v_F,U_142)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(v_F,U_141)))
| ? [U_136] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,U_136)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,U_136))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,U_136)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,U_136))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_142),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_141),c_Arrow__Order__Mirabelle_OProf))
| U_138 = U_139
| U_137 = U_140
| U_139 = U_140
| U_137 = U_138 ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_142,U_141,U_140,U_139,U_138,U_137] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(v_F,U_142)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(v_F,U_141)))
| ? [U_144] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,U_144)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,U_144))) )
| ? [U_143] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,U_143)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,U_143))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_142),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_141),c_Arrow__Order__Mirabelle_OProf))
| U_138 = U_139
| U_137 = U_140
| U_139 = U_140
| U_137 = U_138 ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_142,U_141,U_140,U_139,U_138,U_137] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(v_F,U_142)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(v_F,U_141)))
| ? [U_144] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,U_144)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,U_144))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,sK6(U_142,U_141,U_140,U_139,U_138,U_137))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,sK6(U_142,U_141,U_140,U_139,U_138,U_137)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_142),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_141),c_Arrow__Order__Mirabelle_OProf))
| U_138 = U_139
| U_137 = U_140
| U_139 = U_140
| U_137 = U_138 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_143,sK6(U_142,U_141,U_140,U_139,U_138,U_137))],[f_31_3]) ).
fof(f_31_5,plain,
! [U_142,U_141,U_140,U_139,U_138,U_137] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(v_F,U_142)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(v_F,U_141)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,sK7(U_142,U_141,U_140,U_139,U_138,U_137))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,sK7(U_142,U_141,U_140,U_139,U_138,U_137)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,sK6(U_142,U_141,U_140,U_139,U_138,U_137))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,sK6(U_142,U_141,U_140,U_139,U_138,U_137)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_142),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_141),c_Arrow__Order__Mirabelle_OProf))
| U_138 = U_139
| U_137 = U_140
| U_139 = U_140
| U_137 = U_138 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_144,sK7(U_142,U_141,U_140,U_139,U_138,U_137))],[f_31_4]) ).
fof(f_31_6,plain,
( ! [U_137,U_138,U_139,U_140,U_141,U_142] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,sK7(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP13(U_137,U_138,U_139,U_140,U_141,U_142) )
& ! [U_137,U_138,U_139,U_140,U_141,U_142] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,sK7(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP13(U_137,U_138,U_139,U_140,U_141,U_142) )
& ! [U_137,U_138,U_139,U_140,U_141,U_142] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,sK6(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP12(U_137,U_138,U_139,U_140,U_141,U_142) )
& ! [U_137,U_138,U_139,U_140,U_141,U_142] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,sK6(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP12(U_137,U_138,U_139,U_140,U_141,U_142) )
& ! [U_137,U_138,U_139,U_140,U_141,U_142] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(v_F,U_142)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(v_F,U_141)))
| sP13(U_137,U_138,U_139,U_140,U_141,U_142)
| sP12(U_137,U_138,U_139,U_140,U_141,U_142)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_142),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_141),c_Arrow__Order__Mirabelle_OProf))
| U_138 = U_139
| U_137 = U_140
| U_139 = U_140
| U_137 = U_138 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12,sP13])],[f_31_5]) ).
cnf(f_31_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(v_F,U_142)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(v_F,U_141)))
| sP13(U_137,U_138,U_139,U_140,U_141,U_142)
| sP12(U_137,U_138,U_139,U_140,U_141,U_142)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_142),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_141),c_Arrow__Order__Mirabelle_OProf))
| U_138 = U_139
| U_137 = U_140
| U_139 = U_140
| U_137 = U_138 ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,sK6(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP12(U_137,U_138,U_139,U_140,U_141,U_142) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,sK6(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP12(U_137,U_138,U_139,U_140,U_141,U_142) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_139),U_140)),hAPP(U_142,sK7(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP13(U_137,U_138,U_139,U_140,U_141,U_142) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_137),U_138)),hAPP(U_141,sK7(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ sP13(U_137,U_138,U_139,U_140,U_141,U_142) ),
inference(clausify,[status(thm)],[f_31_6]) ).
fof(f_32_1,plain,
! [V_P_Ha_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_Ha_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_Ha_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) ) )
| ? [B_i] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_Ha_2),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
| V_ba_2 = V_a_H_2
| V_aa_2 = V_b_H_2
| V_a_H_2 = V_b_H_2
| V_aa_2 = V_ba_2 ),
inference(fof_nnf,[status(thm)],[fact__C2_C]) ).
fof(f_32_2,plain,
! [U_151,U_150,U_149,U_148,U_147,U_146] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150))) ) )
| ? [U_145] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,U_145)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,U_145))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,U_145)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,U_145))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_151),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_150),c_Arrow__Order__Mirabelle_OProf))
| U_147 = U_148
| U_146 = U_149
| U_148 = U_149
| U_146 = U_147 ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_151,U_150,U_149,U_148,U_147,U_146] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150))) ) )
| ? [U_153] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,U_153)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,U_153))) )
| ? [U_152] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,U_152)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,U_152))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_151),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_150),c_Arrow__Order__Mirabelle_OProf))
| U_147 = U_148
| U_146 = U_149
| U_148 = U_149
| U_146 = U_147 ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_151,U_150,U_149,U_148,U_147,U_146] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150))) ) )
| ? [U_153] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,U_153)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,U_153))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,sK8(U_151,U_150,U_149,U_148,U_147,U_146))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,sK8(U_151,U_150,U_149,U_148,U_147,U_146)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_151),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_150),c_Arrow__Order__Mirabelle_OProf))
| U_147 = U_148
| U_146 = U_149
| U_148 = U_149
| U_146 = U_147 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_152,sK8(U_151,U_150,U_149,U_148,U_147,U_146))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_151,U_150,U_149,U_148,U_147,U_146] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,sK9(U_151,U_150,U_149,U_148,U_147,U_146))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,sK9(U_151,U_150,U_149,U_148,U_147,U_146)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,sK8(U_151,U_150,U_149,U_148,U_147,U_146))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,sK8(U_151,U_150,U_149,U_148,U_147,U_146)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_151),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_150),c_Arrow__Order__Mirabelle_OProf))
| U_147 = U_148
| U_146 = U_149
| U_148 = U_149
| U_146 = U_147 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_153,sK9(U_151,U_150,U_149,U_148,U_147,U_146))],[f_32_4]) ).
fof(f_32_6,plain,
( ! [U_149,U_146,U_150,U_148,U_147,U_151] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ sP16(U_149,U_146,U_150,U_148,U_147,U_151) )
& ! [U_149,U_146,U_150,U_148,U_147,U_151] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ sP16(U_149,U_146,U_150,U_148,U_147,U_151) )
& ! [U_149,U_146,U_150,U_148,U_147,U_151] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,sK9(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP15(U_149,U_146,U_150,U_148,U_147,U_151) )
& ! [U_149,U_146,U_150,U_148,U_147,U_151] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,sK9(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP15(U_149,U_146,U_150,U_148,U_147,U_151) )
& ! [U_149,U_146,U_150,U_148,U_147,U_151] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,sK8(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP14(U_149,U_146,U_150,U_148,U_147,U_151) )
& ! [U_149,U_146,U_150,U_148,U_147,U_151] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,sK8(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP14(U_149,U_146,U_150,U_148,U_147,U_151) )
& ! [U_149,U_146,U_150,U_148,U_147,U_151] :
( sP16(U_149,U_146,U_150,U_148,U_147,U_151)
| sP15(U_149,U_146,U_150,U_148,U_147,U_151)
| sP14(U_149,U_146,U_150,U_148,U_147,U_151)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_151),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_150),c_Arrow__Order__Mirabelle_OProf))
| U_147 = U_148
| U_146 = U_149
| U_148 = U_149
| U_146 = U_147 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15,sP16])],[f_32_5]) ).
cnf(f_32_7,plain,
( sP16(U_149,U_146,U_150,U_148,U_147,U_151)
| sP15(U_149,U_146,U_150,U_148,U_147,U_151)
| sP14(U_149,U_146,U_150,U_148,U_147,U_151)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_151),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_150),c_Arrow__Order__Mirabelle_OProf))
| U_147 = U_148
| U_146 = U_149
| U_148 = U_149
| U_146 = U_147 ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,sK8(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP14(U_149,U_146,U_150,U_148,U_147,U_151) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,sK8(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP14(U_149,U_146,U_150,U_148,U_147,U_151) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(U_151,sK9(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP15(U_149,U_146,U_150,U_148,U_147,U_151) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(U_150,sK9(U_151,U_150,U_149,U_148,U_147,U_146))))
| ~ sP15(U_149,U_146,U_150,U_148,U_147,U_151) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_12,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ sP16(U_149,U_146,U_150,U_148,U_147,U_151) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_13,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_146),U_147)),hAPP(v_F,U_150)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_148),U_149)),hAPP(v_F,U_151)))
| ~ sP16(U_149,U_146,U_150,U_148,U_147,U_151) ),
inference(clausify,[status(thm)],[f_32_6]) ).
fof(f_33_1,plain,
! [V_S_2,V_R_2,T_b,T_a] :
( ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)
| V_R_2 != V_S_2 )
& ( V_R_2 = V_S_2
| hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) != hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2]) ).
fof(f_33_2,plain,
! [U_157,U_156,U_155,U_154] :
( ( hAPP(hAPP(c_COMBC(U_154,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),U_154),c_COMBC(U_155,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_prod(U_154,U_155)),tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),U_154),hAPP(c_COMBB(tc_prod(U_154,U_155),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool),U_155),c_member(tc_prod(U_154,U_155)))),c_Product__Type_OPair(U_154,U_155)))),U_156) = hAPP(hAPP(c_COMBC(U_154,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),U_154),c_COMBC(U_155,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_prod(U_154,U_155)),tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),U_154),hAPP(c_COMBB(tc_prod(U_154,U_155),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool),U_155),c_member(tc_prod(U_154,U_155)))),c_Product__Type_OPair(U_154,U_155)))),U_157)
| U_156 != U_157 )
& ( U_156 = U_157
| hAPP(hAPP(c_COMBC(U_154,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),U_154),c_COMBC(U_155,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_prod(U_154,U_155)),tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),U_154),hAPP(c_COMBB(tc_prod(U_154,U_155),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool),U_155),c_member(tc_prod(U_154,U_155)))),c_Product__Type_OPair(U_154,U_155)))),U_156) != hAPP(hAPP(c_COMBC(U_154,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_fun(U_155,tc_HOL_Obool)),U_154),c_COMBC(U_155,tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_155,tc_prod(U_154,U_155)),tc_fun(U_155,tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool)),U_154),hAPP(c_COMBB(tc_prod(U_154,U_155),tc_fun(tc_fun(tc_prod(U_154,U_155),tc_HOL_Obool),tc_HOL_Obool),U_155),c_member(tc_prod(U_154,U_155)))),c_Product__Type_OPair(U_154,U_155)))),U_157) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_165,U_163] :
( ! [U_161,U_159] : hAPP(hAPP(c_COMBC(U_159,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),U_159),c_COMBC(U_161,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_prod(U_159,U_161)),tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),U_159),hAPP(c_COMBB(tc_prod(U_159,U_161),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool),U_161),c_member(tc_prod(U_159,U_161)))),c_Product__Type_OPair(U_159,U_161)))),U_163) = hAPP(hAPP(c_COMBC(U_159,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),U_159),c_COMBC(U_161,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_prod(U_159,U_161)),tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),U_159),hAPP(c_COMBB(tc_prod(U_159,U_161),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool),U_161),c_member(tc_prod(U_159,U_161)))),c_Product__Type_OPair(U_159,U_161)))),U_165)
| U_163 != U_165 )
& ! [U_164,U_162] :
( ! [U_160,U_158] : hAPP(hAPP(c_COMBC(U_158,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),U_158),c_COMBC(U_160,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_prod(U_158,U_160)),tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),U_158),hAPP(c_COMBB(tc_prod(U_158,U_160),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool),U_160),c_member(tc_prod(U_158,U_160)))),c_Product__Type_OPair(U_158,U_160)))),U_162) != hAPP(hAPP(c_COMBC(U_158,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),U_158),c_COMBC(U_160,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_prod(U_158,U_160)),tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),U_158),hAPP(c_COMBB(tc_prod(U_158,U_160),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool),U_160),c_member(tc_prod(U_158,U_160)))),c_Product__Type_OPair(U_158,U_160)))),U_164)
| U_162 = U_164 ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_165,U_163,U_159,U_161] :
( hAPP(hAPP(c_COMBC(U_159,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),U_159),c_COMBC(U_161,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_prod(U_159,U_161)),tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),U_159),hAPP(c_COMBB(tc_prod(U_159,U_161),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool),U_161),c_member(tc_prod(U_159,U_161)))),c_Product__Type_OPair(U_159,U_161)))),U_163) = hAPP(hAPP(c_COMBC(U_159,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),U_159),c_COMBC(U_161,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_prod(U_159,U_161)),tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),U_159),hAPP(c_COMBB(tc_prod(U_159,U_161),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool),U_161),c_member(tc_prod(U_159,U_161)))),c_Product__Type_OPair(U_159,U_161)))),U_165)
| U_163 != U_165 )
& ! [U_164,U_160,U_158,U_162] :
( hAPP(hAPP(c_COMBC(U_158,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),U_158),c_COMBC(U_160,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_prod(U_158,U_160)),tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),U_158),hAPP(c_COMBB(tc_prod(U_158,U_160),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool),U_160),c_member(tc_prod(U_158,U_160)))),c_Product__Type_OPair(U_158,U_160)))),U_162) != hAPP(hAPP(c_COMBC(U_158,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),U_158),c_COMBC(U_160,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_prod(U_158,U_160)),tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),U_158),hAPP(c_COMBB(tc_prod(U_158,U_160),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool),U_160),c_member(tc_prod(U_158,U_160)))),c_Product__Type_OPair(U_158,U_160)))),U_164)
| U_162 = U_164 ) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( hAPP(hAPP(c_COMBC(U_158,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),U_158),c_COMBC(U_160,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_prod(U_158,U_160)),tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),U_158),hAPP(c_COMBB(tc_prod(U_158,U_160),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool),U_160),c_member(tc_prod(U_158,U_160)))),c_Product__Type_OPair(U_158,U_160)))),U_162) != hAPP(hAPP(c_COMBC(U_158,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_fun(U_160,tc_HOL_Obool)),U_158),c_COMBC(U_160,tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_160,tc_prod(U_158,U_160)),tc_fun(U_160,tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool)),U_158),hAPP(c_COMBB(tc_prod(U_158,U_160),tc_fun(tc_fun(tc_prod(U_158,U_160),tc_HOL_Obool),tc_HOL_Obool),U_160),c_member(tc_prod(U_158,U_160)))),c_Product__Type_OPair(U_158,U_160)))),U_164)
| U_162 = U_164 ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( hAPP(hAPP(c_COMBC(U_159,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),U_159),c_COMBC(U_161,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_prod(U_159,U_161)),tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),U_159),hAPP(c_COMBB(tc_prod(U_159,U_161),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool),U_161),c_member(tc_prod(U_159,U_161)))),c_Product__Type_OPair(U_159,U_161)))),U_163) = hAPP(hAPP(c_COMBC(U_159,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_fun(U_161,tc_HOL_Obool)),U_159),c_COMBC(U_161,tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_161,tc_prod(U_159,U_161)),tc_fun(U_161,tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool)),U_159),hAPP(c_COMBB(tc_prod(U_159,U_161),tc_fun(tc_fun(tc_prod(U_159,U_161),tc_HOL_Obool),tc_HOL_Obool),U_161),c_member(tc_prod(U_159,U_161)))),c_Product__Type_OPair(U_159,U_161)))),U_165)
| U_163 != U_165 ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [V_ba_2,V_aa_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2),
inference(fof_nnf,[status(thm)],[fact_prod_Orecs]) ).
fof(f_34_2,plain,
! [U_171,U_170,U_169,U_168,U_167,U_166] : c_Product__Type_Oprod_Oprod__rec(U_166,U_167,U_168,U_169,hAPP(hAPP(c_Product__Type_OPair(U_166,U_167),U_170),U_171)) = hAPP(hAPP(U_169,U_170),U_171),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_170,U_169,U_167,U_166,U_168,U_171] : c_Product__Type_Oprod_Oprod__rec(U_166,U_167,U_168,U_169,hAPP(hAPP(c_Product__Type_OPair(U_166,U_167),U_170),U_171)) = hAPP(hAPP(U_169,U_170),U_171),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
c_Product__Type_Oprod_Oprod__rec(U_166,U_167,U_168,U_169,hAPP(hAPP(c_Product__Type_OPair(U_166,U_167),U_170),U_171)) = hAPP(hAPP(U_169,U_170),U_171),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(fof_nnf,[status(thm)],[fact_assms_I1_J]) ).
fof(f_35_2,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(definitional_conversion,[status(esa)],[f_35_1]) ).
cnf(f_35_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_H_2)),V_s_2))
| V_aa_2 != V_a_H_2 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_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_ba_2),V_b_H_2)),V_s_2))
& V_aa_2 = V_a_H_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__lex__prod]) ).
fof(f_36_2,plain,
! [U_179,U_178,U_177,U_176,U_175,U_174,U_173,U_172] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_172,U_173),tc_prod(U_172,U_173))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_172,U_173),tc_prod(U_172,U_173)),hAPP(hAPP(c_Product__Type_OPair(U_172,U_173),U_174),U_175)),hAPP(hAPP(c_Product__Type_OPair(U_172,U_173),U_176),U_177))),c_Wellfounded_Olex__prod(U_172,U_173,U_178,U_179)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_173,U_173)),hAPP(hAPP(c_Product__Type_OPair(U_173,U_173),U_175),U_177)),U_179))
| U_174 != U_176 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_172,U_172)),hAPP(hAPP(c_Product__Type_OPair(U_172,U_172),U_174),U_176)),U_178)) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_173,U_173)),hAPP(hAPP(c_Product__Type_OPair(U_173,U_173),U_175),U_177)),U_179))
& U_174 = U_176 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_172,U_172)),hAPP(hAPP(c_Product__Type_OPair(U_172,U_172),U_174),U_176)),U_178))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_172,U_173),tc_prod(U_172,U_173))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_172,U_173),tc_prod(U_172,U_173)),hAPP(hAPP(c_Product__Type_OPair(U_172,U_173),U_174),U_175)),hAPP(hAPP(c_Product__Type_OPair(U_172,U_173),U_176),U_177))),c_Wellfounded_Olex__prod(U_172,U_173,U_178,U_179))) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_195,U_193,U_191,U_189,U_187,U_185,U_183,U_181] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_181,U_183),tc_prod(U_181,U_183))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_181,U_183),tc_prod(U_181,U_183)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_183),U_185),U_187)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_183),U_189),U_191))),c_Wellfounded_Olex__prod(U_181,U_183,U_193,U_195)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_183,U_183)),hAPP(hAPP(c_Product__Type_OPair(U_183,U_183),U_187),U_191)),U_195))
| U_185 != U_189 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_181,U_181)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_181),U_185),U_189)),U_193)) ) )
& ! [U_194,U_192,U_190,U_188,U_186,U_184,U_182,U_180] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_182,U_182)),hAPP(hAPP(c_Product__Type_OPair(U_182,U_182),U_186),U_190)),U_194))
& U_184 = U_188 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_180,U_180)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_180),U_184),U_188)),U_192))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_180,U_182),tc_prod(U_180,U_182))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_180,U_182),tc_prod(U_180,U_182)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_182),U_184),U_186)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_182),U_188),U_190))),c_Wellfounded_Olex__prod(U_180,U_182,U_192,U_194))) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_183,U_183)),hAPP(hAPP(c_Product__Type_OPair(U_183,U_183),U_187),U_191)),U_195))
| U_185 != U_189
| ~ sP18(U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195) )
& ! [U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_181,U_181)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_181),U_185),U_189)),U_193))
| ~ sP18(U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195) )
& ! [U_182,U_184,U_186,U_188,U_190,U_194] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_182,U_182)),hAPP(hAPP(c_Product__Type_OPair(U_182,U_182),U_186),U_190)),U_194))
| ~ sP17(U_182,U_184,U_186,U_188,U_190,U_194) )
& ! [U_182,U_184,U_186,U_188,U_190,U_194] :
( U_184 = U_188
| ~ sP17(U_182,U_184,U_186,U_188,U_190,U_194) )
& ! [U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_181,U_183),tc_prod(U_181,U_183))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_181,U_183),tc_prod(U_181,U_183)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_183),U_185),U_187)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_183),U_189),U_191))),c_Wellfounded_Olex__prod(U_181,U_183,U_193,U_195)))
| sP18(U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195) )
& ! [U_180,U_182,U_184,U_186,U_188,U_190,U_194,U_192] :
( sP17(U_182,U_184,U_186,U_188,U_190,U_194)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_180,U_180)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_180),U_184),U_188)),U_192))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_180,U_182),tc_prod(U_180,U_182))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_180,U_182),tc_prod(U_180,U_182)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_182),U_184),U_186)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_182),U_188),U_190))),c_Wellfounded_Olex__prod(U_180,U_182,U_192,U_194))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17,sP18])],[f_36_3]) ).
cnf(f_36_5,plain,
( sP17(U_182,U_184,U_186,U_188,U_190,U_194)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_180,U_180)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_180),U_184),U_188)),U_192))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_180,U_182),tc_prod(U_180,U_182))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_180,U_182),tc_prod(U_180,U_182)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_182),U_184),U_186)),hAPP(hAPP(c_Product__Type_OPair(U_180,U_182),U_188),U_190))),c_Wellfounded_Olex__prod(U_180,U_182,U_192,U_194))) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_181,U_183),tc_prod(U_181,U_183))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_181,U_183),tc_prod(U_181,U_183)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_183),U_185),U_187)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_183),U_189),U_191))),c_Wellfounded_Olex__prod(U_181,U_183,U_193,U_195)))
| sP18(U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
( U_184 = U_188
| ~ sP17(U_182,U_184,U_186,U_188,U_190,U_194) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_182,U_182)),hAPP(hAPP(c_Product__Type_OPair(U_182,U_182),U_186),U_190)),U_194))
| ~ sP17(U_182,U_184,U_186,U_188,U_190,U_194) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_181,U_181)),hAPP(hAPP(c_Product__Type_OPair(U_181,U_181),U_185),U_189)),U_193))
| ~ sP18(U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_183,U_183)),hAPP(hAPP(c_Product__Type_OPair(U_183,U_183),U_187),U_191)),U_195))
| U_185 != U_189
| ~ sP18(U_185,U_181,U_183,U_187,U_189,U_191,U_193,U_195) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [V_i_2,V_Fa_2] :
( ( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)
| ? [B_x] :
( hAPP(V_Fa_2,B_x) != hAPP(B_x,V_i_2)
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [B_x] :
( hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ),
inference(fof_nnf,[status(thm)],[fact_dictator__def]) ).
fof(f_37_2,plain,
! [U_199,U_198] :
( ( c_Arrow__Order__Mirabelle_Odictator(U_198,U_199)
| ? [U_197] :
( hAPP(U_198,U_197) != hAPP(U_197,U_199)
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_197),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [U_196] :
( hAPP(U_198,U_196) = hAPP(U_196,U_199)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_196),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Odictator(U_198,U_199) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_203,U_201] :
( c_Arrow__Order__Mirabelle_Odictator(U_201,U_203)
| ? [U_197] :
( hAPP(U_201,U_197) != hAPP(U_197,U_203)
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_197),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_202,U_200] :
( ! [U_196] :
( hAPP(U_200,U_196) = hAPP(U_196,U_202)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_196),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Odictator(U_200,U_202) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_203,U_201] :
( c_Arrow__Order__Mirabelle_Odictator(U_201,U_203)
| ( hAPP(U_201,sK10(U_203,U_201)) != hAPP(sK10(U_203,U_201),U_203)
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK10(U_203,U_201)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_202,U_200] :
( ! [U_196] :
( hAPP(U_200,U_196) = hAPP(U_196,U_202)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_196),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Odictator(U_200,U_202) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_197,sK10(U_203,U_201))],[f_37_3]) ).
fof(f_37_5,plain,
( ! [U_203,U_201] :
( hAPP(U_201,sK10(U_203,U_201)) != hAPP(sK10(U_203,U_201),U_203)
| ~ sP19(U_203,U_201) )
& ! [U_203,U_201] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK10(U_203,U_201)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP19(U_203,U_201) )
& ! [U_203,U_201] :
( c_Arrow__Order__Mirabelle_Odictator(U_201,U_203)
| sP19(U_203,U_201) )
& ! [U_202,U_196,U_200] :
( hAPP(U_200,U_196) = hAPP(U_196,U_202)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_196),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_Odictator(U_200,U_202) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_37_4]) ).
cnf(f_37_6,plain,
( hAPP(U_200,U_196) = hAPP(U_196,U_202)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_196),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_Odictator(U_200,U_202) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_7,plain,
( c_Arrow__Order__Mirabelle_Odictator(U_201,U_203)
| sP19(U_203,U_201) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK10(U_203,U_201)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP19(U_203,U_201) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_9,plain,
( hAPP(U_201,sK10(U_203,U_201)) != hAPP(sK10(U_203,U_201),U_203)
| ~ sP19(U_203,U_201) ),
inference(clausify,[status(thm)],[f_37_5]) ).
fof(f_38_1,plain,
! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_aa_2),V_ba_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
& V_x_2 != V_aa_2 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2))
& V_y_2 != V_ba_2
& V_x_2 = V_aa_2 ) )
& V_y_2 != V_aa_2 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2))
& V_y_2 = V_aa_2 )
| V_x_2 = V_y_2 )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
| V_x_2 = V_aa_2 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2))
| V_y_2 = V_ba_2
| V_x_2 != V_aa_2 ) )
| V_y_2 = V_aa_2 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2))
| V_y_2 != V_aa_2 )
& V_x_2 != V_y_2 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_aa_2),V_ba_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
| V_aa_2 = V_ba_2 ),
inference(fof_nnf,[status(thm)],[fact_in__below]) ).
fof(f_38_2,plain,
! [U_208,U_207,U_206,U_205,U_204] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_206),U_204),U_205)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),U_206))
& U_207 != U_204 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_205),U_208)),U_206))
& U_208 != U_205
& U_207 = U_204 ) )
& U_208 != U_204 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_205)),U_206))
& U_208 = U_204 )
| U_207 = U_208 )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),U_206))
| U_207 = U_204 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_205),U_208)),U_206))
| U_208 = U_205
| U_207 != U_204 ) )
| U_208 = U_204 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_205)),U_206))
| U_208 != U_204 )
& U_207 != U_208 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_206),U_204),U_205))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_206),c_Arrow__Order__Mirabelle_OLin))
| U_204 = U_205 ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_206,U_204,U_207,U_208] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),U_206))
| ~ sP24(U_206,U_204,U_207,U_208) )
& ! [U_206,U_204,U_207,U_208] :
( U_207 != U_204
| ~ sP24(U_206,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_205),U_208)),U_206))
| ~ sP23(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( U_208 != U_205
| ~ sP23(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( U_207 = U_204
| ~ sP23(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( sP24(U_206,U_204,U_207,U_208)
| sP23(U_206,U_205,U_204,U_207,U_208)
| ~ sP25(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( U_208 != U_204
| ~ sP25(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_205)),U_206))
| ~ sP22(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( U_208 = U_204
| ~ sP22(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),U_206))
| U_207 = U_204
| ~ sP20(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_205),U_208)),U_206))
| U_208 = U_205
| U_207 != U_204
| ~ sP20(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( sP20(U_206,U_205,U_204,U_207,U_208)
| U_208 = U_204
| ~ sP21(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_205)),U_206))
| U_208 != U_204
| ~ sP21(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( U_207 != U_208
| ~ sP21(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_206),U_204),U_205)))
| sP25(U_206,U_205,U_204,U_207,U_208)
| sP22(U_206,U_205,U_204,U_207,U_208)
| U_207 = U_208
| ~ sP26(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( sP21(U_206,U_205,U_204,U_207,U_208)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_206),U_204),U_205)))
| ~ sP26(U_206,U_205,U_204,U_207,U_208) )
& ! [U_206,U_205,U_204,U_207,U_208] :
( sP26(U_206,U_205,U_204,U_207,U_208)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_206),c_Arrow__Order__Mirabelle_OLin))
| U_204 = U_205 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20,sP21,sP22,sP23,sP24,sP25,sP26])],[f_38_2]) ).
cnf(f_38_4,plain,
( sP26(U_206,U_205,U_204,U_207,U_208)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_206),c_Arrow__Order__Mirabelle_OLin))
| U_204 = U_205 ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( sP21(U_206,U_205,U_204,U_207,U_208)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_206),U_204),U_205)))
| ~ sP26(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_206),U_204),U_205)))
| sP25(U_206,U_205,U_204,U_207,U_208)
| sP22(U_206,U_205,U_204,U_207,U_208)
| U_207 = U_208
| ~ sP26(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_7,plain,
( U_207 != U_208
| ~ sP21(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_205)),U_206))
| U_208 != U_204
| ~ sP21(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_9,plain,
( sP20(U_206,U_205,U_204,U_207,U_208)
| U_208 = U_204
| ~ sP21(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_205),U_208)),U_206))
| U_208 = U_205
| U_207 != U_204
| ~ sP20(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),U_206))
| U_207 = U_204
| ~ sP20(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_12,plain,
( U_208 = U_204
| ~ sP22(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_205)),U_206))
| ~ sP22(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_14,plain,
( U_208 != U_204
| ~ sP25(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_15,plain,
( sP24(U_206,U_204,U_207,U_208)
| sP23(U_206,U_205,U_204,U_207,U_208)
| ~ sP25(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_16,plain,
( U_207 = U_204
| ~ sP23(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_17,plain,
( U_208 != U_205
| ~ sP23(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_18,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_205),U_208)),U_206))
| ~ sP23(U_206,U_205,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_19,plain,
( U_207 != U_204
| ~ sP24(U_206,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_20,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_207),U_208)),U_206))
| ~ sP24(U_206,U_204,U_207,U_208) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [V_ba_2,V_aa_2,V_ca_2,T_a,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_a,V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_ca_2,V_aa_2),V_ba_2),
inference(fof_nnf,[status(thm)],[fact_internal__split__conv]) ).
fof(f_39_2,plain,
! [U_214,U_213,U_212,U_211,U_210,U_209] : c_Product__Type_Ointernal__split(U_209,U_210,U_211,U_212,hAPP(hAPP(c_Product__Type_OPair(U_209,U_210),U_213),U_214)) = hAPP(hAPP(U_212,U_213),U_214),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_211,U_214,U_210,U_212,U_209,U_213] : c_Product__Type_Ointernal__split(U_209,U_210,U_211,U_212,hAPP(hAPP(c_Product__Type_OPair(U_209,U_210),U_213),U_214)) = hAPP(hAPP(U_212,U_213),U_214),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
c_Product__Type_Ointernal__split(U_209,U_210,U_211,U_212,hAPP(hAPP(c_Product__Type_OPair(U_209,U_210),U_213),U_214)) = hAPP(hAPP(U_212,U_213),U_214),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,V_L_2)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof]) ).
fof(f_40_2,plain,
! [U_215] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,U_215)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_215),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_215] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,U_215)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_215),c_Arrow__Order__Mirabelle_OLin)) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,U_215)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_215),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [V_S_2,V_R_2,T_a] :
( ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)
| V_R_2 != V_S_2 )
& ( V_R_2 = V_S_2
| hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) != hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq]) ).
fof(f_41_2,plain,
! [U_218,U_217,U_216] :
( ( hAPP(hAPP(c_COMBC(U_216,tc_fun(U_216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_216)),U_217) = hAPP(hAPP(c_COMBC(U_216,tc_fun(U_216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_216)),U_218)
| U_217 != U_218 )
& ( U_217 = U_218
| hAPP(hAPP(c_COMBC(U_216,tc_fun(U_216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_216)),U_217) != hAPP(hAPP(c_COMBC(U_216,tc_fun(U_216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_216)),U_218) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_224,U_222] :
( ! [U_220] : hAPP(hAPP(c_COMBC(U_220,tc_fun(U_220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_220)),U_222) = hAPP(hAPP(c_COMBC(U_220,tc_fun(U_220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_220)),U_224)
| U_222 != U_224 )
& ! [U_223,U_221] :
( ! [U_219] : hAPP(hAPP(c_COMBC(U_219,tc_fun(U_219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_219)),U_221) != hAPP(hAPP(c_COMBC(U_219,tc_fun(U_219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_219)),U_223)
| U_221 = U_223 ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_220,U_224,U_222] :
( hAPP(hAPP(c_COMBC(U_220,tc_fun(U_220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_220)),U_222) = hAPP(hAPP(c_COMBC(U_220,tc_fun(U_220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_220)),U_224)
| U_222 != U_224 )
& ! [U_221,U_223,U_219] :
( hAPP(hAPP(c_COMBC(U_219,tc_fun(U_219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_219)),U_221) != hAPP(hAPP(c_COMBC(U_219,tc_fun(U_219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_219)),U_223)
| U_221 = U_223 ) ),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
( hAPP(hAPP(c_COMBC(U_219,tc_fun(U_219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_219)),U_221) != hAPP(hAPP(c_COMBC(U_219,tc_fun(U_219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_219)),U_223)
| U_221 = U_223 ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
( hAPP(hAPP(c_COMBC(U_220,tc_fun(U_220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_220)),U_222) = hAPP(hAPP(c_COMBC(U_220,tc_fun(U_220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_220)),U_224)
| U_222 != U_224 ),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [V_L_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
| V_x_2 = V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_below__Lin]) ).
fof(f_42_2,plain,
! [U_227,U_226,U_225] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_227),U_225),U_226)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_227),c_Arrow__Order__Mirabelle_OLin))
| U_225 = U_226 ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_226,U_225,U_227] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_227),U_225),U_226)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_227),c_Arrow__Order__Mirabelle_OLin))
| U_225 = U_226 ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_227),U_225),U_226)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_227),c_Arrow__Order__Mirabelle_OLin))
| U_225 = U_226 ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [V_x_2,V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_nnf,[status(thm)],[fact_mktop__Lin]) ).
fof(f_43_2,plain,
! [U_229,U_228] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(U_228,U_229)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_228),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_228,U_229] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(U_228,U_229)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_228),c_Arrow__Order__Mirabelle_OLin)) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(U_228,U_229)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_228),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [V_x_2,V_L_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_nnf,[status(thm)],[fact_mkbot__Lin]) ).
fof(f_44_2,plain,
! [U_231,U_230] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(U_230,U_231)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_230),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_231,U_230] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(U_230,U_231)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_230),c_Arrow__Order__Mirabelle_OLin)) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(U_230,U_231)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_230),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),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_a),V_x_2),hAPP(c_fequal,V_y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__mem]) ).
fof(f_45_2,plain,
! [U_234,U_233,U_232] :
( ( hBOOL(hAPP(hAPP(c_member(U_232),U_233),hAPP(c_fequal,U_234)))
| U_233 != U_234 )
& ( U_233 = U_234
| ~ hBOOL(hAPP(hAPP(c_member(U_232),U_233),hAPP(c_fequal,U_234))) ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_240,U_238] :
( ! [U_236] : hBOOL(hAPP(hAPP(c_member(U_236),U_238),hAPP(c_fequal,U_240)))
| U_238 != U_240 )
& ! [U_239,U_237] :
( ! [U_235] : ~ hBOOL(hAPP(hAPP(c_member(U_235),U_237),hAPP(c_fequal,U_239)))
| U_237 = U_239 ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_236,U_240,U_238] :
( hBOOL(hAPP(hAPP(c_member(U_236),U_238),hAPP(c_fequal,U_240)))
| U_238 != U_240 )
& ! [U_237,U_235,U_239] :
( ~ hBOOL(hAPP(hAPP(c_member(U_235),U_237),hAPP(c_fequal,U_239)))
| U_237 = U_239 ) ),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_235),U_237),hAPP(c_fequal,U_239)))
| U_237 = U_239 ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_236),U_238),hAPP(c_fequal,U_240)))
| U_238 != U_240 ),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
! [V_y_2,V_x_2,V_L_2] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) )
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_nnf,[status(thm)],[fact_notin__Lin__iff]) ).
fof(f_46_2,plain,
! [U_243,U_242,U_241] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_242),U_243)),U_241))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_243),U_242)),U_241)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_243),U_242)),U_241))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_242),U_243)),U_241)) ) )
| U_242 = U_243
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_241),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_241,U_242,U_243] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_242),U_243)),U_241))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_243),U_242)),U_241))
| ~ sP27(U_241,U_242,U_243) )
& ! [U_241,U_242,U_243] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_243),U_242)),U_241))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_242),U_243)),U_241))
| ~ sP27(U_241,U_242,U_243) )
& ! [U_241,U_242,U_243] :
( sP27(U_241,U_242,U_243)
| U_242 = U_243
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_241),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_46_2]) ).
cnf(f_46_4,plain,
( sP27(U_241,U_242,U_243)
| U_242 = U_243
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_241),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_243),U_242)),U_241))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_242),U_243)),U_241))
| ~ sP27(U_241,U_242,U_243) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_242),U_243)),U_241))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_243),U_242)),U_241))
| ~ sP27(U_241,U_242,U_243) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [V_ba_2,V_aa_2,V_L_2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_nnf,[status(thm)],[fact_Lin__irrefl]) ).
fof(f_47_2,plain,
! [U_246,U_245,U_244] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_246),U_245)),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_245),U_246)),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_244),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_246,U_244,U_245] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_246),U_245)),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_245),U_246)),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_244),c_Arrow__Order__Mirabelle_OLin)) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_246),U_245)),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_245),U_246)),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_244),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_PiE]) ).
fof(f_48_2,plain,
! [U_252,U_251,U_250,U_249,U_248,U_247] :
( ~ hBOOL(hAPP(hAPP(c_member(U_247),U_252),U_250))
| hBOOL(hAPP(hAPP(c_member(U_248),hAPP(U_249,U_252)),hAPP(U_251,U_252)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_247,U_248)),U_249),c_FuncSet_OPi(U_247,U_248,U_250,U_251))) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_247,U_248,U_249,U_250,U_251,U_252] :
( ~ hBOOL(hAPP(hAPP(c_member(U_247),U_252),U_250))
| hBOOL(hAPP(hAPP(c_member(U_248),hAPP(U_249,U_252)),hAPP(U_251,U_252)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_247,U_248)),U_249),c_FuncSet_OPi(U_247,U_248,U_250,U_251))) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_247),U_252),U_250))
| hBOOL(hAPP(hAPP(c_member(U_248),hAPP(U_249,U_252)),hAPP(U_251,U_252)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_247,U_248)),U_249),c_FuncSet_OPi(U_247,U_248,U_250,U_251))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_aa_2,V_ba_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
& V_y_2 != V_ba_2 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2))
& V_x_2 != V_aa_2
& V_y_2 = V_ba_2 ) )
& V_x_2 != V_ba_2 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2))
& V_x_2 = V_ba_2 )
| V_x_2 = V_y_2 )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
| V_y_2 = V_ba_2 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2))
| V_x_2 = V_aa_2
| V_y_2 != V_ba_2 ) )
| V_x_2 = V_ba_2 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2))
| V_x_2 != V_ba_2 )
& V_x_2 != V_y_2 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_aa_2,V_ba_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
| V_aa_2 = V_ba_2 ),
inference(fof_nnf,[status(thm)],[fact_in__above]) ).
fof(f_49_2,plain,
! [U_257,U_256,U_255,U_254,U_253] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),c_Arrow__Order__Mirabelle_Oabove(U_255,U_253,U_254)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),U_255))
& U_257 != U_254 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_253)),U_255))
& U_256 != U_253
& U_257 = U_254 ) )
& U_256 != U_254 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_253),U_257)),U_255))
& U_256 = U_254 )
| U_256 = U_257 )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),U_255))
| U_257 = U_254 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_253)),U_255))
| U_256 = U_253
| U_257 != U_254 ) )
| U_256 = U_254 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_253),U_257)),U_255))
| U_256 != U_254 )
& U_256 != U_257 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),c_Arrow__Order__Mirabelle_Oabove(U_255,U_253,U_254))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_255),c_Arrow__Order__Mirabelle_OLin))
| U_253 = U_254 ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_255,U_254,U_256,U_257] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),U_255))
| ~ sP32(U_255,U_254,U_256,U_257) )
& ! [U_255,U_254,U_256,U_257] :
( U_257 != U_254
| ~ sP32(U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_253)),U_255))
| ~ sP31(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( U_256 != U_253
| ~ sP31(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( U_257 = U_254
| ~ sP31(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( sP32(U_255,U_254,U_256,U_257)
| sP31(U_253,U_255,U_254,U_256,U_257)
| ~ sP33(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( U_256 != U_254
| ~ sP33(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_253),U_257)),U_255))
| ~ sP30(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( U_256 = U_254
| ~ sP30(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),U_255))
| U_257 = U_254
| ~ sP28(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_253)),U_255))
| U_256 = U_253
| U_257 != U_254
| ~ sP28(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( sP28(U_253,U_255,U_254,U_256,U_257)
| U_256 = U_254
| ~ sP29(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_253),U_257)),U_255))
| U_256 != U_254
| ~ sP29(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( U_256 != U_257
| ~ sP29(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),c_Arrow__Order__Mirabelle_Oabove(U_255,U_253,U_254)))
| sP33(U_253,U_255,U_254,U_256,U_257)
| sP30(U_253,U_255,U_254,U_256,U_257)
| U_256 = U_257
| ~ sP34(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( sP29(U_253,U_255,U_254,U_256,U_257)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),c_Arrow__Order__Mirabelle_Oabove(U_255,U_253,U_254)))
| ~ sP34(U_253,U_255,U_254,U_256,U_257) )
& ! [U_253,U_255,U_254,U_256,U_257] :
( sP34(U_253,U_255,U_254,U_256,U_257)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_255),c_Arrow__Order__Mirabelle_OLin))
| U_253 = U_254 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28,sP29,sP30,sP31,sP32,sP33,sP34])],[f_49_2]) ).
cnf(f_49_4,plain,
( sP34(U_253,U_255,U_254,U_256,U_257)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_255),c_Arrow__Order__Mirabelle_OLin))
| U_253 = U_254 ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( sP29(U_253,U_255,U_254,U_256,U_257)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),c_Arrow__Order__Mirabelle_Oabove(U_255,U_253,U_254)))
| ~ sP34(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),c_Arrow__Order__Mirabelle_Oabove(U_255,U_253,U_254)))
| sP33(U_253,U_255,U_254,U_256,U_257)
| sP30(U_253,U_255,U_254,U_256,U_257)
| U_256 = U_257
| ~ sP34(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_7,plain,
( U_256 != U_257
| ~ sP29(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_253),U_257)),U_255))
| U_256 != U_254
| ~ sP29(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_9,plain,
( sP28(U_253,U_255,U_254,U_256,U_257)
| U_256 = U_254
| ~ sP29(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_253)),U_255))
| U_256 = U_253
| U_257 != U_254
| ~ sP28(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),U_255))
| U_257 = U_254
| ~ sP28(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_12,plain,
( U_256 = U_254
| ~ sP30(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_253),U_257)),U_255))
| ~ sP30(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_14,plain,
( U_256 != U_254
| ~ sP33(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_15,plain,
( sP32(U_255,U_254,U_256,U_257)
| sP31(U_253,U_255,U_254,U_256,U_257)
| ~ sP33(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_16,plain,
( U_257 = U_254
| ~ sP31(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_17,plain,
( U_256 != U_253
| ~ sP31(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_18,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_253)),U_255))
| ~ sP31(U_253,U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_19,plain,
( U_257 != U_254
| ~ sP32(U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_20,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_256),U_257)),U_255))
| ~ sP32(U_255,U_254,U_256,U_257) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [V_i_2,V_Fa_2] :
( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)
| ? [B_x] :
( ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2)))
& B_a != B_b )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(fof_nnf,[status(thm)],[fact_dictatorI]) ).
fof(f_50_2,plain,
! [U_262,U_261] :
( c_Arrow__Order__Mirabelle_Odictator(U_261,U_262)
| ? [U_260] :
( ? [U_259,U_258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_259),U_258)),hAPP(U_261,U_260)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_259),U_258)),hAPP(U_260,U_262)))
& U_259 != U_258 )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_260),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_261),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_262,U_261] :
( c_Arrow__Order__Mirabelle_Odictator(U_261,U_262)
| ( ? [U_259,U_258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_259),U_258)),hAPP(U_261,sK11(U_262,U_261))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_259),U_258)),hAPP(sK11(U_262,U_261),U_262)))
& U_259 != U_258 )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK11(U_262,U_261)),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_261),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_260,sK11(U_262,U_261))],[f_50_2]) ).
fof(f_50_4,plain,
! [U_262,U_261] :
( c_Arrow__Order__Mirabelle_Odictator(U_261,U_262)
| ( ? [U_258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),U_258)),hAPP(U_261,sK11(U_262,U_261))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),U_258)),hAPP(sK11(U_262,U_261),U_262)))
& sK12(U_262,U_261) != U_258 )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK11(U_262,U_261)),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_261),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_259,sK12(U_262,U_261))],[f_50_3]) ).
fof(f_50_5,plain,
! [U_262,U_261] :
( c_Arrow__Order__Mirabelle_Odictator(U_261,U_262)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),sK13(U_262,U_261))),hAPP(U_261,sK11(U_262,U_261))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),sK13(U_262,U_261))),hAPP(sK11(U_262,U_261),U_262)))
& sK12(U_262,U_261) != sK13(U_262,U_261)
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK11(U_262,U_261)),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_261),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_258,sK13(U_262,U_261))],[f_50_4]) ).
fof(f_50_6,plain,
( ! [U_262,U_261] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),sK13(U_262,U_261))),hAPP(U_261,sK11(U_262,U_261))))
| ~ sP35(U_262,U_261) )
& ! [U_262,U_261] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),sK13(U_262,U_261))),hAPP(sK11(U_262,U_261),U_262)))
| ~ sP35(U_262,U_261) )
& ! [U_262,U_261] :
( sK12(U_262,U_261) != sK13(U_262,U_261)
| ~ sP35(U_262,U_261) )
& ! [U_262,U_261] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK11(U_262,U_261)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP35(U_262,U_261) )
& ! [U_262,U_261] :
( c_Arrow__Order__Mirabelle_Odictator(U_261,U_262)
| sP35(U_262,U_261)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_261),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_50_5]) ).
cnf(f_50_7,plain,
( c_Arrow__Order__Mirabelle_Odictator(U_261,U_262)
| sP35(U_262,U_261)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_261),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK11(U_262,U_261)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP35(U_262,U_261) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_9,plain,
( sK12(U_262,U_261) != sK13(U_262,U_261)
| ~ sP35(U_262,U_261) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),sK13(U_262,U_261))),hAPP(sK11(U_262,U_261),U_262)))
| ~ sP35(U_262,U_261) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK12(U_262,U_261)),sK13(U_262,U_261))),hAPP(U_261,sK11(U_262,U_261))))
| ~ sP35(U_262,U_261) ),
inference(clausify,[status(thm)],[f_50_6]) ).
fof(f_51_1,plain,
! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_funcset__mem]) ).
fof(f_51_2,plain,
! [U_268,U_267,U_266,U_265,U_264,U_263] :
( hBOOL(hAPP(hAPP(c_member(U_264),hAPP(U_265,U_268)),U_267))
| ~ hBOOL(hAPP(hAPP(c_member(U_263),U_268),U_266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_263,U_264)),U_265),c_FuncSet_OPi(U_263,U_264,U_266,c_COMBK(tc_fun(U_264,tc_HOL_Obool),U_263,U_267)))) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_263,U_266,U_267,U_265,U_264,U_268] :
( hBOOL(hAPP(hAPP(c_member(U_264),hAPP(U_265,U_268)),U_267))
| ~ hBOOL(hAPP(hAPP(c_member(U_263),U_268),U_266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_263,U_264)),U_265),c_FuncSet_OPi(U_263,U_264,U_266,c_COMBK(tc_fun(U_264,tc_HOL_Obool),U_263,U_267)))) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_264),hAPP(U_265,U_268)),U_267))
| ~ hBOOL(hAPP(hAPP(c_member(U_263),U_268),U_266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_263,U_264)),U_265),c_FuncSet_OPi(U_263,U_264,U_266,c_COMBK(tc_fun(U_264,tc_HOL_Obool),U_263,U_267)))) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_Pi__mem]) ).
fof(f_52_2,plain,
! [U_274,U_273,U_272,U_271,U_270,U_269] :
( hBOOL(hAPP(hAPP(c_member(U_270),hAPP(U_271,U_274)),hAPP(U_273,U_274)))
| ~ hBOOL(hAPP(hAPP(c_member(U_269),U_274),U_272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_269,U_270)),U_271),c_FuncSet_OPi(U_269,U_270,U_272,U_273))) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_270,U_269,U_271,U_273,U_274,U_272] :
( hBOOL(hAPP(hAPP(c_member(U_270),hAPP(U_271,U_274)),hAPP(U_273,U_274)))
| ~ hBOOL(hAPP(hAPP(c_member(U_269),U_274),U_272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_269,U_270)),U_271),c_FuncSet_OPi(U_269,U_270,U_272,U_273))) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_270),hAPP(U_271,U_274)),hAPP(U_273,U_274)))
| ~ hBOOL(hAPP(hAPP(c_member(U_269),U_274),U_272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_269,U_270)),U_271),c_FuncSet_OPi(U_269,U_270,U_272,U_273))) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2)))),
inference(fof_nnf,[status(thm)],[fact_funcset__id]) ).
fof(f_53_2,plain,
! [U_276,U_275] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_275,U_275)),c_COMBI(U_275)),c_FuncSet_OPi(U_275,U_275,U_276,c_COMBK(tc_fun(U_275,tc_HOL_Obool),U_275,U_276)))),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_276,U_275] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_275,U_275)),c_COMBI(U_275)),c_FuncSet_OPi(U_275,U_275,U_276,c_COMBK(tc_fun(U_275,tc_HOL_Obool),U_275,U_276)))),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_275,U_275)),c_COMBI(U_275)),c_FuncSet_OPi(U_275,U_275,U_276,c_COMBK(tc_fun(U_275,tc_HOL_Obool),U_275,U_276)))),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [V_L_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
| V_x_2 = V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_above__Lin]) ).
fof(f_54_2,plain,
! [U_279,U_278,U_277] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(U_279,U_277,U_278)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_279),c_Arrow__Order__Mirabelle_OLin))
| U_277 = U_278 ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_277,U_278,U_279] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(U_279,U_277,U_278)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_279),c_Arrow__Order__Mirabelle_OLin))
| U_277 = U_278 ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(U_279,U_277,U_278)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_279),c_Arrow__Order__Mirabelle_OLin))
| U_277 = U_278 ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [V_Fa_2] :
( ( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2)
| ? [B_x] :
( ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
& ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [B_x] :
( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
| ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_unanimity__def]) ).
fof(f_55_2,plain,
! [U_288] :
( ( c_Arrow__Order__Mirabelle_Ounanimity(U_288)
| ? [U_287] :
( ? [U_286,U_285] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(U_288,U_287)))
& ! [U_284] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(U_287,U_284))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_287),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [U_283] :
( ! [U_282,U_281] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_288,U_283)))
| ? [U_280] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,U_280))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_288) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_290] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_290)
| ? [U_287] :
( ? [U_286,U_285] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(U_290,U_287)))
& ! [U_284] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(U_287,U_284))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_287),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_289] :
( ! [U_283] :
( ! [U_282,U_281] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_289,U_283)))
| ? [U_280] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,U_280))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_289) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
( ! [U_290] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_290)
| ? [U_287] :
( ? [U_286,U_285] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(U_290,U_287)))
& ! [U_284] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(U_287,U_284))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_287),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_289] :
( ! [U_283] :
( ! [U_282,U_281] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_289,U_283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,sK14(U_289,U_283,U_282,U_281)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_289) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_280,sK14(U_289,U_283,U_282,U_281))],[f_55_3]) ).
fof(f_55_5,plain,
( ! [U_290] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_290)
| ( ? [U_286,U_285] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(U_290,sK15(U_290))))
& ! [U_284] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_286),U_285)),hAPP(sK15(U_290),U_284))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK15(U_290)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_289] :
( ! [U_283] :
( ! [U_282,U_281] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_289,U_283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,sK14(U_289,U_283,U_282,U_281)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_289) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_287,sK15(U_290))],[f_55_4]) ).
fof(f_55_6,plain,
( ! [U_290] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_290)
| ( ? [U_285] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),U_285)),hAPP(U_290,sK15(U_290))))
& ! [U_284] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),U_285)),hAPP(sK15(U_290),U_284))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK15(U_290)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_289] :
( ! [U_283] :
( ! [U_282,U_281] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_289,U_283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,sK14(U_289,U_283,U_282,U_281)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_289) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_286,sK16(U_290))],[f_55_5]) ).
fof(f_55_7,plain,
( ! [U_290] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_290)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),sK17(U_290))),hAPP(U_290,sK15(U_290))))
& ! [U_284] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),sK17(U_290))),hAPP(sK15(U_290),U_284)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK15(U_290)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_289] :
( ! [U_283] :
( ! [U_282,U_281] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_289,U_283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,sK14(U_289,U_283,U_282,U_281)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_289) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_285,sK17(U_290))],[f_55_6]) ).
fof(f_55_8,plain,
( ! [U_284,U_290] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),sK17(U_290))),hAPP(U_290,sK15(U_290))))
| ~ sP36(U_284,U_290) )
& ! [U_284,U_290] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),sK17(U_290))),hAPP(sK15(U_290),U_284)))
| ~ sP36(U_284,U_290) )
& ! [U_284,U_290] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK15(U_290)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP36(U_284,U_290) )
& ! [U_284,U_290] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_290)
| sP36(U_284,U_290) )
& ! [U_282,U_281,U_283,U_289] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_289,U_283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,sK14(U_289,U_283,U_282,U_281))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_289) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_55_7]) ).
cnf(f_55_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_289,U_283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_282),U_281)),hAPP(U_283,sK14(U_289,U_283,U_282,U_281))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_283),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_289) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_10,plain,
( c_Arrow__Order__Mirabelle_Ounanimity(U_290)
| sP36(U_284,U_290) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK15(U_290)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP36(U_284,U_290) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_12,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),sK17(U_290))),hAPP(sK15(U_290),U_284)))
| ~ sP36(U_284,U_290) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK16(U_290)),sK17(U_290))),hAPP(U_290,sK15(U_290))))
| ~ sP36(U_284,U_290) ),
inference(clausify,[status(thm)],[f_55_8]) ).
fof(f_56_1,plain,
! [V_Fa_2] :
( ( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2)
| ? [B_x] :
( ? [B_xa] :
( ? [B_a,B_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) )
& ! [B_i] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) ) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( ! [B_a,B_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) )
| ? [B_i] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_IIA__def]) ).
fof(f_56_2,plain,
! [U_301] :
( ( c_Arrow__Order__Mirabelle_OIIA(U_301)
| ? [U_300] :
( ? [U_299] :
( ? [U_298,U_297] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_301,U_300)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_301,U_299))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_301,U_299)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_301,U_300))) ) )
& ! [U_296] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_296)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_296))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_296)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_296))) ) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_299),c_Arrow__Order__Mirabelle_OProf)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_300),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_301,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_301,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_301,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_301,U_295))) ) )
| ? [U_291] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,U_291)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,U_291))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,U_291)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,U_291))) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_301) ) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_307] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| ? [U_300] :
( ? [U_299] :
( ? [U_298,U_297] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_300)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_300))) ) )
& ! [U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_305))) )
& ! [U_304] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_304))) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_299),c_Arrow__Order__Mirabelle_OProf)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_300),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_306] :
( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295))) ) )
| ? [U_303] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,U_303)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,U_303))) )
| ? [U_302] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,U_302)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,U_302))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
( ! [U_307] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| ? [U_300] :
( ? [U_299] :
( ? [U_298,U_297] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_300)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_300))) ) )
& ! [U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_305))) )
& ! [U_304] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_304))) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_299),c_Arrow__Order__Mirabelle_OProf)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_300),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_306] :
( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295))) ) )
| ? [U_303] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,U_303)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,U_303))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_302,sK18(U_306,U_295,U_294,U_293,U_292))],[f_56_3]) ).
fof(f_56_5,plain,
( ! [U_307] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| ? [U_300] :
( ? [U_299] :
( ? [U_298,U_297] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_300)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_300))) ) )
& ! [U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_305))) )
& ! [U_304] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_300,U_304))) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_299),c_Arrow__Order__Mirabelle_OProf)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_300),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_306] :
( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK19(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK19(U_306,U_295,U_294,U_293,U_292)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_303,sK19(U_306,U_295,U_294,U_293,U_292))],[f_56_4]) ).
fof(f_56_6,plain,
( ! [U_307] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| ( ? [U_299] :
( ? [U_298,U_297] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,sK20(U_307))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,U_299)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,sK20(U_307)))) ) )
& ! [U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(sK20(U_307),U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_305))) )
& ! [U_304] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_299,U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(sK20(U_307),U_304))) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_299),c_Arrow__Order__Mirabelle_OProf)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(U_307)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_306] :
( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK19(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK19(U_306,U_295,U_294,U_293,U_292)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_300,sK20(U_307))],[f_56_5]) ).
fof(f_56_7,plain,
( ! [U_307] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| ( ? [U_298,U_297] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,sK20(U_307))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,sK21(U_307)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,sK21(U_307))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(U_307,sK20(U_307)))) ) )
& ! [U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(sK20(U_307),U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(sK21(U_307),U_305))) )
& ! [U_304] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(sK21(U_307),U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_298),U_297)),hAPP(sK20(U_307),U_304))) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK21(U_307)),c_Arrow__Order__Mirabelle_OProf))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(U_307)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_306] :
( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK19(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK19(U_306,U_295,U_294,U_293,U_292)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_299,sK21(U_307))],[f_56_6]) ).
fof(f_56_8,plain,
( ! [U_307] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| ( ? [U_297] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(U_307,sK20(U_307))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(U_307,sK21(U_307)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(U_307,sK21(U_307))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(U_307,sK20(U_307)))) ) )
& ! [U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(sK20(U_307),U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(sK21(U_307),U_305))) )
& ! [U_304] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(sK21(U_307),U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),U_297)),hAPP(sK20(U_307),U_304))) ) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK21(U_307)),c_Arrow__Order__Mirabelle_OProf))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(U_307)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_306] :
( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK19(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK19(U_306,U_295,U_294,U_293,U_292)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_298,sK22(U_307))],[f_56_7]) ).
fof(f_56_9,plain,
( ! [U_307] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK20(U_307))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK21(U_307)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK21(U_307))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK20(U_307)))) ) )
& ! [U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK20(U_307),U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK21(U_307),U_305))) )
& ! [U_304] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK21(U_307),U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK20(U_307),U_304))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK21(U_307)),c_Arrow__Order__Mirabelle_OProf))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(U_307)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_306] :
( ! [U_295] :
( ! [U_294] :
( ! [U_293,U_292] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK19(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK19(U_306,U_295,U_294,U_293,U_292)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_297,sK23(U_307))],[f_56_8]) ).
fof(f_56_10,plain,
( ! [U_307] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK20(U_307))))
| ~ sP41(U_307) )
& ! [U_307] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK21(U_307))))
| ~ sP41(U_307) )
& ! [U_307] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK21(U_307))))
| ~ sP40(U_307) )
& ! [U_307] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK20(U_307))))
| ~ sP40(U_307) )
& ! [U_307,U_304,U_305] :
( sP41(U_307)
| sP40(U_307)
| ~ sP42(U_307,U_304,U_305) )
& ! [U_307,U_304,U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK20(U_307),U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK21(U_307),U_305)))
| ~ sP42(U_307,U_304,U_305) )
& ! [U_307,U_304,U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK21(U_307),U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK20(U_307),U_304)))
| ~ sP42(U_307,U_304,U_305) )
& ! [U_307,U_304,U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK21(U_307)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP42(U_307,U_304,U_305) )
& ! [U_307,U_304,U_305] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(U_307)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP42(U_307,U_304,U_305) )
& ! [U_294,U_292,U_293,U_295,U_306] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ sP39(U_294,U_292,U_293,U_295,U_306) )
& ! [U_294,U_292,U_293,U_295,U_306] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ sP39(U_294,U_292,U_293,U_295,U_306) )
& ! [U_294,U_292,U_293,U_295,U_306] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK19(U_306,U_295,U_294,U_293,U_292))))
| ~ sP38(U_294,U_292,U_293,U_295,U_306) )
& ! [U_294,U_292,U_293,U_295,U_306] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK19(U_306,U_295,U_294,U_293,U_292))))
| ~ sP38(U_294,U_292,U_293,U_295,U_306) )
& ! [U_294,U_292,U_293,U_295,U_306] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
| ~ sP37(U_294,U_292,U_293,U_295,U_306) )
& ! [U_294,U_292,U_293,U_295,U_306] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292))))
| ~ sP37(U_294,U_292,U_293,U_295,U_306) )
& ! [U_307,U_304,U_305] :
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| sP42(U_307,U_304,U_305) )
& ! [U_294,U_292,U_293,U_295,U_306] :
( sP39(U_294,U_292,U_293,U_295,U_306)
| sP38(U_294,U_292,U_293,U_295,U_306)
| sP37(U_294,U_292,U_293,U_295,U_306)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37,sP38,sP39,sP40,sP41,sP42])],[f_56_9]) ).
cnf(f_56_11,plain,
( sP39(U_294,U_292,U_293,U_295,U_306)
| sP38(U_294,U_292,U_293,U_295,U_306)
| sP37(U_294,U_292,U_293,U_295,U_306)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_294),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),U_295),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_306) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_12,plain,
( c_Arrow__Order__Mirabelle_OIIA(U_307)
| sP42(U_307,U_304,U_305) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_13,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK18(U_306,U_295,U_294,U_293,U_292))))
| ~ sP37(U_294,U_292,U_293,U_295,U_306) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_14,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK18(U_306,U_295,U_294,U_293,U_292))))
| ~ sP37(U_294,U_292,U_293,U_295,U_306) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_15,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_294,sK19(U_306,U_295,U_294,U_293,U_292))))
| ~ sP38(U_294,U_292,U_293,U_295,U_306) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_16,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_295,sK19(U_306,U_295,U_294,U_293,U_292))))
| ~ sP38(U_294,U_292,U_293,U_295,U_306) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_17,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ sP39(U_294,U_292,U_293,U_295,U_306) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_18,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_293),U_292)),hAPP(U_306,U_294)))
| ~ sP39(U_294,U_292,U_293,U_295,U_306) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_19,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(U_307)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP42(U_307,U_304,U_305) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_20,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK21(U_307)),c_Arrow__Order__Mirabelle_OProf))
| ~ sP42(U_307,U_304,U_305) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_21,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK21(U_307),U_304)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK20(U_307),U_304)))
| ~ sP42(U_307,U_304,U_305) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_22,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK20(U_307),U_305)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(sK21(U_307),U_305)))
| ~ sP42(U_307,U_304,U_305) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_23,plain,
( sP41(U_307)
| sP40(U_307)
| ~ sP42(U_307,U_304,U_305) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_24,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK20(U_307))))
| ~ sP40(U_307) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_25,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK21(U_307))))
| ~ sP40(U_307) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_26,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK21(U_307))))
| ~ sP41(U_307) ),
inference(clausify,[status(thm)],[f_56_10]) ).
cnf(f_56_27,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(U_307)),sK23(U_307))),hAPP(U_307,sK20(U_307))))
| ~ sP41(U_307) ),
inference(clausify,[status(thm)],[f_56_10]) ).
fof(f_57_1,plain,
! [V_ba_2,V_aa_2] :
( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x),c_Arrow__Order__Mirabelle_OLin)) )
| V_aa_2 = V_ba_2 ),
inference(fof_nnf,[status(thm)],[fact_complete__Lin]) ).
fof(f_57_2,plain,
! [U_310,U_309] :
( ? [U_308] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_309),U_310)),U_308))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_308),c_Arrow__Order__Mirabelle_OLin)) )
| U_309 = U_310 ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_310,U_309] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_309),U_310)),sK24(U_310,U_309)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK24(U_310,U_309)),c_Arrow__Order__Mirabelle_OLin)) )
| U_309 = U_310 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_308,sK24(U_310,U_309))],[f_57_2]) ).
fof(f_57_4,plain,
( ! [U_309,U_310] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_309),U_310)),sK24(U_310,U_309)))
| ~ sP43(U_309,U_310) )
& ! [U_309,U_310] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK24(U_310,U_309)),c_Arrow__Order__Mirabelle_OLin))
| ~ sP43(U_309,U_310) )
& ! [U_309,U_310] :
( sP43(U_309,U_310)
| U_309 = U_310 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_57_3]) ).
cnf(f_57_5,plain,
( sP43(U_309,U_310)
| U_309 = U_310 ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK24(U_310,U_309)),c_Arrow__Order__Mirabelle_OLin))
| ~ sP43(U_309,U_310) ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_309),U_310)),sK24(U_310,U_309)))
| ~ sP43(U_309,U_310) ),
inference(clausify,[status(thm)],[f_57_4]) ).
fof(f_58_1,plain,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Pi__I]) ).
fof(f_58_2,plain,
! [U_316,U_315,U_314,U_313,U_312] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_312,U_314)),U_315),c_FuncSet_OPi(U_312,U_314,U_313,U_316)))
| ? [U_311] :
( ~ hBOOL(hAPP(hAPP(c_member(U_314),hAPP(U_315,U_311)),hAPP(U_316,U_311)))
& hBOOL(hAPP(hAPP(c_member(U_312),U_311),U_313)) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_316,U_315,U_314,U_313,U_312] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_312,U_314)),U_315),c_FuncSet_OPi(U_312,U_314,U_313,U_316)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_314),hAPP(U_315,sK25(U_316,U_315,U_314,U_313,U_312))),hAPP(U_316,sK25(U_316,U_315,U_314,U_313,U_312))))
& hBOOL(hAPP(hAPP(c_member(U_312),sK25(U_316,U_315,U_314,U_313,U_312)),U_313)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_311,sK25(U_316,U_315,U_314,U_313,U_312))],[f_58_2]) ).
fof(f_58_4,plain,
( ! [U_315,U_314,U_316,U_313,U_312] :
( ~ hBOOL(hAPP(hAPP(c_member(U_314),hAPP(U_315,sK25(U_316,U_315,U_314,U_313,U_312))),hAPP(U_316,sK25(U_316,U_315,U_314,U_313,U_312))))
| ~ sP44(U_315,U_314,U_316,U_313,U_312) )
& ! [U_315,U_314,U_316,U_313,U_312] :
( hBOOL(hAPP(hAPP(c_member(U_312),sK25(U_316,U_315,U_314,U_313,U_312)),U_313))
| ~ sP44(U_315,U_314,U_316,U_313,U_312) )
& ! [U_315,U_314,U_316,U_313,U_312] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_312,U_314)),U_315),c_FuncSet_OPi(U_312,U_314,U_313,U_316)))
| sP44(U_315,U_314,U_316,U_313,U_312) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_58_3]) ).
cnf(f_58_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_312,U_314)),U_315),c_FuncSet_OPi(U_312,U_314,U_313,U_316)))
| sP44(U_315,U_314,U_316,U_313,U_312) ),
inference(clausify,[status(thm)],[f_58_4]) ).
cnf(f_58_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_312),sK25(U_316,U_315,U_314,U_313,U_312)),U_313))
| ~ sP44(U_315,U_314,U_316,U_313,U_312) ),
inference(clausify,[status(thm)],[f_58_4]) ).
cnf(f_58_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_314),hAPP(U_315,sK25(U_316,U_315,U_314,U_313,U_312))),hAPP(U_316,sK25(U_316,U_315,U_314,U_313,U_312))))
| ~ sP44(U_315,U_314,U_316,U_313,U_312) ),
inference(clausify,[status(thm)],[f_58_4]) ).
fof(f_59_1,plain,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_funcsetI]) ).
fof(f_59_2,plain,
! [U_322,U_321,U_320,U_319,U_318] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_318,U_320)),U_321),c_FuncSet_OPi(U_318,U_320,U_319,c_COMBK(tc_fun(U_320,tc_HOL_Obool),U_318,U_322))))
| ? [U_317] :
( ~ hBOOL(hAPP(hAPP(c_member(U_320),hAPP(U_321,U_317)),U_322))
& hBOOL(hAPP(hAPP(c_member(U_318),U_317),U_319)) ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_322,U_321,U_320,U_319,U_318] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_318,U_320)),U_321),c_FuncSet_OPi(U_318,U_320,U_319,c_COMBK(tc_fun(U_320,tc_HOL_Obool),U_318,U_322))))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_320),hAPP(U_321,sK26(U_322,U_321,U_320,U_319,U_318))),U_322))
& hBOOL(hAPP(hAPP(c_member(U_318),sK26(U_322,U_321,U_320,U_319,U_318)),U_319)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_317,sK26(U_322,U_321,U_320,U_319,U_318))],[f_59_2]) ).
fof(f_59_4,plain,
( ! [U_318,U_319,U_321,U_322,U_320] :
( ~ hBOOL(hAPP(hAPP(c_member(U_320),hAPP(U_321,sK26(U_322,U_321,U_320,U_319,U_318))),U_322))
| ~ sP45(U_318,U_319,U_321,U_322,U_320) )
& ! [U_318,U_319,U_321,U_322,U_320] :
( hBOOL(hAPP(hAPP(c_member(U_318),sK26(U_322,U_321,U_320,U_319,U_318)),U_319))
| ~ sP45(U_318,U_319,U_321,U_322,U_320) )
& ! [U_318,U_319,U_321,U_322,U_320] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_318,U_320)),U_321),c_FuncSet_OPi(U_318,U_320,U_319,c_COMBK(tc_fun(U_320,tc_HOL_Obool),U_318,U_322))))
| sP45(U_318,U_319,U_321,U_322,U_320) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_59_3]) ).
cnf(f_59_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_318,U_320)),U_321),c_FuncSet_OPi(U_318,U_320,U_319,c_COMBK(tc_fun(U_320,tc_HOL_Obool),U_318,U_322))))
| sP45(U_318,U_319,U_321,U_322,U_320) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_318),sK26(U_322,U_321,U_320,U_319,U_318)),U_319))
| ~ sP45(U_318,U_319,U_321,U_322,U_320) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_320),hAPP(U_321,sK26(U_322,U_321,U_320,U_319,U_318))),U_322))
| ~ sP45(U_318,U_319,U_321,U_322,U_320) ),
inference(clausify,[status(thm)],[f_59_4]) ).
fof(f_60_1,plain,
! [V_y_2,V_x_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,T_a,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),
inference(fof_nnf,[status(thm)],[fact_curry__def]) ).
fof(f_60_2,plain,
! [U_328,U_327,U_326,U_325,U_324,U_323] : hAPP(hAPP(c_Product__Type_Ocurry(U_323,U_324,U_325,U_326),U_327),U_328) = hAPP(U_326,hAPP(hAPP(c_Product__Type_OPair(U_323,U_324),U_327),U_328)),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_325,U_326,U_327,U_328,U_323,U_324] : hAPP(hAPP(c_Product__Type_Ocurry(U_323,U_324,U_325,U_326),U_327),U_328) = hAPP(U_326,hAPP(hAPP(c_Product__Type_OPair(U_323,U_324),U_327),U_328)),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
hAPP(hAPP(c_Product__Type_Ocurry(U_323,U_324,U_325,U_326),U_327),U_328) = hAPP(U_326,hAPP(hAPP(c_Product__Type_OPair(U_323,U_324),U_327),U_328)),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Pi__I_H]) ).
fof(f_61_2,plain,
! [U_334,U_333,U_332,U_331,U_330] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_330,U_332)),U_333),c_FuncSet_OPi(U_330,U_332,U_331,U_334)))
| ? [U_329] :
( ~ hBOOL(hAPP(hAPP(c_member(U_332),hAPP(U_333,U_329)),hAPP(U_334,U_329)))
& hBOOL(hAPP(hAPP(c_member(U_330),U_329),U_331)) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_334,U_333,U_332,U_331,U_330] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_330,U_332)),U_333),c_FuncSet_OPi(U_330,U_332,U_331,U_334)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_332),hAPP(U_333,sK27(U_334,U_333,U_332,U_331,U_330))),hAPP(U_334,sK27(U_334,U_333,U_332,U_331,U_330))))
& hBOOL(hAPP(hAPP(c_member(U_330),sK27(U_334,U_333,U_332,U_331,U_330)),U_331)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_329,sK27(U_334,U_333,U_332,U_331,U_330))],[f_61_2]) ).
fof(f_61_4,plain,
( ! [U_330,U_331,U_332,U_333,U_334] :
( ~ hBOOL(hAPP(hAPP(c_member(U_332),hAPP(U_333,sK27(U_334,U_333,U_332,U_331,U_330))),hAPP(U_334,sK27(U_334,U_333,U_332,U_331,U_330))))
| ~ sP46(U_330,U_331,U_332,U_333,U_334) )
& ! [U_330,U_331,U_332,U_333,U_334] :
( hBOOL(hAPP(hAPP(c_member(U_330),sK27(U_334,U_333,U_332,U_331,U_330)),U_331))
| ~ sP46(U_330,U_331,U_332,U_333,U_334) )
& ! [U_330,U_331,U_332,U_333,U_334] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_330,U_332)),U_333),c_FuncSet_OPi(U_330,U_332,U_331,U_334)))
| sP46(U_330,U_331,U_332,U_333,U_334) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_61_3]) ).
cnf(f_61_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_330,U_332)),U_333),c_FuncSet_OPi(U_330,U_332,U_331,U_334)))
| sP46(U_330,U_331,U_332,U_333,U_334) ),
inference(clausify,[status(thm)],[f_61_4]) ).
cnf(f_61_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_330),sK27(U_334,U_333,U_332,U_331,U_330)),U_331))
| ~ sP46(U_330,U_331,U_332,U_333,U_334) ),
inference(clausify,[status(thm)],[f_61_4]) ).
cnf(f_61_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_332),hAPP(U_333,sK27(U_334,U_333,U_332,U_331,U_330))),hAPP(U_334,sK27(U_334,U_333,U_332,U_331,U_330))))
| ~ sP46(U_330,U_331,U_332,U_333,U_334) ),
inference(clausify,[status(thm)],[f_61_4]) ).
fof(f_62_1,plain,
! [V_B_2,T_b,V_g_2,V_f_2,V_A_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ) )
| ? [B_w] :
( hAPP(V_f_2,B_w) != hAPP(V_g_2,B_w)
& hBOOL(hAPP(hAPP(c_member(T_a),B_w),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Pi__cong]) ).
fof(f_62_2,plain,
! [U_341,U_340,U_339,U_338,U_337,U_336] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341))) ) )
| ? [U_335] :
( hAPP(U_338,U_335) != hAPP(U_339,U_335)
& hBOOL(hAPP(hAPP(c_member(U_336),U_335),U_337)) ) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_341,U_340,U_339,U_338,U_337,U_336] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341))) ) )
| ( hAPP(U_338,sK28(U_341,U_340,U_339,U_338,U_337,U_336)) != hAPP(U_339,sK28(U_341,U_340,U_339,U_338,U_337,U_336))
& hBOOL(hAPP(hAPP(c_member(U_336),sK28(U_341,U_340,U_339,U_338,U_337,U_336)),U_337)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_335,sK28(U_341,U_340,U_339,U_338,U_337,U_336))],[f_62_2]) ).
fof(f_62_4,plain,
( ! [U_337,U_336,U_338,U_339,U_340,U_341] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ sP48(U_337,U_336,U_338,U_339,U_340,U_341) )
& ! [U_337,U_336,U_338,U_339,U_340,U_341] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ sP48(U_337,U_336,U_338,U_339,U_340,U_341) )
& ! [U_337,U_336,U_338,U_339,U_340,U_341] :
( hAPP(U_338,sK28(U_341,U_340,U_339,U_338,U_337,U_336)) != hAPP(U_339,sK28(U_341,U_340,U_339,U_338,U_337,U_336))
| ~ sP47(U_337,U_336,U_338,U_339,U_340,U_341) )
& ! [U_337,U_336,U_338,U_339,U_340,U_341] :
( hBOOL(hAPP(hAPP(c_member(U_336),sK28(U_341,U_340,U_339,U_338,U_337,U_336)),U_337))
| ~ sP47(U_337,U_336,U_338,U_339,U_340,U_341) )
& ! [U_337,U_336,U_338,U_339,U_340,U_341] :
( sP48(U_337,U_336,U_338,U_339,U_340,U_341)
| sP47(U_337,U_336,U_338,U_339,U_340,U_341) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47,sP48])],[f_62_3]) ).
cnf(f_62_5,plain,
( sP48(U_337,U_336,U_338,U_339,U_340,U_341)
| sP47(U_337,U_336,U_338,U_339,U_340,U_341) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_336),sK28(U_341,U_340,U_339,U_338,U_337,U_336)),U_337))
| ~ sP47(U_337,U_336,U_338,U_339,U_340,U_341) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_7,plain,
( hAPP(U_338,sK28(U_341,U_340,U_339,U_338,U_337,U_336)) != hAPP(U_339,sK28(U_341,U_340,U_339,U_338,U_337,U_336))
| ~ sP47(U_337,U_336,U_338,U_339,U_340,U_341) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ sP48(U_337,U_336,U_338,U_339,U_340,U_341) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_338),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_336,U_340)),U_339),c_FuncSet_OPi(U_336,U_340,U_337,U_341)))
| ~ sP48(U_337,U_336,U_338,U_339,U_340,U_341) ),
inference(clausify,[status(thm)],[f_62_4]) ).
fof(f_63_1,plain,
! [V_C_2,V_g_2,T_c,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_c)),c_FuncSet_Ocompose(T_a,T_b,T_c,V_A_2,V_g_2,V_f_2)),c_FuncSet_OPi(T_a,T_c,V_A_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a,V_C_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_c)),V_g_2),c_FuncSet_OPi(T_b,T_c,V_B_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b,V_C_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_funcset__compose]) ).
fof(f_63_2,plain,
! [U_349,U_348,U_347,U_346,U_345,U_344,U_343,U_342] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_342,U_347)),c_FuncSet_Ocompose(U_342,U_343,U_347,U_345,U_348,U_344)),c_FuncSet_OPi(U_342,U_347,U_345,c_COMBK(tc_fun(U_347,tc_HOL_Obool),U_342,U_349))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_343,U_347)),U_348),c_FuncSet_OPi(U_343,U_347,U_346,c_COMBK(tc_fun(U_347,tc_HOL_Obool),U_343,U_349))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_342,U_343)),U_344),c_FuncSet_OPi(U_342,U_343,U_345,c_COMBK(tc_fun(U_343,tc_HOL_Obool),U_342,U_346)))) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_343,U_344,U_342,U_345,U_346,U_347,U_348,U_349] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_342,U_347)),c_FuncSet_Ocompose(U_342,U_343,U_347,U_345,U_348,U_344)),c_FuncSet_OPi(U_342,U_347,U_345,c_COMBK(tc_fun(U_347,tc_HOL_Obool),U_342,U_349))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_343,U_347)),U_348),c_FuncSet_OPi(U_343,U_347,U_346,c_COMBK(tc_fun(U_347,tc_HOL_Obool),U_343,U_349))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_342,U_343)),U_344),c_FuncSet_OPi(U_342,U_343,U_345,c_COMBK(tc_fun(U_343,tc_HOL_Obool),U_342,U_346)))) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_342,U_347)),c_FuncSet_Ocompose(U_342,U_343,U_347,U_345,U_348,U_344)),c_FuncSet_OPi(U_342,U_347,U_345,c_COMBK(tc_fun(U_347,tc_HOL_Obool),U_342,U_349))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_343,U_347)),U_348),c_FuncSet_OPi(U_343,U_347,U_346,c_COMBK(tc_fun(U_347,tc_HOL_Obool),U_343,U_349))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_342,U_343)),U_344),c_FuncSet_OPi(U_342,U_343,U_345,c_COMBK(tc_fun(U_343,tc_HOL_Obool),U_342,U_346)))) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [V_D_2,V_h_2,T_d,V_C_2,V_g_2,T_c,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( c_FuncSet_Ocompose(T_a,T_c,T_d,V_A_2,V_h_2,c_FuncSet_Ocompose(T_a,T_b,T_c,V_A_2,V_g_2,V_f_2)) = c_FuncSet_Ocompose(T_a,T_b,T_d,V_A_2,c_FuncSet_Ocompose(T_b,T_c,T_d,V_B_2,V_h_2,V_g_2),V_f_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,T_d)),V_h_2),c_FuncSet_OPi(T_c,T_d,V_C_2,c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c,V_D_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_c)),V_g_2),c_FuncSet_OPi(T_b,T_c,V_B_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b,V_C_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_compose__assoc]) ).
fof(f_64_2,plain,
! [U_360,U_359,U_358,U_357,U_356,U_355,U_354,U_353,U_352,U_351,U_350] :
( c_FuncSet_Ocompose(U_350,U_355,U_358,U_353,U_359,c_FuncSet_Ocompose(U_350,U_351,U_355,U_353,U_356,U_352)) = c_FuncSet_Ocompose(U_350,U_351,U_358,U_353,c_FuncSet_Ocompose(U_351,U_355,U_358,U_354,U_359,U_356),U_352)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_355,U_358)),U_359),c_FuncSet_OPi(U_355,U_358,U_357,c_COMBK(tc_fun(U_358,tc_HOL_Obool),U_355,U_360))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_351,U_355)),U_356),c_FuncSet_OPi(U_351,U_355,U_354,c_COMBK(tc_fun(U_355,tc_HOL_Obool),U_351,U_357))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_350,U_351)),U_352),c_FuncSet_OPi(U_350,U_351,U_353,c_COMBK(tc_fun(U_351,tc_HOL_Obool),U_350,U_354)))) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_351,U_350,U_352,U_353,U_354,U_355,U_356,U_357,U_358,U_359,U_360] :
( c_FuncSet_Ocompose(U_350,U_355,U_358,U_353,U_359,c_FuncSet_Ocompose(U_350,U_351,U_355,U_353,U_356,U_352)) = c_FuncSet_Ocompose(U_350,U_351,U_358,U_353,c_FuncSet_Ocompose(U_351,U_355,U_358,U_354,U_359,U_356),U_352)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_355,U_358)),U_359),c_FuncSet_OPi(U_355,U_358,U_357,c_COMBK(tc_fun(U_358,tc_HOL_Obool),U_355,U_360))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_351,U_355)),U_356),c_FuncSet_OPi(U_351,U_355,U_354,c_COMBK(tc_fun(U_355,tc_HOL_Obool),U_351,U_357))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_350,U_351)),U_352),c_FuncSet_OPi(U_350,U_351,U_353,c_COMBK(tc_fun(U_351,tc_HOL_Obool),U_350,U_354)))) ),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
( c_FuncSet_Ocompose(U_350,U_355,U_358,U_353,U_359,c_FuncSet_Ocompose(U_350,U_351,U_355,U_353,U_356,U_352)) = c_FuncSet_Ocompose(U_350,U_351,U_358,U_353,c_FuncSet_Ocompose(U_351,U_355,U_358,U_354,U_359,U_356),U_352)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_355,U_358)),U_359),c_FuncSet_OPi(U_355,U_358,U_357,c_COMBK(tc_fun(U_358,tc_HOL_Obool),U_355,U_360))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_351,U_355)),U_356),c_FuncSet_OPi(U_351,U_355,U_354,c_COMBK(tc_fun(U_355,tc_HOL_Obool),U_351,U_357))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_350,U_351)),U_352),c_FuncSet_OPi(U_350,U_351,U_353,c_COMBK(tc_fun(U_351,tc_HOL_Obool),U_350,U_354)))) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [V_aa_2,V_r_2,V_ba_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acc__downward]) ).
fof(f_65_2,plain,
! [U_364,U_363,U_362,U_361] :
( hBOOL(hAPP(hAPP(c_member(U_361),U_364),c_Wellfounded_Oacc(U_361,U_363)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_361,U_361)),hAPP(hAPP(c_Product__Type_OPair(U_361,U_361),U_364),U_362)),U_363))
| ~ hBOOL(hAPP(hAPP(c_member(U_361),U_362),c_Wellfounded_Oacc(U_361,U_363))) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_361,U_362,U_363,U_364] :
( hBOOL(hAPP(hAPP(c_member(U_361),U_364),c_Wellfounded_Oacc(U_361,U_363)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_361,U_361)),hAPP(hAPP(c_Product__Type_OPair(U_361,U_361),U_364),U_362)),U_363))
| ~ hBOOL(hAPP(hAPP(c_member(U_361),U_362),c_Wellfounded_Oacc(U_361,U_363))) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_361),U_364),c_Wellfounded_Oacc(U_361,U_363)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_361,U_361)),hAPP(hAPP(c_Product__Type_OPair(U_361,U_361),U_364),U_362)),U_363))
| ~ hBOOL(hAPP(hAPP(c_member(U_361),U_362),c_Wellfounded_Oacc(U_361,U_363))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [V_r_2,V_aa_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_aa_2)),V_r_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_aa_2)),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_acc_Osimps]) ).
fof(f_66_2,plain,
! [U_369,U_368,U_367] :
( ( hBOOL(hAPP(hAPP(c_member(U_367),U_368),c_Wellfounded_Oacc(U_367,U_369)))
| ? [U_366] :
( ~ hBOOL(hAPP(hAPP(c_member(U_367),U_366),c_Wellfounded_Oacc(U_367,U_369)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_367,U_367)),hAPP(hAPP(c_Product__Type_OPair(U_367,U_367),U_366),U_368)),U_369)) ) )
& ( ! [U_365] :
( hBOOL(hAPP(hAPP(c_member(U_367),U_365),c_Wellfounded_Oacc(U_367,U_369)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_367,U_367)),hAPP(hAPP(c_Product__Type_OPair(U_367,U_367),U_365),U_368)),U_369)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_367),U_368),c_Wellfounded_Oacc(U_367,U_369))) ) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_375,U_373,U_371] :
( hBOOL(hAPP(hAPP(c_member(U_371),U_373),c_Wellfounded_Oacc(U_371,U_375)))
| ? [U_366] :
( ~ hBOOL(hAPP(hAPP(c_member(U_371),U_366),c_Wellfounded_Oacc(U_371,U_375)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_371,U_371)),hAPP(hAPP(c_Product__Type_OPair(U_371,U_371),U_366),U_373)),U_375)) ) )
& ! [U_374,U_372,U_370] :
( ! [U_365] :
( hBOOL(hAPP(hAPP(c_member(U_370),U_365),c_Wellfounded_Oacc(U_370,U_374)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_370,U_370)),hAPP(hAPP(c_Product__Type_OPair(U_370,U_370),U_365),U_372)),U_374)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_370),U_372),c_Wellfounded_Oacc(U_370,U_374))) ) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
( ! [U_375,U_373,U_371] :
( hBOOL(hAPP(hAPP(c_member(U_371),U_373),c_Wellfounded_Oacc(U_371,U_375)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_371),sK29(U_375,U_373,U_371)),c_Wellfounded_Oacc(U_371,U_375)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_371,U_371)),hAPP(hAPP(c_Product__Type_OPair(U_371,U_371),sK29(U_375,U_373,U_371)),U_373)),U_375)) ) )
& ! [U_374,U_372,U_370] :
( ! [U_365] :
( hBOOL(hAPP(hAPP(c_member(U_370),U_365),c_Wellfounded_Oacc(U_370,U_374)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_370,U_370)),hAPP(hAPP(c_Product__Type_OPair(U_370,U_370),U_365),U_372)),U_374)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_370),U_372),c_Wellfounded_Oacc(U_370,U_374))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_366,sK29(U_375,U_373,U_371))],[f_66_3]) ).
fof(f_66_5,plain,
( ! [U_375,U_371,U_373] :
( ~ hBOOL(hAPP(hAPP(c_member(U_371),sK29(U_375,U_373,U_371)),c_Wellfounded_Oacc(U_371,U_375)))
| ~ sP49(U_375,U_371,U_373) )
& ! [U_375,U_371,U_373] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_371,U_371)),hAPP(hAPP(c_Product__Type_OPair(U_371,U_371),sK29(U_375,U_373,U_371)),U_373)),U_375))
| ~ sP49(U_375,U_371,U_373) )
& ! [U_375,U_371,U_373] :
( hBOOL(hAPP(hAPP(c_member(U_371),U_373),c_Wellfounded_Oacc(U_371,U_375)))
| sP49(U_375,U_371,U_373) )
& ! [U_372,U_374,U_365,U_370] :
( hBOOL(hAPP(hAPP(c_member(U_370),U_365),c_Wellfounded_Oacc(U_370,U_374)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_370,U_370)),hAPP(hAPP(c_Product__Type_OPair(U_370,U_370),U_365),U_372)),U_374))
| ~ hBOOL(hAPP(hAPP(c_member(U_370),U_372),c_Wellfounded_Oacc(U_370,U_374))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_66_4]) ).
cnf(f_66_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_370),U_365),c_Wellfounded_Oacc(U_370,U_374)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_370,U_370)),hAPP(hAPP(c_Product__Type_OPair(U_370,U_370),U_365),U_372)),U_374))
| ~ hBOOL(hAPP(hAPP(c_member(U_370),U_372),c_Wellfounded_Oacc(U_370,U_374))) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_371),U_373),c_Wellfounded_Oacc(U_371,U_375)))
| sP49(U_375,U_371,U_373) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_371,U_371)),hAPP(hAPP(c_Product__Type_OPair(U_371,U_371),sK29(U_375,U_373,U_371)),U_373)),U_375))
| ~ sP49(U_375,U_371,U_373) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_371),sK29(U_375,U_373,U_371)),c_Wellfounded_Oacc(U_371,U_375)))
| ~ sP49(U_375,U_371,U_373) ),
inference(clausify,[status(thm)],[f_66_5]) ).
fof(f_67_1,plain,
! [V_ba_2,V_aa_2,T_b,T_a,V_f_2] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2))
| ~ hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))) ),
inference(fof_nnf,[status(thm)],[fact_curryI]) ).
fof(f_67_2,plain,
! [U_380,U_379,U_378,U_377,U_376] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_377,U_378,tc_HOL_Obool,U_376),U_379),U_380))
| ~ hBOOL(hAPP(U_376,hAPP(hAPP(c_Product__Type_OPair(U_377,U_378),U_379),U_380))) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_377,U_378,U_376,U_379,U_380] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_377,U_378,tc_HOL_Obool,U_376),U_379),U_380))
| ~ hBOOL(hAPP(U_376,hAPP(hAPP(c_Product__Type_OPair(U_377,U_378),U_379),U_380))) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_377,U_378,tc_HOL_Obool,U_376),U_379),U_380))
| ~ hBOOL(hAPP(U_376,hAPP(hAPP(c_Product__Type_OPair(U_377,U_378),U_379),U_380))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [V_f_2,V_g_2,T_b,T_c,V_A_2,V_x_2,T_a] :
( hAPP(c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2),V_x_2) = hAPP(V_g_2,hAPP(V_f_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_compose__eq]) ).
fof(f_68_2,plain,
! [U_387,U_386,U_385,U_384,U_383,U_382,U_381] :
( hAPP(c_FuncSet_Ocompose(U_381,U_384,U_385,U_383,U_386,U_387),U_382) = hAPP(U_386,hAPP(U_387,U_382))
| ~ hBOOL(hAPP(hAPP(c_member(U_381),U_382),U_383)) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_382,U_381,U_383,U_384,U_385,U_386,U_387] :
( hAPP(c_FuncSet_Ocompose(U_381,U_384,U_385,U_383,U_386,U_387),U_382) = hAPP(U_386,hAPP(U_387,U_382))
| ~ hBOOL(hAPP(hAPP(c_member(U_381),U_382),U_383)) ),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
( hAPP(c_FuncSet_Ocompose(U_381,U_384,U_385,U_383,U_386,U_387),U_382) = hAPP(U_386,hAPP(U_387,U_382))
| ~ hBOOL(hAPP(hAPP(c_member(U_381),U_382),U_383)) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [V_ba_2,V_aa_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_curryD]) ).
fof(f_69_2,plain,
! [U_392,U_391,U_390,U_389,U_388] :
( hBOOL(hAPP(U_390,hAPP(hAPP(c_Product__Type_OPair(U_388,U_389),U_391),U_392)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_388,U_389,tc_HOL_Obool,U_390),U_391),U_392)) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_388,U_389,U_390,U_391,U_392] :
( hBOOL(hAPP(U_390,hAPP(hAPP(c_Product__Type_OPair(U_388,U_389),U_391),U_392)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_388,U_389,tc_HOL_Obool,U_390),U_391),U_392)) ),
inference(definitional_conversion,[status(esa)],[f_69_2]) ).
cnf(f_69_4,plain,
( hBOOL(hAPP(U_390,hAPP(hAPP(c_Product__Type_OPair(U_388,U_389),U_391),U_392)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_388,U_389,tc_HOL_Obool,U_390),U_391),U_392)) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_1,plain,
! [V_ba_2,V_aa_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_curryE]) ).
fof(f_70_2,plain,
! [U_397,U_396,U_395,U_394,U_393] :
( hBOOL(hAPP(U_395,hAPP(hAPP(c_Product__Type_OPair(U_393,U_394),U_396),U_397)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_393,U_394,tc_HOL_Obool,U_395),U_396),U_397)) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_393,U_394,U_395,U_396,U_397] :
( hBOOL(hAPP(U_395,hAPP(hAPP(c_Product__Type_OPair(U_393,U_394),U_396),U_397)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_393,U_394,tc_HOL_Obool,U_395),U_396),U_397)) ),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
( hBOOL(hAPP(U_395,hAPP(hAPP(c_Product__Type_OPair(U_393,U_394),U_396),U_397)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_393,U_394,tc_HOL_Obool,U_395),U_396),U_397)) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [V_ba_2,V_aa_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,T_a,V_f_2),V_aa_2),V_ba_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)),
inference(fof_nnf,[status(thm)],[fact_curry__conv]) ).
fof(f_71_2,plain,
! [U_403,U_402,U_401,U_400,U_399,U_398] : hAPP(hAPP(c_Product__Type_Ocurry(U_398,U_399,U_400,U_401),U_402),U_403) = hAPP(U_401,hAPP(hAPP(c_Product__Type_OPair(U_398,U_399),U_402),U_403)),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_398,U_399,U_400,U_401,U_402,U_403] : hAPP(hAPP(c_Product__Type_Ocurry(U_398,U_399,U_400,U_401),U_402),U_403) = hAPP(U_401,hAPP(hAPP(c_Product__Type_OPair(U_398,U_399),U_402),U_403)),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
hAPP(hAPP(c_Product__Type_Ocurry(U_398,U_399,U_400,U_401),U_402),U_403) = hAPP(U_401,hAPP(hAPP(c_Product__Type_OPair(U_398,U_399),U_402),U_403)),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
! [V_x_2,V_r_2,T_a] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp__acc__eq]) ).
fof(f_72_2,plain,
! [U_406,U_405,U_404] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_404,hAPP(hAPP(c_COMBC(U_404,tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_fun(U_404,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_404,tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_fun(U_404,tc_HOL_Obool)),U_404),c_COMBC(U_404,tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_404,tc_prod(U_404,U_404)),tc_fun(U_404,tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool)),U_404),hAPP(c_COMBB(tc_prod(U_404,U_404),tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool),U_404),c_member(tc_prod(U_404,U_404)))),c_Product__Type_OPair(U_404,U_404)))),U_405)),U_406))
| ~ hBOOL(hAPP(hAPP(c_member(U_404),U_406),c_Wellfounded_Oacc(U_404,U_405))) )
& ( hBOOL(hAPP(hAPP(c_member(U_404),U_406),c_Wellfounded_Oacc(U_404,U_405)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_404,hAPP(hAPP(c_COMBC(U_404,tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_fun(U_404,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_404,tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_fun(U_404,tc_HOL_Obool)),U_404),c_COMBC(U_404,tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_404,tc_prod(U_404,U_404)),tc_fun(U_404,tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool)),U_404),hAPP(c_COMBB(tc_prod(U_404,U_404),tc_fun(tc_fun(tc_prod(U_404,U_404),tc_HOL_Obool),tc_HOL_Obool),U_404),c_member(tc_prod(U_404,U_404)))),c_Product__Type_OPair(U_404,U_404)))),U_405)),U_406)) ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ! [U_412,U_410,U_408] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_408,hAPP(hAPP(c_COMBC(U_408,tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_fun(U_408,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_408,tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_fun(U_408,tc_HOL_Obool)),U_408),c_COMBC(U_408,tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_408,tc_prod(U_408,U_408)),tc_fun(U_408,tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),U_408),hAPP(c_COMBB(tc_prod(U_408,U_408),tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool),U_408),c_member(tc_prod(U_408,U_408)))),c_Product__Type_OPair(U_408,U_408)))),U_410)),U_412))
| ~ hBOOL(hAPP(hAPP(c_member(U_408),U_412),c_Wellfounded_Oacc(U_408,U_410))) )
& ! [U_411,U_409,U_407] :
( hBOOL(hAPP(hAPP(c_member(U_407),U_411),c_Wellfounded_Oacc(U_407,U_409)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_407,hAPP(hAPP(c_COMBC(U_407,tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_fun(U_407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_407,tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_fun(U_407,tc_HOL_Obool)),U_407),c_COMBC(U_407,tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_407,tc_prod(U_407,U_407)),tc_fun(U_407,tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),U_407),hAPP(c_COMBB(tc_prod(U_407,U_407),tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool),U_407),c_member(tc_prod(U_407,U_407)))),c_Product__Type_OPair(U_407,U_407)))),U_409)),U_411)) ) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
( ! [U_408,U_410,U_412] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_408,hAPP(hAPP(c_COMBC(U_408,tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_fun(U_408,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_408,tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_fun(U_408,tc_HOL_Obool)),U_408),c_COMBC(U_408,tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_408,tc_prod(U_408,U_408)),tc_fun(U_408,tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),U_408),hAPP(c_COMBB(tc_prod(U_408,U_408),tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool),U_408),c_member(tc_prod(U_408,U_408)))),c_Product__Type_OPair(U_408,U_408)))),U_410)),U_412))
| ~ hBOOL(hAPP(hAPP(c_member(U_408),U_412),c_Wellfounded_Oacc(U_408,U_410))) )
& ! [U_407,U_411,U_409] :
( hBOOL(hAPP(hAPP(c_member(U_407),U_411),c_Wellfounded_Oacc(U_407,U_409)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_407,hAPP(hAPP(c_COMBC(U_407,tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_fun(U_407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_407,tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_fun(U_407,tc_HOL_Obool)),U_407),c_COMBC(U_407,tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_407,tc_prod(U_407,U_407)),tc_fun(U_407,tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),U_407),hAPP(c_COMBB(tc_prod(U_407,U_407),tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool),U_407),c_member(tc_prod(U_407,U_407)))),c_Product__Type_OPair(U_407,U_407)))),U_409)),U_411)) ) ),
inference(definitional_conversion,[status(esa)],[f_72_3]) ).
cnf(f_72_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_407),U_411),c_Wellfounded_Oacc(U_407,U_409)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_407,hAPP(hAPP(c_COMBC(U_407,tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_fun(U_407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_407,tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_fun(U_407,tc_HOL_Obool)),U_407),c_COMBC(U_407,tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_407,tc_prod(U_407,U_407)),tc_fun(U_407,tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool)),U_407),hAPP(c_COMBB(tc_prod(U_407,U_407),tc_fun(tc_fun(tc_prod(U_407,U_407),tc_HOL_Obool),tc_HOL_Obool),U_407),c_member(tc_prod(U_407,U_407)))),c_Product__Type_OPair(U_407,U_407)))),U_409)),U_411)) ),
inference(clausify,[status(thm)],[f_72_4]) ).
cnf(f_72_6,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_408,hAPP(hAPP(c_COMBC(U_408,tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_fun(U_408,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_408,tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_fun(U_408,tc_HOL_Obool)),U_408),c_COMBC(U_408,tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_408,tc_prod(U_408,U_408)),tc_fun(U_408,tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool)),U_408),hAPP(c_COMBB(tc_prod(U_408,U_408),tc_fun(tc_fun(tc_prod(U_408,U_408),tc_HOL_Obool),tc_HOL_Obool),U_408),c_member(tc_prod(U_408,U_408)))),c_Product__Type_OPair(U_408,U_408)))),U_410)),U_412))
| ~ hBOOL(hAPP(hAPP(c_member(U_408),U_412),c_Wellfounded_Oacc(U_408,U_410))) ),
inference(clausify,[status(thm)],[f_72_4]) ).
fof(f_73_1,plain,
! [V_r_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_acc_OaccI]) ).
fof(f_73_2,plain,
! [U_416,U_415,U_414] :
( hBOOL(hAPP(hAPP(c_member(U_414),U_415),c_Wellfounded_Oacc(U_414,U_416)))
| ? [U_413] :
( ~ hBOOL(hAPP(hAPP(c_member(U_414),U_413),c_Wellfounded_Oacc(U_414,U_416)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_414,U_414)),hAPP(hAPP(c_Product__Type_OPair(U_414,U_414),U_413),U_415)),U_416)) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_416,U_415,U_414] :
( hBOOL(hAPP(hAPP(c_member(U_414),U_415),c_Wellfounded_Oacc(U_414,U_416)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_414),sK30(U_416,U_415,U_414)),c_Wellfounded_Oacc(U_414,U_416)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_414,U_414)),hAPP(hAPP(c_Product__Type_OPair(U_414,U_414),sK30(U_416,U_415,U_414)),U_415)),U_416)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_413,sK30(U_416,U_415,U_414))],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_415,U_416,U_414] :
( ~ hBOOL(hAPP(hAPP(c_member(U_414),sK30(U_416,U_415,U_414)),c_Wellfounded_Oacc(U_414,U_416)))
| ~ sP50(U_415,U_416,U_414) )
& ! [U_415,U_416,U_414] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_414,U_414)),hAPP(hAPP(c_Product__Type_OPair(U_414,U_414),sK30(U_416,U_415,U_414)),U_415)),U_416))
| ~ sP50(U_415,U_416,U_414) )
& ! [U_415,U_416,U_414] :
( hBOOL(hAPP(hAPP(c_member(U_414),U_415),c_Wellfounded_Oacc(U_414,U_416)))
| sP50(U_415,U_416,U_414) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_73_3]) ).
cnf(f_73_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_414),U_415),c_Wellfounded_Oacc(U_414,U_416)))
| sP50(U_415,U_416,U_414) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_414,U_414)),hAPP(hAPP(c_Product__Type_OPair(U_414,U_414),sK30(U_416,U_415,U_414)),U_415)),U_416))
| ~ sP50(U_415,U_416,U_414) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_414),sK30(U_416,U_415,U_414)),c_Wellfounded_Oacc(U_414,U_416)))
| ~ sP50(U_415,U_416,U_414) ),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_1,plain,
! [V_R_2,V_x_2,T_a] :
( ? [B_z] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) )
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_not__acc__down]) ).
fof(f_74_2,plain,
! [U_420,U_419,U_418] :
( ? [U_417] :
( ~ hBOOL(hAPP(hAPP(c_member(U_418),U_417),c_Wellfounded_Oacc(U_418,U_420)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_418,U_418)),hAPP(hAPP(c_Product__Type_OPair(U_418,U_418),U_417),U_419)),U_420)) )
| hBOOL(hAPP(hAPP(c_member(U_418),U_419),c_Wellfounded_Oacc(U_418,U_420))) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_420,U_419,U_418] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_418),sK31(U_420,U_419,U_418)),c_Wellfounded_Oacc(U_418,U_420)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_418,U_418)),hAPP(hAPP(c_Product__Type_OPair(U_418,U_418),sK31(U_420,U_419,U_418)),U_419)),U_420)) )
| hBOOL(hAPP(hAPP(c_member(U_418),U_419),c_Wellfounded_Oacc(U_418,U_420))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_417,sK31(U_420,U_419,U_418))],[f_74_2]) ).
fof(f_74_4,plain,
( ! [U_418,U_419,U_420] :
( ~ hBOOL(hAPP(hAPP(c_member(U_418),sK31(U_420,U_419,U_418)),c_Wellfounded_Oacc(U_418,U_420)))
| ~ sP51(U_418,U_419,U_420) )
& ! [U_418,U_419,U_420] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_418,U_418)),hAPP(hAPP(c_Product__Type_OPair(U_418,U_418),sK31(U_420,U_419,U_418)),U_419)),U_420))
| ~ sP51(U_418,U_419,U_420) )
& ! [U_418,U_419,U_420] :
( sP51(U_418,U_419,U_420)
| hBOOL(hAPP(hAPP(c_member(U_418),U_419),c_Wellfounded_Oacc(U_418,U_420))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_74_3]) ).
cnf(f_74_5,plain,
( sP51(U_418,U_419,U_420)
| hBOOL(hAPP(hAPP(c_member(U_418),U_419),c_Wellfounded_Oacc(U_418,U_420))) ),
inference(clausify,[status(thm)],[f_74_4]) ).
cnf(f_74_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_418,U_418)),hAPP(hAPP(c_Product__Type_OPair(U_418,U_418),sK31(U_420,U_419,U_418)),U_419)),U_420))
| ~ sP51(U_418,U_419,U_420) ),
inference(clausify,[status(thm)],[f_74_4]) ).
cnf(f_74_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_418),sK31(U_420,U_419,U_418)),c_Wellfounded_Oacc(U_418,U_420)))
| ~ sP51(U_418,U_419,U_420) ),
inference(clausify,[status(thm)],[f_74_4]) ).
fof(f_75_1,plain,
! [V_g_2,V_f_2,V_A_2,T_c,T_b,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_f_2,V_g_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2))),
inference(fof_nnf,[status(thm)],[fact_compose__extensional]) ).
fof(f_75_2,plain,
! [U_426,U_425,U_424,U_423,U_422,U_421] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_421,U_422)),c_FuncSet_Ocompose(U_421,U_423,U_422,U_424,U_425,U_426)),c_FuncSet_Oextensional(U_421,U_422,U_424))),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_422,U_421,U_423,U_424,U_425,U_426] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_421,U_422)),c_FuncSet_Ocompose(U_421,U_423,U_422,U_424,U_425,U_426)),c_FuncSet_Oextensional(U_421,U_422,U_424))),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_421,U_422)),c_FuncSet_Ocompose(U_421,U_423,U_422,U_424,U_425,U_426)),c_FuncSet_Oextensional(U_421,U_422,U_424))),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [V_ba_2,V_r_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acc__downwards]) ).
fof(f_76_2,plain,
! [U_430,U_429,U_428,U_427] :
( hBOOL(hAPP(hAPP(c_member(U_427),U_430),c_Wellfounded_Oacc(U_427,U_429)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_427,U_427)),hAPP(hAPP(c_Product__Type_OPair(U_427,U_427),U_430),U_428)),c_Transitive__Closure_Ortrancl(U_427,U_429)))
| ~ hBOOL(hAPP(hAPP(c_member(U_427),U_428),c_Wellfounded_Oacc(U_427,U_429))) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_427,U_428,U_429,U_430] :
( hBOOL(hAPP(hAPP(c_member(U_427),U_430),c_Wellfounded_Oacc(U_427,U_429)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_427,U_427)),hAPP(hAPP(c_Product__Type_OPair(U_427,U_427),U_430),U_428)),c_Transitive__Closure_Ortrancl(U_427,U_429)))
| ~ hBOOL(hAPP(hAPP(c_member(U_427),U_428),c_Wellfounded_Oacc(U_427,U_429))) ),
inference(definitional_conversion,[status(esa)],[f_76_2]) ).
cnf(f_76_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_427),U_430),c_Wellfounded_Oacc(U_427,U_429)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_427,U_427)),hAPP(hAPP(c_Product__Type_OPair(U_427,U_427),U_430),U_428)),c_Transitive__Closure_Ortrancl(U_427,U_429)))
| ~ hBOOL(hAPP(hAPP(c_member(U_427),U_428),c_Wellfounded_Oacc(U_427,U_429))) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [V_r_2,V_aa_2,V_ba_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux]) ).
fof(f_77_2,plain,
! [U_434,U_433,U_432,U_431] :
( hBOOL(hAPP(hAPP(c_member(U_431),U_432),c_Wellfounded_Oacc(U_431,U_434)))
| ~ hBOOL(hAPP(hAPP(c_member(U_431),U_433),c_Wellfounded_Oacc(U_431,U_434)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_431,U_431)),hAPP(hAPP(c_Product__Type_OPair(U_431,U_431),U_432),U_433)),c_Transitive__Closure_Ortrancl(U_431,U_434))) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_431,U_432,U_433,U_434] :
( hBOOL(hAPP(hAPP(c_member(U_431),U_432),c_Wellfounded_Oacc(U_431,U_434)))
| ~ hBOOL(hAPP(hAPP(c_member(U_431),U_433),c_Wellfounded_Oacc(U_431,U_434)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_431,U_431)),hAPP(hAPP(c_Product__Type_OPair(U_431,U_431),U_432),U_433)),c_Transitive__Closure_Ortrancl(U_431,U_434))) ),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_431),U_432),c_Wellfounded_Oacc(U_431,U_434)))
| ~ hBOOL(hAPP(hAPP(c_member(U_431),U_433),c_Wellfounded_Oacc(U_431,U_434)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_431,U_431)),hAPP(hAPP(c_Product__Type_OPair(U_431,U_431),U_432),U_433)),c_Transitive__Closure_Ortrancl(U_431,U_434))) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [V_a2_2,V_a1_2,V_Fa_2,V_R_2,T_b,T_a] :
( ( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2),hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2)))
| ! [B_g] :
( ? [B_z] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(B_g,B_z)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_a1_2)),V_R_2)) )
| hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2) != hAPP(hAPP(V_Fa_2,B_g),V_a1_2) ) )
& ( ? [B_g] :
( ! [B_z] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(B_g,B_z)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_a1_2)),V_R_2)) )
& hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2) = hAPP(hAPP(V_Fa_2,B_g),V_a1_2) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2),hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_wfrec__rel_Oequations]) ).
fof(f_78_2,plain,
! [U_444,U_443,U_442,U_441,U_440,U_439] :
( ( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_439,U_440,U_441,U_442,U_443),hAPP(hAPP(U_442,U_444),U_443)))
| ! [U_438] :
( ? [U_437] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_439,U_440,U_441,U_442,U_437),hAPP(U_438,U_437)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_439,U_439)),hAPP(hAPP(c_Product__Type_OPair(U_439,U_439),U_437),U_443)),U_441)) )
| hAPP(hAPP(U_442,U_444),U_443) != hAPP(hAPP(U_442,U_438),U_443) ) )
& ( ? [U_436] :
( ! [U_435] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_439,U_440,U_441,U_442,U_435),hAPP(U_436,U_435)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_439,U_439)),hAPP(hAPP(c_Product__Type_OPair(U_439,U_439),U_435),U_443)),U_441)) )
& hAPP(hAPP(U_442,U_444),U_443) = hAPP(hAPP(U_442,U_436),U_443) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_439,U_440,U_441,U_442,U_443),hAPP(hAPP(U_442,U_444),U_443))) ) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_456,U_454,U_452,U_450,U_448,U_446] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,U_454),hAPP(hAPP(U_452,U_456),U_454)))
| ! [U_438] :
( ? [U_437] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,U_437),hAPP(U_438,U_437)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_446,U_446)),hAPP(hAPP(c_Product__Type_OPair(U_446,U_446),U_437),U_454)),U_450)) )
| hAPP(hAPP(U_452,U_456),U_454) != hAPP(hAPP(U_452,U_438),U_454) ) )
& ! [U_455,U_453,U_451,U_449,U_447,U_445] :
( ? [U_436] :
( ! [U_435] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_435),hAPP(U_436,U_435)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_445,U_445)),hAPP(hAPP(c_Product__Type_OPair(U_445,U_445),U_435),U_453)),U_449)) )
& hAPP(hAPP(U_451,U_455),U_453) = hAPP(hAPP(U_451,U_436),U_453) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_453),hAPP(hAPP(U_451,U_455),U_453))) ) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
fof(f_78_4,plain,
( ! [U_456,U_454,U_452,U_450,U_448,U_446] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,U_454),hAPP(hAPP(U_452,U_456),U_454)))
| ! [U_438] :
( ? [U_437] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,U_437),hAPP(U_438,U_437)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_446,U_446)),hAPP(hAPP(c_Product__Type_OPair(U_446,U_446),U_437),U_454)),U_450)) )
| hAPP(hAPP(U_452,U_456),U_454) != hAPP(hAPP(U_452,U_438),U_454) ) )
& ! [U_455,U_453,U_451,U_449,U_447,U_445] :
( ( ! [U_435] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_435),hAPP(sK32(U_455,U_453,U_451,U_449,U_447,U_445),U_435)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_445,U_445)),hAPP(hAPP(c_Product__Type_OPair(U_445,U_445),U_435),U_453)),U_449)) )
& hAPP(hAPP(U_451,U_455),U_453) = hAPP(hAPP(U_451,sK32(U_455,U_453,U_451,U_449,U_447,U_445)),U_453) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_453),hAPP(hAPP(U_451,U_455),U_453))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_436,sK32(U_455,U_453,U_451,U_449,U_447,U_445))],[f_78_3]) ).
fof(f_78_5,plain,
( ! [U_456,U_454,U_452,U_450,U_448,U_446] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,U_454),hAPP(hAPP(U_452,U_456),U_454)))
| ! [U_438] :
( ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438)),hAPP(U_438,sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_446,U_446)),hAPP(hAPP(c_Product__Type_OPair(U_446,U_446),sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438)),U_454)),U_450)) )
| hAPP(hAPP(U_452,U_456),U_454) != hAPP(hAPP(U_452,U_438),U_454) ) )
& ! [U_455,U_453,U_451,U_449,U_447,U_445] :
( ( ! [U_435] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_435),hAPP(sK32(U_455,U_453,U_451,U_449,U_447,U_445),U_435)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_445,U_445)),hAPP(hAPP(c_Product__Type_OPair(U_445,U_445),U_435),U_453)),U_449)) )
& hAPP(hAPP(U_451,U_455),U_453) = hAPP(hAPP(U_451,sK32(U_455,U_453,U_451,U_449,U_447,U_445)),U_453) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_453),hAPP(hAPP(U_451,U_455),U_453))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_437,sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438))],[f_78_4]) ).
fof(f_78_6,plain,
( ! [U_448,U_450,U_438,U_456,U_446,U_452,U_454] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438)),hAPP(U_438,sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438))))
| ~ sP53(U_448,U_450,U_438,U_456,U_446,U_452,U_454) )
& ! [U_448,U_450,U_438,U_456,U_446,U_452,U_454] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_446,U_446)),hAPP(hAPP(c_Product__Type_OPair(U_446,U_446),sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438)),U_454)),U_450))
| ~ sP53(U_448,U_450,U_438,U_456,U_446,U_452,U_454) )
& ! [U_445,U_453,U_435,U_447,U_449,U_451,U_455] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_435),hAPP(sK32(U_455,U_453,U_451,U_449,U_447,U_445),U_435)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_445,U_445)),hAPP(hAPP(c_Product__Type_OPair(U_445,U_445),U_435),U_453)),U_449))
| ~ sP52(U_445,U_453,U_435,U_447,U_449,U_451,U_455) )
& ! [U_445,U_453,U_435,U_447,U_449,U_451,U_455] :
( hAPP(hAPP(U_451,U_455),U_453) = hAPP(hAPP(U_451,sK32(U_455,U_453,U_451,U_449,U_447,U_445)),U_453)
| ~ sP52(U_445,U_453,U_435,U_447,U_449,U_451,U_455) )
& ! [U_448,U_450,U_438,U_456,U_446,U_452,U_454] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,U_454),hAPP(hAPP(U_452,U_456),U_454)))
| sP53(U_448,U_450,U_438,U_456,U_446,U_452,U_454)
| hAPP(hAPP(U_452,U_456),U_454) != hAPP(hAPP(U_452,U_438),U_454) )
& ! [U_445,U_453,U_435,U_447,U_449,U_451,U_455] :
( sP52(U_445,U_453,U_435,U_447,U_449,U_451,U_455)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_453),hAPP(hAPP(U_451,U_455),U_453))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52,sP53])],[f_78_5]) ).
cnf(f_78_7,plain,
( sP52(U_445,U_453,U_435,U_447,U_449,U_451,U_455)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_453),hAPP(hAPP(U_451,U_455),U_453))) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_8,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,U_454),hAPP(hAPP(U_452,U_456),U_454)))
| sP53(U_448,U_450,U_438,U_456,U_446,U_452,U_454)
| hAPP(hAPP(U_452,U_456),U_454) != hAPP(hAPP(U_452,U_438),U_454) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_9,plain,
( hAPP(hAPP(U_451,U_455),U_453) = hAPP(hAPP(U_451,sK32(U_455,U_453,U_451,U_449,U_447,U_445)),U_453)
| ~ sP52(U_445,U_453,U_435,U_447,U_449,U_451,U_455) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_10,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_445,U_447,U_449,U_451,U_435),hAPP(sK32(U_455,U_453,U_451,U_449,U_447,U_445),U_435)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_445,U_445)),hAPP(hAPP(c_Product__Type_OPair(U_445,U_445),U_435),U_453)),U_449))
| ~ sP52(U_445,U_453,U_435,U_447,U_449,U_451,U_455) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_446,U_446)),hAPP(hAPP(c_Product__Type_OPair(U_446,U_446),sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438)),U_454)),U_450))
| ~ sP53(U_448,U_450,U_438,U_456,U_446,U_452,U_454) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_12,plain,
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_446,U_448,U_450,U_452,sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438)),hAPP(U_438,sK33(U_456,U_454,U_452,U_450,U_448,U_446,U_438))))
| ~ sP53(U_448,U_450,U_438,U_456,U_446,U_452,U_454) ),
inference(clausify,[status(thm)],[f_78_6]) ).
fof(f_79_1,plain,
! [T_b,V_aa_2,V_x_2,T_a,B_f,B_R] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),B_f),B_R),V_aa_2),V_x_2) = hAPP(B_f,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),B_R)) ),
inference(fof_nnf,[status(thm)],[fact_tfl__cut__apply]) ).
fof(f_79_2,plain,
! [U_462,U_461,U_460,U_459,U_458,U_457] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_459,U_462),U_458),U_457),U_461),U_460) = hAPP(U_458,U_460)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_459,U_459)),hAPP(hAPP(c_Product__Type_OPair(U_459,U_459),U_460),U_461)),U_457)) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_459,U_458,U_457,U_462,U_460,U_461] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_459,U_462),U_458),U_457),U_461),U_460) = hAPP(U_458,U_460)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_459,U_459)),hAPP(hAPP(c_Product__Type_OPair(U_459,U_459),U_460),U_461)),U_457)) ),
inference(definitional_conversion,[status(esa)],[f_79_2]) ).
cnf(f_79_4,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_459,U_462),U_458),U_457),U_461),U_460) = hAPP(U_458,U_460)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_459,U_459)),hAPP(hAPP(c_Product__Type_OPair(U_459,U_459),U_460),U_461)),U_457)) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [V_g_2,V_x_2,V_r_2,V_f_2,T_b,T_a] :
( ( hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2) = hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_g_2),V_r_2),V_x_2)
| ? [B_y] :
( hAPP(V_f_2,B_y) != hAPP(V_g_2,B_y)
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) ) )
& ( ! [B_y] :
( hAPP(V_f_2,B_y) = hAPP(V_g_2,B_y)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2) != hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_g_2),V_r_2),V_x_2) ) ),
inference(fof_nnf,[status(thm)],[fact_cuts__eq]) ).
fof(f_80_2,plain,
! [U_470,U_469,U_468,U_467,U_466,U_465] :
( ( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_465,U_466),U_467),U_468),U_469) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_465,U_466),U_470),U_468),U_469)
| ? [U_464] :
( hAPP(U_467,U_464) != hAPP(U_470,U_464)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_465,U_465)),hAPP(hAPP(c_Product__Type_OPair(U_465,U_465),U_464),U_469)),U_468)) ) )
& ( ! [U_463] :
( hAPP(U_467,U_463) = hAPP(U_470,U_463)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_465,U_465)),hAPP(hAPP(c_Product__Type_OPair(U_465,U_465),U_463),U_469)),U_468)) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_465,U_466),U_467),U_468),U_469) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_465,U_466),U_470),U_468),U_469) ) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_482,U_480,U_478,U_476,U_474,U_472] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_476),U_478),U_480) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_482),U_478),U_480)
| ? [U_464] :
( hAPP(U_476,U_464) != hAPP(U_482,U_464)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_472,U_472)),hAPP(hAPP(c_Product__Type_OPair(U_472,U_472),U_464),U_480)),U_478)) ) )
& ! [U_481,U_479,U_477,U_475,U_473,U_471] :
( ! [U_463] :
( hAPP(U_475,U_463) = hAPP(U_481,U_463)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_471,U_471)),hAPP(hAPP(c_Product__Type_OPair(U_471,U_471),U_463),U_479)),U_477)) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_475),U_477),U_479) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_481),U_477),U_479) ) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
fof(f_80_4,plain,
( ! [U_482,U_480,U_478,U_476,U_474,U_472] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_476),U_478),U_480) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_482),U_478),U_480)
| ( hAPP(U_476,sK34(U_482,U_480,U_478,U_476,U_474,U_472)) != hAPP(U_482,sK34(U_482,U_480,U_478,U_476,U_474,U_472))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_472,U_472)),hAPP(hAPP(c_Product__Type_OPair(U_472,U_472),sK34(U_482,U_480,U_478,U_476,U_474,U_472)),U_480)),U_478)) ) )
& ! [U_481,U_479,U_477,U_475,U_473,U_471] :
( ! [U_463] :
( hAPP(U_475,U_463) = hAPP(U_481,U_463)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_471,U_471)),hAPP(hAPP(c_Product__Type_OPair(U_471,U_471),U_463),U_479)),U_477)) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_475),U_477),U_479) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_481),U_477),U_479) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_464,sK34(U_482,U_480,U_478,U_476,U_474,U_472))],[f_80_3]) ).
fof(f_80_5,plain,
( ! [U_476,U_472,U_474,U_478,U_480,U_482] :
( hAPP(U_476,sK34(U_482,U_480,U_478,U_476,U_474,U_472)) != hAPP(U_482,sK34(U_482,U_480,U_478,U_476,U_474,U_472))
| ~ sP54(U_476,U_472,U_474,U_478,U_480,U_482) )
& ! [U_476,U_472,U_474,U_478,U_480,U_482] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_472,U_472)),hAPP(hAPP(c_Product__Type_OPair(U_472,U_472),sK34(U_482,U_480,U_478,U_476,U_474,U_472)),U_480)),U_478))
| ~ sP54(U_476,U_472,U_474,U_478,U_480,U_482) )
& ! [U_476,U_472,U_474,U_478,U_480,U_482] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_476),U_478),U_480) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_482),U_478),U_480)
| sP54(U_476,U_472,U_474,U_478,U_480,U_482) )
& ! [U_471,U_479,U_481,U_475,U_473,U_477,U_463] :
( hAPP(U_475,U_463) = hAPP(U_481,U_463)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_471,U_471)),hAPP(hAPP(c_Product__Type_OPair(U_471,U_471),U_463),U_479)),U_477))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_475),U_477),U_479) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_481),U_477),U_479) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_80_4]) ).
cnf(f_80_6,plain,
( hAPP(U_475,U_463) = hAPP(U_481,U_463)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_471,U_471)),hAPP(hAPP(c_Product__Type_OPair(U_471,U_471),U_463),U_479)),U_477))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_475),U_477),U_479) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_471,U_473),U_481),U_477),U_479) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_7,plain,
( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_476),U_478),U_480) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_472,U_474),U_482),U_478),U_480)
| sP54(U_476,U_472,U_474,U_478,U_480,U_482) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_472,U_472)),hAPP(hAPP(c_Product__Type_OPair(U_472,U_472),sK34(U_482,U_480,U_478,U_476,U_474,U_472)),U_480)),U_478))
| ~ sP54(U_476,U_472,U_474,U_478,U_480,U_482) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_9,plain,
( hAPP(U_476,sK34(U_482,U_480,U_478,U_476,U_474,U_472)) != hAPP(U_482,sK34(U_482,U_480,U_478,U_476,U_474,U_472))
| ~ sP54(U_476,U_472,U_474,U_478,U_480,U_482) ),
inference(clausify,[status(thm)],[f_80_5]) ).
fof(f_81_1,plain,
! [V_aa_2,V_ba_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_accp__downward]) ).
fof(f_81_2,plain,
! [U_486,U_485,U_484,U_483] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_483,U_484),U_486))
| ~ hBOOL(hAPP(hAPP(U_484,U_486),U_485))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_483,U_484),U_485)) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_483,U_484,U_485,U_486] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_483,U_484),U_486))
| ~ hBOOL(hAPP(hAPP(U_484,U_486),U_485))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_483,U_484),U_485)) ),
inference(definitional_conversion,[status(esa)],[f_81_2]) ).
cnf(f_81_4,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_483,U_484),U_486))
| ~ hBOOL(hAPP(hAPP(U_484,U_486),U_485))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_483,U_484),U_485)) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [V_aa_2,V_r_2,T_a] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
& hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
| ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp_Oequations]) ).
fof(f_82_2,plain,
! [U_491,U_490,U_489] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_489,U_490),U_491))
| ? [U_488] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_489,U_490),U_488))
& hBOOL(hAPP(hAPP(U_490,U_488),U_491)) ) )
& ( ! [U_487] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_489,U_490),U_487))
| ~ hBOOL(hAPP(hAPP(U_490,U_487),U_491)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_489,U_490),U_491)) ) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_497,U_495,U_493] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),U_497))
| ? [U_488] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),U_488))
& hBOOL(hAPP(hAPP(U_495,U_488),U_497)) ) )
& ! [U_496,U_494,U_492] :
( ! [U_487] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_487))
| ~ hBOOL(hAPP(hAPP(U_494,U_487),U_496)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_496)) ) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
fof(f_82_4,plain,
( ! [U_497,U_495,U_493] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),U_497))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),sK35(U_497,U_495,U_493)))
& hBOOL(hAPP(hAPP(U_495,sK35(U_497,U_495,U_493)),U_497)) ) )
& ! [U_496,U_494,U_492] :
( ! [U_487] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_487))
| ~ hBOOL(hAPP(hAPP(U_494,U_487),U_496)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_496)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_488,sK35(U_497,U_495,U_493))],[f_82_3]) ).
fof(f_82_5,plain,
( ! [U_497,U_493,U_495] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),sK35(U_497,U_495,U_493)))
| ~ sP55(U_497,U_493,U_495) )
& ! [U_497,U_493,U_495] :
( hBOOL(hAPP(hAPP(U_495,sK35(U_497,U_495,U_493)),U_497))
| ~ sP55(U_497,U_493,U_495) )
& ! [U_497,U_493,U_495] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),U_497))
| sP55(U_497,U_493,U_495) )
& ! [U_494,U_487,U_492,U_496] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_487))
| ~ hBOOL(hAPP(hAPP(U_494,U_487),U_496))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_496)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_82_4]) ).
cnf(f_82_6,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_487))
| ~ hBOOL(hAPP(hAPP(U_494,U_487),U_496))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_492,U_494),U_496)) ),
inference(clausify,[status(thm)],[f_82_5]) ).
cnf(f_82_7,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),U_497))
| sP55(U_497,U_493,U_495) ),
inference(clausify,[status(thm)],[f_82_5]) ).
cnf(f_82_8,plain,
( hBOOL(hAPP(hAPP(U_495,sK35(U_497,U_495,U_493)),U_497))
| ~ sP55(U_497,U_493,U_495) ),
inference(clausify,[status(thm)],[f_82_5]) ).
cnf(f_82_9,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_493,U_495),sK35(U_497,U_495,U_493)))
| ~ sP55(U_497,U_493,U_495) ),
inference(clausify,[status(thm)],[f_82_5]) ).
fof(f_83_1,plain,
! [V_aa_2,V_r_2,T_a] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
& hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
| ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp_Osimps]) ).
fof(f_83_2,plain,
! [U_502,U_501,U_500] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_500,U_501),U_502))
| ? [U_499] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_500,U_501),U_499))
& hBOOL(hAPP(hAPP(U_501,U_499),U_502)) ) )
& ( ! [U_498] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_500,U_501),U_498))
| ~ hBOOL(hAPP(hAPP(U_501,U_498),U_502)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_500,U_501),U_502)) ) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_508,U_506,U_504] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),U_508))
| ? [U_499] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),U_499))
& hBOOL(hAPP(hAPP(U_506,U_499),U_508)) ) )
& ! [U_507,U_505,U_503] :
( ! [U_498] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_498))
| ~ hBOOL(hAPP(hAPP(U_505,U_498),U_507)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_507)) ) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
fof(f_83_4,plain,
( ! [U_508,U_506,U_504] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),U_508))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),sK36(U_508,U_506,U_504)))
& hBOOL(hAPP(hAPP(U_506,sK36(U_508,U_506,U_504)),U_508)) ) )
& ! [U_507,U_505,U_503] :
( ! [U_498] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_498))
| ~ hBOOL(hAPP(hAPP(U_505,U_498),U_507)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_507)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_499,sK36(U_508,U_506,U_504))],[f_83_3]) ).
fof(f_83_5,plain,
( ! [U_506,U_508,U_504] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),sK36(U_508,U_506,U_504)))
| ~ sP56(U_506,U_508,U_504) )
& ! [U_506,U_508,U_504] :
( hBOOL(hAPP(hAPP(U_506,sK36(U_508,U_506,U_504)),U_508))
| ~ sP56(U_506,U_508,U_504) )
& ! [U_506,U_508,U_504] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),U_508))
| sP56(U_506,U_508,U_504) )
& ! [U_507,U_505,U_498,U_503] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_498))
| ~ hBOOL(hAPP(hAPP(U_505,U_498),U_507))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_507)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_83_4]) ).
cnf(f_83_6,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_498))
| ~ hBOOL(hAPP(hAPP(U_505,U_498),U_507))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_503,U_505),U_507)) ),
inference(clausify,[status(thm)],[f_83_5]) ).
cnf(f_83_7,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),U_508))
| sP56(U_506,U_508,U_504) ),
inference(clausify,[status(thm)],[f_83_5]) ).
cnf(f_83_8,plain,
( hBOOL(hAPP(hAPP(U_506,sK36(U_508,U_506,U_504)),U_508))
| ~ sP56(U_506,U_508,U_504) ),
inference(clausify,[status(thm)],[f_83_5]) ).
cnf(f_83_9,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_504,U_506),sK36(U_508,U_506,U_504)))
| ~ sP56(U_506,U_508,U_504) ),
inference(clausify,[status(thm)],[f_83_5]) ).
fof(f_84_1,plain,
! [V_f_2,T_b,V_r_2,V_aa_2,V_x_2,T_a] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_aa_2),V_x_2) = hAPP(V_f_2,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_cut__apply]) ).
fof(f_84_2,plain,
! [U_514,U_513,U_512,U_511,U_510,U_509] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_509,U_513),U_514),U_512),U_511),U_510) = hAPP(U_514,U_510)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_509,U_509)),hAPP(hAPP(c_Product__Type_OPair(U_509,U_509),U_510),U_511)),U_512)) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_510,U_509,U_511,U_512,U_513,U_514] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_509,U_513),U_514),U_512),U_511),U_510) = hAPP(U_514,U_510)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_509,U_509)),hAPP(hAPP(c_Product__Type_OPair(U_509,U_509),U_510),U_511)),U_512)) ),
inference(definitional_conversion,[status(esa)],[f_84_2]) ).
cnf(f_84_4,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_509,U_513),U_514),U_512),U_511),U_510) = hAPP(U_514,U_510)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_509,U_509)),hAPP(hAPP(c_Product__Type_OPair(U_509,U_509),U_510),U_511)),U_512)) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [V_r_2,V_aa_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))),
inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
fof(f_85_2,plain,
! [U_517,U_516,U_515] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_515,U_515)),hAPP(hAPP(c_Product__Type_OPair(U_515,U_515),U_516),U_516)),c_Transitive__Closure_Ortrancl(U_515,U_517))),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_515,U_516,U_517] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_515,U_515)),hAPP(hAPP(c_Product__Type_OPair(U_515,U_515),U_516),U_516)),c_Transitive__Closure_Ortrancl(U_515,U_517))),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(U_515,U_515)),hAPP(hAPP(c_Product__Type_OPair(U_515,U_515),U_516),U_516)),c_Transitive__Closure_Ortrancl(U_515,U_517))),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [V_r_2,V_p_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl]) ).
fof(f_86_2,plain,
! [U_520,U_519,U_518] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_518,U_518)),U_519),c_Transitive__Closure_Ortrancl(U_518,U_520)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_518,U_518)),U_519),U_520)) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_518,U_519,U_520] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_518,U_518)),U_519),c_Transitive__Closure_Ortrancl(U_518,U_520)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_518,U_518)),U_519),U_520)) ),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_518,U_518)),U_519),c_Transitive__Closure_Ortrancl(U_518,U_520)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_518,U_518)),U_519),U_520)) ),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__trans]) ).
fof(f_87_2,plain,
! [U_525,U_524,U_523,U_522,U_521] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_522),U_525)),c_Transitive__Closure_Ortrancl(U_521,U_524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_523),U_525)),c_Transitive__Closure_Ortrancl(U_521,U_524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_522),U_523)),c_Transitive__Closure_Ortrancl(U_521,U_524))) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_521,U_522,U_523,U_524,U_525] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_522),U_525)),c_Transitive__Closure_Ortrancl(U_521,U_524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_523),U_525)),c_Transitive__Closure_Ortrancl(U_521,U_524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_522),U_523)),c_Transitive__Closure_Ortrancl(U_521,U_524))) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_522),U_525)),c_Transitive__Closure_Ortrancl(U_521,U_524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_523),U_525)),c_Transitive__Closure_Ortrancl(U_521,U_524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_521,U_521)),hAPP(hAPP(c_Product__Type_OPair(U_521,U_521),U_522),U_523)),c_Transitive__Closure_Ortrancl(U_521,U_524))) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl]) ).
fof(f_88_2,plain,
! [U_530,U_529,U_528,U_527,U_526] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_527),U_530)),c_Transitive__Closure_Ortrancl(U_526,U_529)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_528),U_530)),U_529))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_527),U_528)),c_Transitive__Closure_Ortrancl(U_526,U_529))) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_526,U_527,U_528,U_529,U_530] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_527),U_530)),c_Transitive__Closure_Ortrancl(U_526,U_529)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_528),U_530)),U_529))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_527),U_528)),c_Transitive__Closure_Ortrancl(U_526,U_529))) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_527),U_530)),c_Transitive__Closure_Ortrancl(U_526,U_529)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_528),U_530)),U_529))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_526,U_526)),hAPP(hAPP(c_Product__Type_OPair(U_526,U_526),U_527),U_528)),c_Transitive__Closure_Ortrancl(U_526,U_529))) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl]) ).
fof(f_89_2,plain,
! [U_535,U_534,U_533,U_532,U_531] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_532),U_535)),c_Transitive__Closure_Ortrancl(U_531,U_534)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_533),U_535)),c_Transitive__Closure_Ortrancl(U_531,U_534)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_532),U_533)),U_534)) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_532,U_533,U_531,U_534,U_535] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_532),U_535)),c_Transitive__Closure_Ortrancl(U_531,U_534)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_533),U_535)),c_Transitive__Closure_Ortrancl(U_531,U_534)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_532),U_533)),U_534)) ),
inference(definitional_conversion,[status(esa)],[f_89_2]) ).
cnf(f_89_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_532),U_535)),c_Transitive__Closure_Ortrancl(U_531,U_534)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_533),U_535)),c_Transitive__Closure_Ortrancl(U_531,U_534)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_531,U_531)),hAPP(hAPP(c_Product__Type_OPair(U_531,U_531),U_532),U_533)),U_534)) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
( c_FuncSet_Ocompose(T_a,T_b,T_b,V_A_2,c_FuncSet_Orestrict(T_b,T_b,c_COMBI(T_b),V_B_2),V_f_2) = V_f_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_Id__compose]) ).
fof(f_90_2,plain,
! [U_540,U_539,U_538,U_537,U_536] :
( c_FuncSet_Ocompose(U_536,U_537,U_537,U_539,c_FuncSet_Orestrict(U_537,U_537,c_COMBI(U_537),U_540),U_538) = U_538
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_536,U_537)),U_538),c_FuncSet_Oextensional(U_536,U_537,U_539)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_536,U_537)),U_538),c_FuncSet_OPi(U_536,U_537,U_539,c_COMBK(tc_fun(U_537,tc_HOL_Obool),U_536,U_540)))) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_536,U_537,U_538,U_539,U_540] :
( c_FuncSet_Ocompose(U_536,U_537,U_537,U_539,c_FuncSet_Orestrict(U_537,U_537,c_COMBI(U_537),U_540),U_538) = U_538
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_536,U_537)),U_538),c_FuncSet_Oextensional(U_536,U_537,U_539)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_536,U_537)),U_538),c_FuncSet_OPi(U_536,U_537,U_539,c_COMBK(tc_fun(U_537,tc_HOL_Obool),U_536,U_540)))) ),
inference(definitional_conversion,[status(esa)],[f_90_2]) ).
cnf(f_90_4,plain,
( c_FuncSet_Ocompose(U_536,U_537,U_537,U_539,c_FuncSet_Orestrict(U_537,U_537,c_COMBI(U_537),U_540),U_538) = U_538
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_536,U_537)),U_538),c_FuncSet_Oextensional(U_536,U_537,U_539)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_536,U_537)),U_538),c_FuncSet_OPi(U_536,U_537,U_539,c_COMBK(tc_fun(U_537,tc_HOL_Obool),U_536,U_540)))) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [V_B_2,V_A_2,V_g_2,T_b,T_a] :
( c_FuncSet_Ocompose(T_a,T_a,T_b,V_A_2,V_g_2,c_FuncSet_Orestrict(T_a,T_a,c_COMBI(T_a),V_A_2)) = V_g_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_compose__Id]) ).
fof(f_91_2,plain,
! [U_545,U_544,U_543,U_542,U_541] :
( c_FuncSet_Ocompose(U_541,U_541,U_542,U_544,U_543,c_FuncSet_Orestrict(U_541,U_541,c_COMBI(U_541),U_544)) = U_543
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_541,U_542)),U_543),c_FuncSet_Oextensional(U_541,U_542,U_544)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_541,U_542)),U_543),c_FuncSet_OPi(U_541,U_542,U_544,c_COMBK(tc_fun(U_542,tc_HOL_Obool),U_541,U_545)))) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_541,U_542,U_543,U_544,U_545] :
( c_FuncSet_Ocompose(U_541,U_541,U_542,U_544,U_543,c_FuncSet_Orestrict(U_541,U_541,c_COMBI(U_541),U_544)) = U_543
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_541,U_542)),U_543),c_FuncSet_Oextensional(U_541,U_542,U_544)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_541,U_542)),U_543),c_FuncSet_OPi(U_541,U_542,U_544,c_COMBK(tc_fun(U_542,tc_HOL_Obool),U_541,U_545)))) ),
inference(definitional_conversion,[status(esa)],[f_91_2]) ).
cnf(f_91_4,plain,
( c_FuncSet_Ocompose(U_541,U_541,U_542,U_544,U_543,c_FuncSet_Orestrict(U_541,U_541,c_COMBI(U_541),U_544)) = U_543
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_541,U_542)),U_543),c_FuncSet_Oextensional(U_541,U_542,U_544)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_541,U_542)),U_543),c_FuncSet_OPi(U_541,U_542,U_544,c_COMBK(tc_fun(U_542,tc_HOL_Obool),U_541,U_545)))) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [V_Fa_2,V_R_2,T_b,T_a] : c_Recdef_Oadm__wf(T_a,T_b,V_R_2,hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(T_a,T_a),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),c_COMBS(T_a,T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),hAPP(c_COMBB(tc_fun(T_a,T_b),tc_fun(T_a,T_b),T_a),V_Fa_2)),hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_fun(T_a,T_b))),c_Recdef_Ocut(T_a,T_b)),V_R_2)))),c_COMBI(T_a))),
inference(fof_nnf,[status(thm)],[fact_adm__lemma]) ).
fof(f_92_2,plain,
! [U_549,U_548,U_547,U_546] : c_Recdef_Oadm__wf(U_546,U_547,U_548,hAPP(hAPP(c_COMBC(tc_fun(U_546,U_547),tc_fun(U_546,U_546),tc_fun(U_546,U_547)),hAPP(hAPP(c_COMBB(tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(tc_fun(U_546,U_546),tc_fun(U_546,U_547)),tc_fun(U_546,U_547)),c_COMBS(U_546,U_546,U_547)),hAPP(hAPP(c_COMBB(tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(U_546,U_547)),hAPP(c_COMBB(tc_fun(U_546,U_547),tc_fun(U_546,U_547),U_546),U_549)),hAPP(hAPP(c_COMBC(tc_fun(U_546,U_547),tc_fun(tc_prod(U_546,U_546),tc_HOL_Obool),tc_fun(U_546,tc_fun(U_546,U_547))),c_Recdef_Ocut(U_546,U_547)),U_548)))),c_COMBI(U_546))),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_546,U_547,U_548,U_549] : c_Recdef_Oadm__wf(U_546,U_547,U_548,hAPP(hAPP(c_COMBC(tc_fun(U_546,U_547),tc_fun(U_546,U_546),tc_fun(U_546,U_547)),hAPP(hAPP(c_COMBB(tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(tc_fun(U_546,U_546),tc_fun(U_546,U_547)),tc_fun(U_546,U_547)),c_COMBS(U_546,U_546,U_547)),hAPP(hAPP(c_COMBB(tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(U_546,U_547)),hAPP(c_COMBB(tc_fun(U_546,U_547),tc_fun(U_546,U_547),U_546),U_549)),hAPP(hAPP(c_COMBC(tc_fun(U_546,U_547),tc_fun(tc_prod(U_546,U_546),tc_HOL_Obool),tc_fun(U_546,tc_fun(U_546,U_547))),c_Recdef_Ocut(U_546,U_547)),U_548)))),c_COMBI(U_546))),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
c_Recdef_Oadm__wf(U_546,U_547,U_548,hAPP(hAPP(c_COMBC(tc_fun(U_546,U_547),tc_fun(U_546,U_546),tc_fun(U_546,U_547)),hAPP(hAPP(c_COMBB(tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(tc_fun(U_546,U_546),tc_fun(U_546,U_547)),tc_fun(U_546,U_547)),c_COMBS(U_546,U_546,U_547)),hAPP(hAPP(c_COMBB(tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(U_546,tc_fun(U_546,U_547)),tc_fun(U_546,U_547)),hAPP(c_COMBB(tc_fun(U_546,U_547),tc_fun(U_546,U_547),U_546),U_549)),hAPP(hAPP(c_COMBC(tc_fun(U_546,U_547),tc_fun(tc_prod(U_546,U_546),tc_HOL_Obool),tc_fun(U_546,tc_fun(U_546,U_547))),c_Recdef_Ocut(U_546,U_547)),U_548)))),c_COMBI(U_546))),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [V_f_2,V_g_2,V_A_2,T_b,T_c,T_a] : c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2) = c_FuncSet_Orestrict(T_a,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_a),V_g_2),V_f_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_compose__def]) ).
fof(f_93_2,plain,
! [U_555,U_554,U_553,U_552,U_551,U_550] : c_FuncSet_Ocompose(U_550,U_551,U_552,U_553,U_554,U_555) = c_FuncSet_Orestrict(U_550,U_552,hAPP(hAPP(c_COMBB(U_551,U_552,U_550),U_554),U_555),U_553),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_551,U_550,U_552,U_553,U_554,U_555] : c_FuncSet_Ocompose(U_550,U_551,U_552,U_553,U_554,U_555) = c_FuncSet_Orestrict(U_550,U_552,hAPP(hAPP(c_COMBB(U_551,U_552,U_550),U_554),U_555),U_553),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_4,plain,
c_FuncSet_Ocompose(U_550,U_551,U_552,U_553,U_554,U_555) = c_FuncSet_Orestrict(U_550,U_552,hAPP(hAPP(c_COMBB(U_551,U_552,U_550),U_554),U_555),U_553),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [V_A_2,V_f_2,T_b,T_a] :
( c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2) = V_f_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_extensional__restrict]) ).
fof(f_94_2,plain,
! [U_559,U_558,U_557,U_556] :
( c_FuncSet_Orestrict(U_556,U_557,U_558,U_559) = U_558
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_556,U_557)),U_558),c_FuncSet_Oextensional(U_556,U_557,U_559))) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_556,U_557,U_558,U_559] :
( c_FuncSet_Orestrict(U_556,U_557,U_558,U_559) = U_558
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_556,U_557)),U_558),c_FuncSet_Oextensional(U_556,U_557,U_559))) ),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
( c_FuncSet_Orestrict(U_556,U_557,U_558,U_559) = U_558
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_556,U_557)),U_558),c_FuncSet_Oextensional(U_556,U_557,U_559))) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2))),
inference(fof_nnf,[status(thm)],[fact_restrict__extensional]) ).
fof(f_95_2,plain,
! [U_563,U_562,U_561,U_560] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_560,U_561)),c_FuncSet_Orestrict(U_560,U_561,U_562,U_563)),c_FuncSet_Oextensional(U_560,U_561,U_563))),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_560,U_561,U_562,U_563] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_560,U_561)),c_FuncSet_Orestrict(U_560,U_561,U_562,U_563)),c_FuncSet_Oextensional(U_560,U_561,U_563))),
inference(definitional_conversion,[status(esa)],[f_95_2]) ).
cnf(f_95_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_560,U_561)),c_FuncSet_Orestrict(U_560,U_561,U_562,U_563)),c_FuncSet_Oextensional(U_560,U_561,U_563))),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp]) ).
fof(f_96_2,plain,
! [U_565,U_564] : c_Transitive__Closure_Ortrancl(U_564,c_Transitive__Closure_Ortrancl(U_564,U_565)) = c_Transitive__Closure_Ortrancl(U_564,U_565),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_564,U_565] : c_Transitive__Closure_Ortrancl(U_564,c_Transitive__Closure_Ortrancl(U_564,U_565)) = c_Transitive__Closure_Ortrancl(U_564,U_565),
inference(definitional_conversion,[status(esa)],[f_96_2]) ).
cnf(f_96_4,plain,
c_Transitive__Closure_Ortrancl(U_564,c_Transitive__Closure_Ortrancl(U_564,U_565)) = c_Transitive__Closure_Ortrancl(U_564,U_565),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_restrictI]) ).
fof(f_97_2,plain,
! [U_571,U_570,U_569,U_568,U_567] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_567,U_569)),c_FuncSet_Orestrict(U_567,U_569,U_570,U_568)),c_FuncSet_OPi(U_567,U_569,U_568,U_571)))
| ? [U_566] :
( ~ hBOOL(hAPP(hAPP(c_member(U_569),hAPP(U_570,U_566)),hAPP(U_571,U_566)))
& hBOOL(hAPP(hAPP(c_member(U_567),U_566),U_568)) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_571,U_570,U_569,U_568,U_567] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_567,U_569)),c_FuncSet_Orestrict(U_567,U_569,U_570,U_568)),c_FuncSet_OPi(U_567,U_569,U_568,U_571)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_569),hAPP(U_570,sK37(U_571,U_570,U_569,U_568,U_567))),hAPP(U_571,sK37(U_571,U_570,U_569,U_568,U_567))))
& hBOOL(hAPP(hAPP(c_member(U_567),sK37(U_571,U_570,U_569,U_568,U_567)),U_568)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_566,sK37(U_571,U_570,U_569,U_568,U_567))],[f_97_2]) ).
fof(f_97_4,plain,
( ! [U_567,U_568,U_569,U_570,U_571] :
( ~ hBOOL(hAPP(hAPP(c_member(U_569),hAPP(U_570,sK37(U_571,U_570,U_569,U_568,U_567))),hAPP(U_571,sK37(U_571,U_570,U_569,U_568,U_567))))
| ~ sP57(U_567,U_568,U_569,U_570,U_571) )
& ! [U_567,U_568,U_569,U_570,U_571] :
( hBOOL(hAPP(hAPP(c_member(U_567),sK37(U_571,U_570,U_569,U_568,U_567)),U_568))
| ~ sP57(U_567,U_568,U_569,U_570,U_571) )
& ! [U_567,U_568,U_569,U_570,U_571] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_567,U_569)),c_FuncSet_Orestrict(U_567,U_569,U_570,U_568)),c_FuncSet_OPi(U_567,U_569,U_568,U_571)))
| sP57(U_567,U_568,U_569,U_570,U_571) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_97_3]) ).
cnf(f_97_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_567,U_569)),c_FuncSet_Orestrict(U_567,U_569,U_570,U_568)),c_FuncSet_OPi(U_567,U_569,U_568,U_571)))
| sP57(U_567,U_568,U_569,U_570,U_571) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_567),sK37(U_571,U_570,U_569,U_568,U_567)),U_568))
| ~ sP57(U_567,U_568,U_569,U_570,U_571) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_569),hAPP(U_570,sK37(U_571,U_570,U_569,U_568,U_567))),hAPP(U_571,sK37(U_571,U_570,U_569,U_568,U_567))))
| ~ sP57(U_567,U_568,U_569,U_570,U_571) ),
inference(clausify,[status(thm)],[f_97_4]) ).
fof(f_98_1,plain,
! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_restrict__in__funcset]) ).
fof(f_98_2,plain,
! [U_577,U_576,U_575,U_574,U_573] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_573,U_575)),c_FuncSet_Orestrict(U_573,U_575,U_576,U_574)),c_FuncSet_OPi(U_573,U_575,U_574,c_COMBK(tc_fun(U_575,tc_HOL_Obool),U_573,U_577))))
| ? [U_572] :
( ~ hBOOL(hAPP(hAPP(c_member(U_575),hAPP(U_576,U_572)),U_577))
& hBOOL(hAPP(hAPP(c_member(U_573),U_572),U_574)) ) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_577,U_576,U_575,U_574,U_573] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_573,U_575)),c_FuncSet_Orestrict(U_573,U_575,U_576,U_574)),c_FuncSet_OPi(U_573,U_575,U_574,c_COMBK(tc_fun(U_575,tc_HOL_Obool),U_573,U_577))))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_575),hAPP(U_576,sK38(U_577,U_576,U_575,U_574,U_573))),U_577))
& hBOOL(hAPP(hAPP(c_member(U_573),sK38(U_577,U_576,U_575,U_574,U_573)),U_574)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_572,sK38(U_577,U_576,U_575,U_574,U_573))],[f_98_2]) ).
fof(f_98_4,plain,
( ! [U_574,U_573,U_575,U_576,U_577] :
( ~ hBOOL(hAPP(hAPP(c_member(U_575),hAPP(U_576,sK38(U_577,U_576,U_575,U_574,U_573))),U_577))
| ~ sP58(U_574,U_573,U_575,U_576,U_577) )
& ! [U_574,U_573,U_575,U_576,U_577] :
( hBOOL(hAPP(hAPP(c_member(U_573),sK38(U_577,U_576,U_575,U_574,U_573)),U_574))
| ~ sP58(U_574,U_573,U_575,U_576,U_577) )
& ! [U_574,U_573,U_575,U_576,U_577] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_573,U_575)),c_FuncSet_Orestrict(U_573,U_575,U_576,U_574)),c_FuncSet_OPi(U_573,U_575,U_574,c_COMBK(tc_fun(U_575,tc_HOL_Obool),U_573,U_577))))
| sP58(U_574,U_573,U_575,U_576,U_577) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_98_3]) ).
cnf(f_98_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_573,U_575)),c_FuncSet_Orestrict(U_573,U_575,U_576,U_574)),c_FuncSet_OPi(U_573,U_575,U_574,c_COMBK(tc_fun(U_575,tc_HOL_Obool),U_573,U_577))))
| sP58(U_574,U_573,U_575,U_576,U_577) ),
inference(clausify,[status(thm)],[f_98_4]) ).
cnf(f_98_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_573),sK38(U_577,U_576,U_575,U_574,U_573)),U_574))
| ~ sP58(U_574,U_573,U_575,U_576,U_577) ),
inference(clausify,[status(thm)],[f_98_4]) ).
cnf(f_98_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_575),hAPP(U_576,sK38(U_577,U_576,U_575,U_574,U_573))),U_577))
| ~ sP58(U_574,U_573,U_575,U_576,U_577) ),
inference(clausify,[status(thm)],[f_98_4]) ).
fof(f_99_1,plain,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ c_Relation_Osingle__valued(T_a,T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__confluent]) ).
fof(f_99_2,plain,
! [U_582,U_581,U_580,U_579,U_578] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_582),U_581)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_581),U_582)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_580),U_582)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_580),U_581)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ c_Relation_Osingle__valued(U_578,U_578,U_579) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_578,U_579,U_580,U_581,U_582] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_582),U_581)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_581),U_582)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_580),U_582)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_580),U_581)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ c_Relation_Osingle__valued(U_578,U_578,U_579) ),
inference(definitional_conversion,[status(esa)],[f_99_2]) ).
cnf(f_99_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_582),U_581)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_581),U_582)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_580),U_582)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_578,U_578)),hAPP(hAPP(c_Product__Type_OPair(U_578,U_578),U_580),U_581)),c_Transitive__Closure_Ortrancl(U_578,U_579)))
| ~ c_Relation_Osingle__valued(U_578,U_578,U_579) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [V_Fa_2,V_R_2,T_b,T_a] :
( ( c_Recdef_Oadm__wf(T_a,T_b,V_R_2,V_Fa_2)
| ? [B_f,B_g,B_x] :
( hAPP(hAPP(V_Fa_2,B_f),B_x) != hAPP(hAPP(V_Fa_2,B_g),B_x)
& ! [B_z] :
( hAPP(B_f,B_z) = hAPP(B_g,B_z)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),B_x)),V_R_2)) ) ) )
& ( ! [B_f,B_g,B_x] :
( hAPP(hAPP(V_Fa_2,B_f),B_x) = hAPP(hAPP(V_Fa_2,B_g),B_x)
| ? [B_z] :
( hAPP(B_f,B_z) != hAPP(B_g,B_z)
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),B_x)),V_R_2)) ) )
| ~ c_Recdef_Oadm__wf(T_a,T_b,V_R_2,V_Fa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_adm__wf__def]) ).
fof(f_100_2,plain,
! [U_594,U_593,U_592,U_591] :
( ( c_Recdef_Oadm__wf(U_591,U_592,U_593,U_594)
| ? [U_590,U_589,U_588] :
( hAPP(hAPP(U_594,U_590),U_588) != hAPP(hAPP(U_594,U_589),U_588)
& ! [U_587] :
( hAPP(U_590,U_587) = hAPP(U_589,U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_591,U_591)),hAPP(hAPP(c_Product__Type_OPair(U_591,U_591),U_587),U_588)),U_593)) ) ) )
& ( ! [U_586,U_585,U_584] :
( hAPP(hAPP(U_594,U_586),U_584) = hAPP(hAPP(U_594,U_585),U_584)
| ? [U_583] :
( hAPP(U_586,U_583) != hAPP(U_585,U_583)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_591,U_591)),hAPP(hAPP(c_Product__Type_OPair(U_591,U_591),U_583),U_584)),U_593)) ) )
| ~ c_Recdef_Oadm__wf(U_591,U_592,U_593,U_594) ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ! [U_602,U_600,U_598,U_596] :
( c_Recdef_Oadm__wf(U_596,U_598,U_600,U_602)
| ? [U_590,U_589,U_588] :
( hAPP(hAPP(U_602,U_590),U_588) != hAPP(hAPP(U_602,U_589),U_588)
& ! [U_587] :
( hAPP(U_590,U_587) = hAPP(U_589,U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_596,U_596)),hAPP(hAPP(c_Product__Type_OPair(U_596,U_596),U_587),U_588)),U_600)) ) ) )
& ! [U_601,U_599,U_597,U_595] :
( ! [U_586,U_585,U_584] :
( hAPP(hAPP(U_601,U_586),U_584) = hAPP(hAPP(U_601,U_585),U_584)
| ? [U_583] :
( hAPP(U_586,U_583) != hAPP(U_585,U_583)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_595,U_595)),hAPP(hAPP(c_Product__Type_OPair(U_595,U_595),U_583),U_584)),U_599)) ) )
| ~ c_Recdef_Oadm__wf(U_595,U_597,U_599,U_601) ) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
fof(f_100_4,plain,
( ! [U_602,U_600,U_598,U_596] :
( c_Recdef_Oadm__wf(U_596,U_598,U_600,U_602)
| ? [U_590,U_589,U_588] :
( hAPP(hAPP(U_602,U_590),U_588) != hAPP(hAPP(U_602,U_589),U_588)
& ! [U_587] :
( hAPP(U_590,U_587) = hAPP(U_589,U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_596,U_596)),hAPP(hAPP(c_Product__Type_OPair(U_596,U_596),U_587),U_588)),U_600)) ) ) )
& ! [U_601,U_599,U_597,U_595] :
( ! [U_586,U_585,U_584] :
( hAPP(hAPP(U_601,U_586),U_584) = hAPP(hAPP(U_601,U_585),U_584)
| ( hAPP(U_586,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)) != hAPP(U_585,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_595,U_595)),hAPP(hAPP(c_Product__Type_OPair(U_595,U_595),sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)),U_584)),U_599)) ) )
| ~ c_Recdef_Oadm__wf(U_595,U_597,U_599,U_601) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_583,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584))],[f_100_3]) ).
fof(f_100_5,plain,
( ! [U_602,U_600,U_598,U_596] :
( c_Recdef_Oadm__wf(U_596,U_598,U_600,U_602)
| ? [U_589,U_588] :
( hAPP(hAPP(U_602,sK40(U_602,U_600,U_598,U_596)),U_588) != hAPP(hAPP(U_602,U_589),U_588)
& ! [U_587] :
( hAPP(sK40(U_602,U_600,U_598,U_596),U_587) = hAPP(U_589,U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_596,U_596)),hAPP(hAPP(c_Product__Type_OPair(U_596,U_596),U_587),U_588)),U_600)) ) ) )
& ! [U_601,U_599,U_597,U_595] :
( ! [U_586,U_585,U_584] :
( hAPP(hAPP(U_601,U_586),U_584) = hAPP(hAPP(U_601,U_585),U_584)
| ( hAPP(U_586,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)) != hAPP(U_585,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_595,U_595)),hAPP(hAPP(c_Product__Type_OPair(U_595,U_595),sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)),U_584)),U_599)) ) )
| ~ c_Recdef_Oadm__wf(U_595,U_597,U_599,U_601) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_590,sK40(U_602,U_600,U_598,U_596))],[f_100_4]) ).
fof(f_100_6,plain,
( ! [U_602,U_600,U_598,U_596] :
( c_Recdef_Oadm__wf(U_596,U_598,U_600,U_602)
| ? [U_588] :
( hAPP(hAPP(U_602,sK40(U_602,U_600,U_598,U_596)),U_588) != hAPP(hAPP(U_602,sK41(U_602,U_600,U_598,U_596)),U_588)
& ! [U_587] :
( hAPP(sK40(U_602,U_600,U_598,U_596),U_587) = hAPP(sK41(U_602,U_600,U_598,U_596),U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_596,U_596)),hAPP(hAPP(c_Product__Type_OPair(U_596,U_596),U_587),U_588)),U_600)) ) ) )
& ! [U_601,U_599,U_597,U_595] :
( ! [U_586,U_585,U_584] :
( hAPP(hAPP(U_601,U_586),U_584) = hAPP(hAPP(U_601,U_585),U_584)
| ( hAPP(U_586,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)) != hAPP(U_585,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_595,U_595)),hAPP(hAPP(c_Product__Type_OPair(U_595,U_595),sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)),U_584)),U_599)) ) )
| ~ c_Recdef_Oadm__wf(U_595,U_597,U_599,U_601) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_589,sK41(U_602,U_600,U_598,U_596))],[f_100_5]) ).
fof(f_100_7,plain,
( ! [U_602,U_600,U_598,U_596] :
( c_Recdef_Oadm__wf(U_596,U_598,U_600,U_602)
| ( hAPP(hAPP(U_602,sK40(U_602,U_600,U_598,U_596)),sK42(U_602,U_600,U_598,U_596)) != hAPP(hAPP(U_602,sK41(U_602,U_600,U_598,U_596)),sK42(U_602,U_600,U_598,U_596))
& ! [U_587] :
( hAPP(sK40(U_602,U_600,U_598,U_596),U_587) = hAPP(sK41(U_602,U_600,U_598,U_596),U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_596,U_596)),hAPP(hAPP(c_Product__Type_OPair(U_596,U_596),U_587),sK42(U_602,U_600,U_598,U_596))),U_600)) ) ) )
& ! [U_601,U_599,U_597,U_595] :
( ! [U_586,U_585,U_584] :
( hAPP(hAPP(U_601,U_586),U_584) = hAPP(hAPP(U_601,U_585),U_584)
| ( hAPP(U_586,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)) != hAPP(U_585,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_595,U_595)),hAPP(hAPP(c_Product__Type_OPair(U_595,U_595),sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)),U_584)),U_599)) ) )
| ~ c_Recdef_Oadm__wf(U_595,U_597,U_599,U_601) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_588,sK42(U_602,U_600,U_598,U_596))],[f_100_6]) ).
fof(f_100_8,plain,
( ! [U_598,U_587,U_596,U_600,U_602] :
( hAPP(hAPP(U_602,sK40(U_602,U_600,U_598,U_596)),sK42(U_602,U_600,U_598,U_596)) != hAPP(hAPP(U_602,sK41(U_602,U_600,U_598,U_596)),sK42(U_602,U_600,U_598,U_596))
| ~ sP60(U_598,U_587,U_596,U_600,U_602) )
& ! [U_598,U_587,U_596,U_600,U_602] :
( hAPP(sK40(U_602,U_600,U_598,U_596),U_587) = hAPP(sK41(U_602,U_600,U_598,U_596),U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_596,U_596)),hAPP(hAPP(c_Product__Type_OPair(U_596,U_596),U_587),sK42(U_602,U_600,U_598,U_596))),U_600))
| ~ sP60(U_598,U_587,U_596,U_600,U_602) )
& ! [U_584,U_599,U_585,U_586,U_597,U_595,U_601] :
( hAPP(U_586,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)) != hAPP(U_585,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584))
| ~ sP59(U_584,U_599,U_585,U_586,U_597,U_595,U_601) )
& ! [U_584,U_599,U_585,U_586,U_597,U_595,U_601] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_595,U_595)),hAPP(hAPP(c_Product__Type_OPair(U_595,U_595),sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)),U_584)),U_599))
| ~ sP59(U_584,U_599,U_585,U_586,U_597,U_595,U_601) )
& ! [U_598,U_587,U_596,U_600,U_602] :
( c_Recdef_Oadm__wf(U_596,U_598,U_600,U_602)
| sP60(U_598,U_587,U_596,U_600,U_602) )
& ! [U_584,U_599,U_585,U_586,U_597,U_595,U_601] :
( hAPP(hAPP(U_601,U_586),U_584) = hAPP(hAPP(U_601,U_585),U_584)
| sP59(U_584,U_599,U_585,U_586,U_597,U_595,U_601)
| ~ c_Recdef_Oadm__wf(U_595,U_597,U_599,U_601) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59,sP60])],[f_100_7]) ).
cnf(f_100_9,plain,
( hAPP(hAPP(U_601,U_586),U_584) = hAPP(hAPP(U_601,U_585),U_584)
| sP59(U_584,U_599,U_585,U_586,U_597,U_595,U_601)
| ~ c_Recdef_Oadm__wf(U_595,U_597,U_599,U_601) ),
inference(clausify,[status(thm)],[f_100_8]) ).
cnf(f_100_10,plain,
( c_Recdef_Oadm__wf(U_596,U_598,U_600,U_602)
| sP60(U_598,U_587,U_596,U_600,U_602) ),
inference(clausify,[status(thm)],[f_100_8]) ).
cnf(f_100_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_595,U_595)),hAPP(hAPP(c_Product__Type_OPair(U_595,U_595),sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)),U_584)),U_599))
| ~ sP59(U_584,U_599,U_585,U_586,U_597,U_595,U_601) ),
inference(clausify,[status(thm)],[f_100_8]) ).
cnf(f_100_12,plain,
( hAPP(U_586,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584)) != hAPP(U_585,sK39(U_601,U_599,U_597,U_595,U_586,U_585,U_584))
| ~ sP59(U_584,U_599,U_585,U_586,U_597,U_595,U_601) ),
inference(clausify,[status(thm)],[f_100_8]) ).
cnf(f_100_13,plain,
( hAPP(sK40(U_602,U_600,U_598,U_596),U_587) = hAPP(sK41(U_602,U_600,U_598,U_596),U_587)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_596,U_596)),hAPP(hAPP(c_Product__Type_OPair(U_596,U_596),U_587),sK42(U_602,U_600,U_598,U_596))),U_600))
| ~ sP60(U_598,U_587,U_596,U_600,U_602) ),
inference(clausify,[status(thm)],[f_100_8]) ).
cnf(f_100_14,plain,
( hAPP(hAPP(U_602,sK40(U_602,U_600,U_598,U_596)),sK42(U_602,U_600,U_598,U_596)) != hAPP(hAPP(U_602,sK41(U_602,U_600,U_598,U_596)),sK42(U_602,U_600,U_598,U_596))
| ~ sP60(U_598,U_587,U_596,U_600,U_602) ),
inference(clausify,[status(thm)],[f_100_8]) ).
fof(f_101_1,plain,
! [V_f_2,T_b,V_r_2,V_x_2,V_y_2,T_a] :
( ( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2),V_y_2) = c_HOL_Oundefined(T_b)
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) )
& ( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2),V_y_2) = hAPP(V_f_2,V_y_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_cut__def]) ).
fof(f_101_2,plain,
! [U_608,U_607,U_606,U_605,U_604,U_603] :
( ( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_603,U_607),U_608),U_606),U_605),U_604) = c_HOL_Oundefined(U_607)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_603,U_603)),hAPP(hAPP(c_Product__Type_OPair(U_603,U_603),U_604),U_605)),U_606)) )
& ( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_603,U_607),U_608),U_606),U_605),U_604) = hAPP(U_608,U_604)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_603,U_603)),hAPP(hAPP(c_Product__Type_OPair(U_603,U_603),U_604),U_605)),U_606)) ) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
( ! [U_620,U_618,U_616,U_614,U_612,U_610] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_610,U_618),U_620),U_616),U_614),U_612) = c_HOL_Oundefined(U_618)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_610,U_610)),hAPP(hAPP(c_Product__Type_OPair(U_610,U_610),U_612),U_614)),U_616)) )
& ! [U_619,U_617,U_615,U_613,U_611,U_609] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_609,U_617),U_619),U_615),U_613),U_611) = hAPP(U_619,U_611)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_609,U_609)),hAPP(hAPP(c_Product__Type_OPair(U_609,U_609),U_611),U_613)),U_615)) ) ),
inference(miniscope,[status(thm)],[f_101_2]) ).
fof(f_101_4,plain,
( ! [U_610,U_612,U_614,U_616,U_618,U_620] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_610,U_618),U_620),U_616),U_614),U_612) = c_HOL_Oundefined(U_618)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_610,U_610)),hAPP(hAPP(c_Product__Type_OPair(U_610,U_610),U_612),U_614)),U_616)) )
& ! [U_609,U_613,U_611,U_615,U_617,U_619] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_609,U_617),U_619),U_615),U_613),U_611) = hAPP(U_619,U_611)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_609,U_609)),hAPP(hAPP(c_Product__Type_OPair(U_609,U_609),U_611),U_613)),U_615)) ) ),
inference(definitional_conversion,[status(esa)],[f_101_3]) ).
cnf(f_101_5,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_609,U_617),U_619),U_615),U_613),U_611) = hAPP(U_619,U_611)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_609,U_609)),hAPP(hAPP(c_Product__Type_OPair(U_609,U_609),U_611),U_613)),U_615)) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_6,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_610,U_618),U_620),U_616),U_614),U_612) = c_HOL_Oundefined(U_618)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_610,U_610)),hAPP(hAPP(c_Product__Type_OPair(U_610,U_610),U_612),U_614)),U_616)) ),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
! [V_y_2,V_R_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) )
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_a,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(f_102_2,plain,
! [U_624,U_623,U_622,U_621] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_621,U_621)),hAPP(hAPP(c_Product__Type_OPair(U_621,U_621),U_622),U_624)),c_Transitive__Closure_Ortrancl(U_621,U_623)))
| U_622 != U_624 )
& ( U_622 = U_624
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_621,U_621)),hAPP(hAPP(c_Product__Type_OPair(U_621,U_621),U_622),U_624)),c_Transitive__Closure_Ortrancl(U_621,U_623))) ) )
| hBOOL(hAPP(hAPP(c_member(U_621),U_622),c_Relation_ODomain(U_621,U_621,U_623))) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
( ! [U_621,U_622,U_623,U_624] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_621,U_621)),hAPP(hAPP(c_Product__Type_OPair(U_621,U_621),U_622),U_624)),c_Transitive__Closure_Ortrancl(U_621,U_623)))
| U_622 != U_624
| ~ sP61(U_621,U_622,U_623,U_624) )
& ! [U_621,U_622,U_623,U_624] :
( U_622 = U_624
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_621,U_621)),hAPP(hAPP(c_Product__Type_OPair(U_621,U_621),U_622),U_624)),c_Transitive__Closure_Ortrancl(U_621,U_623)))
| ~ sP61(U_621,U_622,U_623,U_624) )
& ! [U_621,U_622,U_623,U_624] :
( sP61(U_621,U_622,U_623,U_624)
| hBOOL(hAPP(hAPP(c_member(U_621),U_622),c_Relation_ODomain(U_621,U_621,U_623))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_102_2]) ).
cnf(f_102_4,plain,
( sP61(U_621,U_622,U_623,U_624)
| hBOOL(hAPP(hAPP(c_member(U_621),U_622),c_Relation_ODomain(U_621,U_621,U_623))) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( U_622 = U_624
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_621,U_621)),hAPP(hAPP(c_Product__Type_OPair(U_621,U_621),U_622),U_624)),c_Transitive__Closure_Ortrancl(U_621,U_623)))
| ~ sP61(U_621,U_622,U_623,U_624) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_621,U_621)),hAPP(hAPP(c_Product__Type_OPair(U_621,U_621),U_622),U_624)),c_Transitive__Closure_Ortrancl(U_621,U_623)))
| U_622 != U_624
| ~ sP61(U_621,U_622,U_623,U_624) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_b,T_a] :
( ? [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))),V_r_2)) )
| hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtranclE2]) ).
fof(f_103_2,plain,
! [U_633,U_632,U_631,U_630,U_629,U_628,U_627] :
( ? [U_626,U_625] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_626),U_625)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_626),U_625))),U_633)) )
| hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630) = hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633))) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_633,U_632,U_631,U_630,U_629,U_628,U_627] :
( ? [U_625] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),U_625)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),U_625))),U_633)) )
| hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630) = hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_626,sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627))],[f_103_2]) ).
fof(f_103_4,plain,
! [U_633,U_632,U_631,U_630,U_629,U_628,U_627] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),sK44(U_633,U_632,U_631,U_630,U_629,U_628,U_627))),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),sK44(U_633,U_632,U_631,U_630,U_629,U_628,U_627)))),U_633)) )
| hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630) = hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_625,sK44(U_633,U_632,U_631,U_630,U_629,U_628,U_627))],[f_103_3]) ).
fof(f_103_5,plain,
( ! [U_627,U_628,U_629,U_630,U_631,U_632,U_633] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),sK44(U_633,U_632,U_631,U_630,U_629,U_628,U_627))),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633)))
| ~ sP62(U_627,U_628,U_629,U_630,U_631,U_632,U_633) )
& ! [U_627,U_628,U_629,U_630,U_631,U_632,U_633] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),sK44(U_633,U_632,U_631,U_630,U_629,U_628,U_627)))),U_633))
| ~ sP62(U_627,U_628,U_629,U_630,U_631,U_632,U_633) )
& ! [U_627,U_628,U_629,U_630,U_631,U_632,U_633] :
( sP62(U_627,U_628,U_629,U_630,U_631,U_632,U_633)
| hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630) = hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_103_4]) ).
cnf(f_103_6,plain,
( sP62(U_627,U_628,U_629,U_630,U_631,U_632,U_633)
| hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630) = hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633))) ),
inference(clausify,[status(thm)],[f_103_5]) ).
cnf(f_103_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_629),U_630)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),sK44(U_633,U_632,U_631,U_630,U_629,U_628,U_627)))),U_633))
| ~ sP62(U_627,U_628,U_629,U_630,U_631,U_632,U_633) ),
inference(clausify,[status(thm)],[f_103_5]) ).
cnf(f_103_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_627,U_628),tc_prod(U_627,U_628))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_627,U_628),tc_prod(U_627,U_628)),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),sK43(U_633,U_632,U_631,U_630,U_629,U_628,U_627)),sK44(U_633,U_632,U_631,U_630,U_629,U_628,U_627))),hAPP(hAPP(c_Product__Type_OPair(U_627,U_628),U_631),U_632))),c_Transitive__Closure_Ortrancl(tc_prod(U_627,U_628),U_633)))
| ~ sP62(U_627,U_628,U_629,U_630,U_631,U_632,U_633) ),
inference(clausify,[status(thm)],[f_103_5]) ).
fof(f_104_1,plain,
! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
| ? [B_a,B_b,B_aa,B_ba] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
& hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct2]) ).
fof(f_104_2,plain,
! [U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638] :
( hBOOL(hAPP(hAPP(U_645,U_640),U_641))
| ? [U_637,U_636,U_635,U_634] :
( ~ hBOOL(hAPP(hAPP(U_645,U_637),U_636))
& hBOOL(hAPP(hAPP(U_645,U_635),U_634))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_635),U_634)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_637),U_636)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_635),U_634))),U_644)) )
| ~ hBOOL(hAPP(hAPP(U_645,U_642),U_643))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_640),U_641)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644))) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638] :
( hBOOL(hAPP(hAPP(U_645,U_640),U_641))
| ? [U_636,U_635,U_634] :
( ~ hBOOL(hAPP(hAPP(U_645,sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),U_636))
& hBOOL(hAPP(hAPP(U_645,U_635),U_634))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_635),U_634)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),U_636)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_635),U_634))),U_644)) )
| ~ hBOOL(hAPP(hAPP(U_645,U_642),U_643))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_640),U_641)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_637,sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))],[f_104_2]) ).
fof(f_104_4,plain,
! [U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638] :
( hBOOL(hAPP(hAPP(U_645,U_640),U_641))
| ? [U_635,U_634] :
( ~ hBOOL(hAPP(hAPP(U_645,sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
& hBOOL(hAPP(hAPP(U_645,U_635),U_634))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_635),U_634)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_635),U_634))),U_644)) )
| ~ hBOOL(hAPP(hAPP(U_645,U_642),U_643))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_640),U_641)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_636,sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))],[f_104_3]) ).
fof(f_104_5,plain,
! [U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638] :
( hBOOL(hAPP(hAPP(U_645,U_640),U_641))
| ? [U_634] :
( ~ hBOOL(hAPP(hAPP(U_645,sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
& hBOOL(hAPP(hAPP(U_645,sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),U_634))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),U_634)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),U_634))),U_644)) )
| ~ hBOOL(hAPP(hAPP(U_645,U_642),U_643))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_640),U_641)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_635,sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))],[f_104_4]) ).
fof(f_104_6,plain,
! [U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638] :
( hBOOL(hAPP(hAPP(U_645,U_640),U_641))
| ( ~ hBOOL(hAPP(hAPP(U_645,sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
& hBOOL(hAPP(hAPP(U_645,sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))),U_644)) )
| ~ hBOOL(hAPP(hAPP(U_645,U_642),U_643))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_640),U_641)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_634,sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))],[f_104_5]) ).
fof(f_104_7,plain,
( ! [U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645] :
( ~ hBOOL(hAPP(hAPP(U_645,sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) )
& ! [U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645] :
( hBOOL(hAPP(hAPP(U_645,sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) )
& ! [U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644)))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) )
& ! [U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))),U_644))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) )
& ! [U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645] :
( hBOOL(hAPP(hAPP(U_645,U_640),U_641))
| sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645)
| ~ hBOOL(hAPP(hAPP(U_645,U_642),U_643))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_640),U_641)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_104_6]) ).
cnf(f_104_8,plain,
( hBOOL(hAPP(hAPP(U_645,U_640),U_641))
| sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645)
| ~ hBOOL(hAPP(hAPP(U_645,U_642),U_643))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_640),U_641)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644))) ),
inference(clausify,[status(thm)],[f_104_7]) ).
cnf(f_104_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))),U_644))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) ),
inference(clausify,[status(thm)],[f_104_7]) ).
cnf(f_104_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_638,U_639),tc_prod(U_638,U_639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_638,U_639),tc_prod(U_638,U_639)),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638))),hAPP(hAPP(c_Product__Type_OPair(U_638,U_639),U_642),U_643))),c_Transitive__Closure_Ortrancl(tc_prod(U_638,U_639),U_644)))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) ),
inference(clausify,[status(thm)],[f_104_7]) ).
cnf(f_104_11,plain,
( hBOOL(hAPP(hAPP(U_645,sK47(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK48(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) ),
inference(clausify,[status(thm)],[f_104_7]) ).
cnf(f_104_12,plain,
( ~ hBOOL(hAPP(hAPP(U_645,sK45(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)),sK46(U_645,U_644,U_643,U_642,U_641,U_640,U_639,U_638)))
| ~ sP63(U_638,U_639,U_640,U_641,U_642,U_643,U_644,U_645) ),
inference(clausify,[status(thm)],[f_104_7]) ).
fof(f_105_1,plain,
! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
( ( hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = c_HOL_Oundefined(T_b)
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
& ( hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = hAPP(V_f_2,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_restrict__def]) ).
fof(f_105_2,plain,
! [U_650,U_649,U_648,U_647,U_646] :
( ( hAPP(c_FuncSet_Orestrict(U_646,U_649,U_650,U_648),U_647) = c_HOL_Oundefined(U_649)
| hBOOL(hAPP(hAPP(c_member(U_646),U_647),U_648)) )
& ( hAPP(c_FuncSet_Orestrict(U_646,U_649,U_650,U_648),U_647) = hAPP(U_650,U_647)
| ~ hBOOL(hAPP(hAPP(c_member(U_646),U_647),U_648)) ) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( ! [U_660,U_658,U_656,U_654,U_652] :
( hAPP(c_FuncSet_Orestrict(U_652,U_658,U_660,U_656),U_654) = c_HOL_Oundefined(U_658)
| hBOOL(hAPP(hAPP(c_member(U_652),U_654),U_656)) )
& ! [U_659,U_657,U_655,U_653,U_651] :
( hAPP(c_FuncSet_Orestrict(U_651,U_657,U_659,U_655),U_653) = hAPP(U_659,U_653)
| ~ hBOOL(hAPP(hAPP(c_member(U_651),U_653),U_655)) ) ),
inference(miniscope,[status(thm)],[f_105_2]) ).
fof(f_105_4,plain,
( ! [U_652,U_654,U_656,U_658,U_660] :
( hAPP(c_FuncSet_Orestrict(U_652,U_658,U_660,U_656),U_654) = c_HOL_Oundefined(U_658)
| hBOOL(hAPP(hAPP(c_member(U_652),U_654),U_656)) )
& ! [U_653,U_655,U_659,U_651,U_657] :
( hAPP(c_FuncSet_Orestrict(U_651,U_657,U_659,U_655),U_653) = hAPP(U_659,U_653)
| ~ hBOOL(hAPP(hAPP(c_member(U_651),U_653),U_655)) ) ),
inference(definitional_conversion,[status(esa)],[f_105_3]) ).
cnf(f_105_5,plain,
( hAPP(c_FuncSet_Orestrict(U_651,U_657,U_659,U_655),U_653) = hAPP(U_659,U_653)
| ~ hBOOL(hAPP(hAPP(c_member(U_651),U_653),U_655)) ),
inference(clausify,[status(thm)],[f_105_4]) ).
cnf(f_105_6,plain,
( hAPP(c_FuncSet_Orestrict(U_652,U_658,U_660,U_656),U_654) = c_HOL_Oundefined(U_658)
| hBOOL(hAPP(hAPP(c_member(U_652),U_654),U_656)) ),
inference(clausify,[status(thm)],[f_105_4]) ).
fof(f_106_1,plain,
! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
( ( hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = c_HOL_Oundefined(T_b)
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
& ( hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = hAPP(V_f_2,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_restrict__apply]) ).
fof(f_106_2,plain,
! [U_665,U_664,U_663,U_662,U_661] :
( ( hAPP(c_FuncSet_Orestrict(U_661,U_664,U_665,U_663),U_662) = c_HOL_Oundefined(U_664)
| hBOOL(hAPP(hAPP(c_member(U_661),U_662),U_663)) )
& ( hAPP(c_FuncSet_Orestrict(U_661,U_664,U_665,U_663),U_662) = hAPP(U_665,U_662)
| ~ hBOOL(hAPP(hAPP(c_member(U_661),U_662),U_663)) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_675,U_673,U_671,U_669,U_667] :
( hAPP(c_FuncSet_Orestrict(U_667,U_673,U_675,U_671),U_669) = c_HOL_Oundefined(U_673)
| hBOOL(hAPP(hAPP(c_member(U_667),U_669),U_671)) )
& ! [U_674,U_672,U_670,U_668,U_666] :
( hAPP(c_FuncSet_Orestrict(U_666,U_672,U_674,U_670),U_668) = hAPP(U_674,U_668)
| ~ hBOOL(hAPP(hAPP(c_member(U_666),U_668),U_670)) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
( ! [U_667,U_671,U_673,U_669,U_675] :
( hAPP(c_FuncSet_Orestrict(U_667,U_673,U_675,U_671),U_669) = c_HOL_Oundefined(U_673)
| hBOOL(hAPP(hAPP(c_member(U_667),U_669),U_671)) )
& ! [U_666,U_668,U_674,U_670,U_672] :
( hAPP(c_FuncSet_Orestrict(U_666,U_672,U_674,U_670),U_668) = hAPP(U_674,U_668)
| ~ hBOOL(hAPP(hAPP(c_member(U_666),U_668),U_670)) ) ),
inference(definitional_conversion,[status(esa)],[f_106_3]) ).
cnf(f_106_5,plain,
( hAPP(c_FuncSet_Orestrict(U_666,U_672,U_674,U_670),U_668) = hAPP(U_674,U_668)
| ~ hBOOL(hAPP(hAPP(c_member(U_666),U_668),U_670)) ),
inference(clausify,[status(thm)],[f_106_4]) ).
cnf(f_106_6,plain,
( hAPP(c_FuncSet_Orestrict(U_667,U_673,U_675,U_671),U_669) = c_HOL_Oundefined(U_673)
| hBOOL(hAPP(hAPP(c_member(U_667),U_669),U_671)) ),
inference(clausify,[status(thm)],[f_106_4]) ).
fof(f_107_1,plain,
! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
( hAPP(V_f_2,V_x_2) = c_HOL_Oundefined(T_b)
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_extensional__arb]) ).
fof(f_107_2,plain,
! [U_680,U_679,U_678,U_677,U_676] :
( hAPP(U_678,U_680) = c_HOL_Oundefined(U_677)
| hBOOL(hAPP(hAPP(c_member(U_676),U_680),U_679))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_676,U_677)),U_678),c_FuncSet_Oextensional(U_676,U_677,U_679))) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_676,U_677,U_678,U_679,U_680] :
( hAPP(U_678,U_680) = c_HOL_Oundefined(U_677)
| hBOOL(hAPP(hAPP(c_member(U_676),U_680),U_679))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_676,U_677)),U_678),c_FuncSet_Oextensional(U_676,U_677,U_679))) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( hAPP(U_678,U_680) = c_HOL_Oundefined(U_677)
| hBOOL(hAPP(hAPP(c_member(U_676),U_680),U_679))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_676,U_677)),U_678),c_FuncSet_Oextensional(U_676,U_677,U_679))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_DomainI]) ).
fof(f_108_2,plain,
! [U_685,U_684,U_683,U_682,U_681] :
( hBOOL(hAPP(hAPP(c_member(U_681),U_683),c_Relation_ODomain(U_681,U_682,U_685)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_681,U_682)),hAPP(hAPP(c_Product__Type_OPair(U_681,U_682),U_683),U_684)),U_685)) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_681,U_682,U_683,U_684,U_685] :
( hBOOL(hAPP(hAPP(c_member(U_681),U_683),c_Relation_ODomain(U_681,U_682,U_685)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_681,U_682)),hAPP(hAPP(c_Product__Type_OPair(U_681,U_682),U_683),U_684)),U_685)) ),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_681),U_683),c_Relation_ODomain(U_681,U_682,U_685)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_681,U_682)),hAPP(hAPP(c_Product__Type_OPair(U_681,U_682),U_683),U_684)),U_685)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [V_r_2,T_b,V_aa_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2)))
| ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2)) )
& ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Domain__iff]) ).
fof(f_109_2,plain,
! [U_691,U_690,U_689,U_688] :
( ( hBOOL(hAPP(hAPP(c_member(U_688),U_689),c_Relation_ODomain(U_688,U_690,U_691)))
| ! [U_687] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_688,U_690)),hAPP(hAPP(c_Product__Type_OPair(U_688,U_690),U_689),U_687)),U_691)) )
& ( ? [U_686] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_688,U_690)),hAPP(hAPP(c_Product__Type_OPair(U_688,U_690),U_689),U_686)),U_691))
| ~ hBOOL(hAPP(hAPP(c_member(U_688),U_689),c_Relation_ODomain(U_688,U_690,U_691))) ) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_699,U_697,U_695,U_693] :
( hBOOL(hAPP(hAPP(c_member(U_693),U_695),c_Relation_ODomain(U_693,U_697,U_699)))
| ! [U_687] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_693,U_697)),hAPP(hAPP(c_Product__Type_OPair(U_693,U_697),U_695),U_687)),U_699)) )
& ! [U_698,U_696,U_694,U_692] :
( ? [U_686] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_692,U_696)),hAPP(hAPP(c_Product__Type_OPair(U_692,U_696),U_694),U_686)),U_698))
| ~ hBOOL(hAPP(hAPP(c_member(U_692),U_694),c_Relation_ODomain(U_692,U_696,U_698))) ) ),
inference(miniscope,[status(thm)],[f_109_2]) ).
fof(f_109_4,plain,
( ! [U_699,U_697,U_695,U_693] :
( hBOOL(hAPP(hAPP(c_member(U_693),U_695),c_Relation_ODomain(U_693,U_697,U_699)))
| ! [U_687] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_693,U_697)),hAPP(hAPP(c_Product__Type_OPair(U_693,U_697),U_695),U_687)),U_699)) )
& ! [U_698,U_696,U_694,U_692] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_692,U_696)),hAPP(hAPP(c_Product__Type_OPair(U_692,U_696),U_694),sK49(U_698,U_696,U_694,U_692))),U_698))
| ~ hBOOL(hAPP(hAPP(c_member(U_692),U_694),c_Relation_ODomain(U_692,U_696,U_698))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_686,sK49(U_698,U_696,U_694,U_692))],[f_109_3]) ).
fof(f_109_5,plain,
( ! [U_687,U_693,U_695,U_697,U_699] :
( hBOOL(hAPP(hAPP(c_member(U_693),U_695),c_Relation_ODomain(U_693,U_697,U_699)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_693,U_697)),hAPP(hAPP(c_Product__Type_OPair(U_693,U_697),U_695),U_687)),U_699)) )
& ! [U_694,U_696,U_692,U_698] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_692,U_696)),hAPP(hAPP(c_Product__Type_OPair(U_692,U_696),U_694),sK49(U_698,U_696,U_694,U_692))),U_698))
| ~ hBOOL(hAPP(hAPP(c_member(U_692),U_694),c_Relation_ODomain(U_692,U_696,U_698))) ) ),
inference(definitional_conversion,[status(esa)],[f_109_4]) ).
cnf(f_109_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_692,U_696)),hAPP(hAPP(c_Product__Type_OPair(U_692,U_696),U_694),sK49(U_698,U_696,U_694,U_692))),U_698))
| ~ hBOOL(hAPP(hAPP(c_member(U_692),U_694),c_Relation_ODomain(U_692,U_696,U_698))) ),
inference(clausify,[status(thm)],[f_109_5]) ).
cnf(f_109_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_693),U_695),c_Relation_ODomain(U_693,U_697,U_699)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_693,U_697)),hAPP(hAPP(c_Product__Type_OPair(U_693,U_697),U_695),U_687)),U_699)) ),
inference(clausify,[status(thm)],[f_109_5]) ).
fof(f_110_1,plain,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
( V_y_2 = V_z_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2))
| ~ c_Relation_Osingle__valued(T_a,T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valuedD]) ).
fof(f_110_2,plain,
! [U_705,U_704,U_703,U_702,U_701,U_700] :
( U_704 = U_705
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_700,U_701)),hAPP(hAPP(c_Product__Type_OPair(U_700,U_701),U_703),U_705)),U_702))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_700,U_701)),hAPP(hAPP(c_Product__Type_OPair(U_700,U_701),U_703),U_704)),U_702))
| ~ c_Relation_Osingle__valued(U_700,U_701,U_702) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_702,U_700,U_701,U_703,U_704,U_705] :
( U_704 = U_705
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_700,U_701)),hAPP(hAPP(c_Product__Type_OPair(U_700,U_701),U_703),U_705)),U_702))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_700,U_701)),hAPP(hAPP(c_Product__Type_OPair(U_700,U_701),U_703),U_704)),U_702))
| ~ c_Relation_Osingle__valued(U_700,U_701,U_702) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( U_704 = U_705
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_700,U_701)),hAPP(hAPP(c_Product__Type_OPair(U_700,U_701),U_703),U_705)),U_702))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_700,U_701)),hAPP(hAPP(c_Product__Type_OPair(U_700,U_701),U_703),U_704)),U_702))
| ~ c_Relation_Osingle__valued(U_700,U_701,U_702) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [V_r_2,T_b,T_a] :
( ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
| ? [B_x,B_y] :
( ? [B_z] :
( B_y != B_z
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) )
| ~ c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__def]) ).
fof(f_111_2,plain,
! [U_714,U_713,U_712] :
( ( c_Relation_Osingle__valued(U_712,U_713,U_714)
| ? [U_711,U_710] :
( ? [U_709] :
( U_710 != U_709
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_712,U_713)),hAPP(hAPP(c_Product__Type_OPair(U_712,U_713),U_711),U_709)),U_714)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_712,U_713)),hAPP(hAPP(c_Product__Type_OPair(U_712,U_713),U_711),U_710)),U_714)) ) )
& ( ! [U_708,U_707] :
( ! [U_706] :
( U_707 = U_706
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_712,U_713)),hAPP(hAPP(c_Product__Type_OPair(U_712,U_713),U_708),U_706)),U_714)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_712,U_713)),hAPP(hAPP(c_Product__Type_OPair(U_712,U_713),U_708),U_707)),U_714)) )
| ~ c_Relation_Osingle__valued(U_712,U_713,U_714) ) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
( ! [U_720,U_718,U_716] :
( c_Relation_Osingle__valued(U_716,U_718,U_720)
| ? [U_711,U_710] :
( ? [U_709] :
( U_710 != U_709
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),U_711),U_709)),U_720)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),U_711),U_710)),U_720)) ) )
& ! [U_719,U_717,U_715] :
( ! [U_708,U_707] :
( ! [U_706] :
( U_707 = U_706
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_706)),U_719)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_707)),U_719)) )
| ~ c_Relation_Osingle__valued(U_715,U_717,U_719) ) ),
inference(miniscope,[status(thm)],[f_111_2]) ).
fof(f_111_4,plain,
( ! [U_720,U_718,U_716] :
( c_Relation_Osingle__valued(U_716,U_718,U_720)
| ? [U_710] :
( ? [U_709] :
( U_710 != U_709
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),U_709)),U_720)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),U_710)),U_720)) ) )
& ! [U_719,U_717,U_715] :
( ! [U_708,U_707] :
( ! [U_706] :
( U_707 = U_706
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_706)),U_719)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_707)),U_719)) )
| ~ c_Relation_Osingle__valued(U_715,U_717,U_719) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_711,sK50(U_720,U_718,U_716))],[f_111_3]) ).
fof(f_111_5,plain,
( ! [U_720,U_718,U_716] :
( c_Relation_Osingle__valued(U_716,U_718,U_720)
| ( ? [U_709] :
( sK51(U_720,U_718,U_716) != U_709
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),U_709)),U_720)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),sK51(U_720,U_718,U_716))),U_720)) ) )
& ! [U_719,U_717,U_715] :
( ! [U_708,U_707] :
( ! [U_706] :
( U_707 = U_706
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_706)),U_719)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_707)),U_719)) )
| ~ c_Relation_Osingle__valued(U_715,U_717,U_719) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_710,sK51(U_720,U_718,U_716))],[f_111_4]) ).
fof(f_111_6,plain,
( ! [U_720,U_718,U_716] :
( c_Relation_Osingle__valued(U_716,U_718,U_720)
| ( sK51(U_720,U_718,U_716) != sK52(U_720,U_718,U_716)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),sK52(U_720,U_718,U_716))),U_720))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),sK51(U_720,U_718,U_716))),U_720)) ) )
& ! [U_719,U_717,U_715] :
( ! [U_708,U_707] :
( ! [U_706] :
( U_707 = U_706
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_706)),U_719)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_707)),U_719)) )
| ~ c_Relation_Osingle__valued(U_715,U_717,U_719) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_709,sK52(U_720,U_718,U_716))],[f_111_5]) ).
fof(f_111_7,plain,
( ! [U_718,U_716,U_720] :
( sK51(U_720,U_718,U_716) != sK52(U_720,U_718,U_716)
| ~ sP64(U_718,U_716,U_720) )
& ! [U_718,U_716,U_720] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),sK52(U_720,U_718,U_716))),U_720))
| ~ sP64(U_718,U_716,U_720) )
& ! [U_718,U_716,U_720] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),sK51(U_720,U_718,U_716))),U_720))
| ~ sP64(U_718,U_716,U_720) )
& ! [U_718,U_716,U_720] :
( c_Relation_Osingle__valued(U_716,U_718,U_720)
| sP64(U_718,U_716,U_720) )
& ! [U_719,U_707,U_706,U_717,U_708,U_715] :
( U_707 = U_706
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_706)),U_719))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_707)),U_719))
| ~ c_Relation_Osingle__valued(U_715,U_717,U_719) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_111_6]) ).
cnf(f_111_8,plain,
( U_707 = U_706
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_706)),U_719))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_715,U_717)),hAPP(hAPP(c_Product__Type_OPair(U_715,U_717),U_708),U_707)),U_719))
| ~ c_Relation_Osingle__valued(U_715,U_717,U_719) ),
inference(clausify,[status(thm)],[f_111_7]) ).
cnf(f_111_9,plain,
( c_Relation_Osingle__valued(U_716,U_718,U_720)
| sP64(U_718,U_716,U_720) ),
inference(clausify,[status(thm)],[f_111_7]) ).
cnf(f_111_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),sK51(U_720,U_718,U_716))),U_720))
| ~ sP64(U_718,U_716,U_720) ),
inference(clausify,[status(thm)],[f_111_7]) ).
cnf(f_111_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_716,U_718)),hAPP(hAPP(c_Product__Type_OPair(U_716,U_718),sK50(U_720,U_718,U_716)),sK52(U_720,U_718,U_716))),U_720))
| ~ sP64(U_718,U_716,U_720) ),
inference(clausify,[status(thm)],[f_111_7]) ).
cnf(f_111_12,plain,
( sK51(U_720,U_718,U_716) != sK52(U_720,U_718,U_716)
| ~ sP64(U_718,U_716,U_720) ),
inference(clausify,[status(thm)],[f_111_7]) ).
fof(f_112_1,plain,
! [V_x_2,V_r_2,T_b,T_a] :
( ( c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_b,V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_b,V_r_2)))
| ~ c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2) ) ),
inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq]) ).
fof(f_112_2,plain,
! [U_724,U_723,U_722,U_721] :
( ( c_Predicate_ODomainP(U_721,U_722,hAPP(hAPP(c_COMBC(U_721,tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_fun(U_722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_722,tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_fun(U_722,tc_HOL_Obool)),U_721),c_COMBC(U_722,tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_722,tc_prod(U_721,U_722)),tc_fun(U_722,tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool)),U_721),hAPP(c_COMBB(tc_prod(U_721,U_722),tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool),U_722),c_member(tc_prod(U_721,U_722)))),c_Product__Type_OPair(U_721,U_722)))),U_723),U_724)
| ~ hBOOL(hAPP(hAPP(c_member(U_721),U_724),c_Relation_ODomain(U_721,U_722,U_723))) )
& ( hBOOL(hAPP(hAPP(c_member(U_721),U_724),c_Relation_ODomain(U_721,U_722,U_723)))
| ~ c_Predicate_ODomainP(U_721,U_722,hAPP(hAPP(c_COMBC(U_721,tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_fun(U_722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_722,tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_fun(U_722,tc_HOL_Obool)),U_721),c_COMBC(U_722,tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_722,tc_prod(U_721,U_722)),tc_fun(U_722,tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool)),U_721),hAPP(c_COMBB(tc_prod(U_721,U_722),tc_fun(tc_fun(tc_prod(U_721,U_722),tc_HOL_Obool),tc_HOL_Obool),U_722),c_member(tc_prod(U_721,U_722)))),c_Product__Type_OPair(U_721,U_722)))),U_723),U_724) ) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
( ! [U_732,U_730,U_728,U_726] :
( c_Predicate_ODomainP(U_726,U_728,hAPP(hAPP(c_COMBC(U_726,tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_fun(U_728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_728,tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_fun(U_728,tc_HOL_Obool)),U_726),c_COMBC(U_728,tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_728,tc_prod(U_726,U_728)),tc_fun(U_728,tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),U_726),hAPP(c_COMBB(tc_prod(U_726,U_728),tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool),U_728),c_member(tc_prod(U_726,U_728)))),c_Product__Type_OPair(U_726,U_728)))),U_730),U_732)
| ~ hBOOL(hAPP(hAPP(c_member(U_726),U_732),c_Relation_ODomain(U_726,U_728,U_730))) )
& ! [U_731,U_729,U_727,U_725] :
( hBOOL(hAPP(hAPP(c_member(U_725),U_731),c_Relation_ODomain(U_725,U_727,U_729)))
| ~ c_Predicate_ODomainP(U_725,U_727,hAPP(hAPP(c_COMBC(U_725,tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_fun(U_727,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_727,tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_fun(U_727,tc_HOL_Obool)),U_725),c_COMBC(U_727,tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_727,tc_prod(U_725,U_727)),tc_fun(U_727,tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),U_725),hAPP(c_COMBB(tc_prod(U_725,U_727),tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool),U_727),c_member(tc_prod(U_725,U_727)))),c_Product__Type_OPair(U_725,U_727)))),U_729),U_731) ) ),
inference(miniscope,[status(thm)],[f_112_2]) ).
fof(f_112_4,plain,
( ! [U_726,U_728,U_732,U_730] :
( c_Predicate_ODomainP(U_726,U_728,hAPP(hAPP(c_COMBC(U_726,tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_fun(U_728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_728,tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_fun(U_728,tc_HOL_Obool)),U_726),c_COMBC(U_728,tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_728,tc_prod(U_726,U_728)),tc_fun(U_728,tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),U_726),hAPP(c_COMBB(tc_prod(U_726,U_728),tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool),U_728),c_member(tc_prod(U_726,U_728)))),c_Product__Type_OPair(U_726,U_728)))),U_730),U_732)
| ~ hBOOL(hAPP(hAPP(c_member(U_726),U_732),c_Relation_ODomain(U_726,U_728,U_730))) )
& ! [U_731,U_725,U_729,U_727] :
( hBOOL(hAPP(hAPP(c_member(U_725),U_731),c_Relation_ODomain(U_725,U_727,U_729)))
| ~ c_Predicate_ODomainP(U_725,U_727,hAPP(hAPP(c_COMBC(U_725,tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_fun(U_727,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_727,tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_fun(U_727,tc_HOL_Obool)),U_725),c_COMBC(U_727,tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_727,tc_prod(U_725,U_727)),tc_fun(U_727,tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),U_725),hAPP(c_COMBB(tc_prod(U_725,U_727),tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool),U_727),c_member(tc_prod(U_725,U_727)))),c_Product__Type_OPair(U_725,U_727)))),U_729),U_731) ) ),
inference(definitional_conversion,[status(esa)],[f_112_3]) ).
cnf(f_112_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_725),U_731),c_Relation_ODomain(U_725,U_727,U_729)))
| ~ c_Predicate_ODomainP(U_725,U_727,hAPP(hAPP(c_COMBC(U_725,tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_fun(U_727,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_727,tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_fun(U_727,tc_HOL_Obool)),U_725),c_COMBC(U_727,tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_727,tc_prod(U_725,U_727)),tc_fun(U_727,tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool)),U_725),hAPP(c_COMBB(tc_prod(U_725,U_727),tc_fun(tc_fun(tc_prod(U_725,U_727),tc_HOL_Obool),tc_HOL_Obool),U_727),c_member(tc_prod(U_725,U_727)))),c_Product__Type_OPair(U_725,U_727)))),U_729),U_731) ),
inference(clausify,[status(thm)],[f_112_4]) ).
cnf(f_112_6,plain,
( c_Predicate_ODomainP(U_726,U_728,hAPP(hAPP(c_COMBC(U_726,tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_fun(U_728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_728,tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_fun(U_728,tc_HOL_Obool)),U_726),c_COMBC(U_728,tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_728,tc_prod(U_726,U_728)),tc_fun(U_728,tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool)),U_726),hAPP(c_COMBB(tc_prod(U_726,U_728),tc_fun(tc_fun(tc_prod(U_726,U_728),tc_HOL_Obool),tc_HOL_Obool),U_728),c_member(tc_prod(U_726,U_728)))),c_Product__Type_OPair(U_726,U_728)))),U_730),U_732)
| ~ hBOOL(hAPP(hAPP(c_member(U_726),U_732),c_Relation_ODomain(U_726,U_728,U_730))) ),
inference(clausify,[status(thm)],[f_112_4]) ).
fof(f_113_1,plain,
! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
| ? [B_a,B_b] :
( ? [B_aa,B_ba] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
& hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) )
| ~ hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2]) ).
fof(f_113_2,plain,
! [U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737] :
( hBOOL(hAPP(hAPP(U_744,U_741),U_742))
| ? [U_736,U_735] :
( ? [U_734,U_733] :
( ~ hBOOL(hAPP(hAPP(U_744,U_734),U_733))
& hBOOL(hAPP(hAPP(U_744,U_736),U_735))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_736),U_735)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_734),U_733))),U_743)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_736),U_735))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) )
| ~ hBOOL(hAPP(hAPP(U_744,U_739),U_740))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_741),U_742))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737] :
( hBOOL(hAPP(hAPP(U_744,U_741),U_742))
| ? [U_735] :
( ? [U_734,U_733] :
( ~ hBOOL(hAPP(hAPP(U_744,U_734),U_733))
& hBOOL(hAPP(hAPP(U_744,sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),U_735))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),U_735)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_734),U_733))),U_743)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),U_735))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) )
| ~ hBOOL(hAPP(hAPP(U_744,U_739),U_740))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_741),U_742))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_736,sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))],[f_113_2]) ).
fof(f_113_4,plain,
! [U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737] :
( hBOOL(hAPP(hAPP(U_744,U_741),U_742))
| ( ? [U_734,U_733] :
( ~ hBOOL(hAPP(hAPP(U_744,U_734),U_733))
& hBOOL(hAPP(hAPP(U_744,sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_734),U_733))),U_743)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) )
| ~ hBOOL(hAPP(hAPP(U_744,U_739),U_740))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_741),U_742))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_735,sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))],[f_113_3]) ).
fof(f_113_5,plain,
! [U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737] :
( hBOOL(hAPP(hAPP(U_744,U_741),U_742))
| ( ? [U_733] :
( ~ hBOOL(hAPP(hAPP(U_744,sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),U_733))
& hBOOL(hAPP(hAPP(U_744,sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),U_733))),U_743)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) )
| ~ hBOOL(hAPP(hAPP(U_744,U_739),U_740))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_741),U_742))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_734,sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))],[f_113_4]) ).
fof(f_113_6,plain,
! [U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737] :
( hBOOL(hAPP(hAPP(U_744,U_741),U_742))
| ( ~ hBOOL(hAPP(hAPP(U_744,sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK56(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
& hBOOL(hAPP(hAPP(U_744,sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK56(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),U_743))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) )
| ~ hBOOL(hAPP(hAPP(U_744,U_739),U_740))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_741),U_742))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_733,sK56(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))],[f_113_5]) ).
fof(f_113_7,plain,
( ! [U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744] :
( ~ hBOOL(hAPP(hAPP(U_744,sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK56(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) )
& ! [U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744] :
( hBOOL(hAPP(hAPP(U_744,sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) )
& ! [U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK56(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),U_743))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) )
& ! [U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743)))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) )
& ! [U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744] :
( hBOOL(hAPP(hAPP(U_744,U_741),U_742))
| sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744)
| ~ hBOOL(hAPP(hAPP(U_744,U_739),U_740))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_741),U_742))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_113_6]) ).
cnf(f_113_8,plain,
( hBOOL(hAPP(hAPP(U_744,U_741),U_742))
| sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744)
| ~ hBOOL(hAPP(hAPP(U_744,U_739),U_740))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_741),U_742))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743))) ),
inference(clausify,[status(thm)],[f_113_7]) ).
cnf(f_113_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),U_739),U_740)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),c_Transitive__Closure_Ortrancl(tc_prod(U_737,U_738),U_743)))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) ),
inference(clausify,[status(thm)],[f_113_7]) ).
cnf(f_113_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_737,U_738),tc_prod(U_737,U_738))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_737,U_738),tc_prod(U_737,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737))),hAPP(hAPP(c_Product__Type_OPair(U_737,U_738),sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK56(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))),U_743))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) ),
inference(clausify,[status(thm)],[f_113_7]) ).
cnf(f_113_11,plain,
( hBOOL(hAPP(hAPP(U_744,sK53(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK54(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) ),
inference(clausify,[status(thm)],[f_113_7]) ).
cnf(f_113_12,plain,
( ~ hBOOL(hAPP(hAPP(U_744,sK55(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)),sK56(U_744,U_743,U_742,U_741,U_740,U_739,U_738,U_737)))
| ~ sP65(U_737,U_738,U_739,U_740,U_741,U_742,U_743,U_744) ),
inference(clausify,[status(thm)],[f_113_7]) ).
fof(f_114_1,plain,
! [V_x_2,V_T_2,V_S_2,V_f_2,T_b,T_a] :
( hAPP(V_f_2,V_x_2) = c_HOL_Oundefined(T_b)
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2))) ),
inference(fof_nnf,[status(thm)],[fact_extensional__funcset__arb]) ).
fof(f_114_2,plain,
! [U_750,U_749,U_748,U_747,U_746,U_745] :
( hAPP(U_747,U_750) = c_HOL_Oundefined(U_746)
| hBOOL(hAPP(hAPP(c_member(U_745),U_750),U_748))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_745,U_746)),U_747),c_FuncSet_Oextensional__funcset(U_745,U_746,U_748,U_749))) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_750,U_747,U_749,U_745,U_746,U_748] :
( hAPP(U_747,U_750) = c_HOL_Oundefined(U_746)
| hBOOL(hAPP(hAPP(c_member(U_745),U_750),U_748))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_745,U_746)),U_747),c_FuncSet_Oextensional__funcset(U_745,U_746,U_748,U_749))) ),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
( hAPP(U_747,U_750) = c_HOL_Oundefined(U_746)
| hBOOL(hAPP(hAPP(c_member(U_745),U_750),U_748))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_745,U_746)),U_747),c_FuncSet_Oextensional__funcset(U_745,U_746,U_748,U_749))) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [T_b,T_a,V_ba_2,V_aa_2,V_r_2] :
( c_Predicate_ODomainP(T_a,T_b,V_r_2,V_aa_2)
| ~ hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros]) ).
fof(f_115_2,plain,
! [U_755,U_754,U_753,U_752,U_751] :
( c_Predicate_ODomainP(U_754,U_755,U_751,U_752)
| ~ hBOOL(hAPP(hAPP(U_751,U_752),U_753)) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_751,U_752,U_753,U_754,U_755] :
( c_Predicate_ODomainP(U_754,U_755,U_751,U_752)
| ~ hBOOL(hAPP(hAPP(U_751,U_752),U_753)) ),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
( c_Predicate_ODomainP(U_754,U_755,U_751,U_752)
| ~ hBOOL(hAPP(hAPP(U_751,U_752),U_753)) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [V_x_2,V_T_2,V_S_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_T_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2))) ),
inference(fof_nnf,[status(thm)],[fact_extensional__funcset__mem]) ).
fof(f_116_2,plain,
! [U_761,U_760,U_759,U_758,U_757,U_756] :
( hBOOL(hAPP(hAPP(c_member(U_757),hAPP(U_758,U_761)),U_760))
| ~ hBOOL(hAPP(hAPP(c_member(U_756),U_761),U_759))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_756,U_757)),U_758),c_FuncSet_Oextensional__funcset(U_756,U_757,U_759,U_760))) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_756,U_757,U_758,U_759,U_760,U_761] :
( hBOOL(hAPP(hAPP(c_member(U_757),hAPP(U_758,U_761)),U_760))
| ~ hBOOL(hAPP(hAPP(c_member(U_756),U_761),U_759))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_756,U_757)),U_758),c_FuncSet_Oextensional__funcset(U_756,U_757,U_759,U_760))) ),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_757),hAPP(U_758,U_761)),U_760))
| ~ hBOOL(hAPP(hAPP(c_member(U_756),U_761),U_759))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_756,U_757)),U_758),c_FuncSet_Oextensional__funcset(U_756,U_757,U_759,U_760))) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [V_r_2,T_a] :
( ( c_Relation_Oirrefl(T_a,V_r_2)
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
& ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
| ~ c_Relation_Oirrefl(T_a,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_irrefl__def]) ).
fof(f_117_2,plain,
! [U_765,U_764] :
( ( c_Relation_Oirrefl(U_764,U_765)
| ? [U_763] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_764,U_764)),hAPP(hAPP(c_Product__Type_OPair(U_764,U_764),U_763),U_763)),U_765)) )
& ( ! [U_762] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_764,U_764)),hAPP(hAPP(c_Product__Type_OPair(U_764,U_764),U_762),U_762)),U_765))
| ~ c_Relation_Oirrefl(U_764,U_765) ) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_769,U_767] :
( c_Relation_Oirrefl(U_767,U_769)
| ? [U_763] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_767,U_767)),hAPP(hAPP(c_Product__Type_OPair(U_767,U_767),U_763),U_763)),U_769)) )
& ! [U_768,U_766] :
( ! [U_762] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_766,U_766)),hAPP(hAPP(c_Product__Type_OPair(U_766,U_766),U_762),U_762)),U_768))
| ~ c_Relation_Oirrefl(U_766,U_768) ) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
fof(f_117_4,plain,
( ! [U_769,U_767] :
( c_Relation_Oirrefl(U_767,U_769)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_767,U_767)),hAPP(hAPP(c_Product__Type_OPair(U_767,U_767),sK57(U_769,U_767)),sK57(U_769,U_767))),U_769)) )
& ! [U_768,U_766] :
( ! [U_762] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_766,U_766)),hAPP(hAPP(c_Product__Type_OPair(U_766,U_766),U_762),U_762)),U_768))
| ~ c_Relation_Oirrefl(U_766,U_768) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_763,sK57(U_769,U_767))],[f_117_3]) ).
fof(f_117_5,plain,
( ! [U_769,U_767] :
( c_Relation_Oirrefl(U_767,U_769)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_767,U_767)),hAPP(hAPP(c_Product__Type_OPair(U_767,U_767),sK57(U_769,U_767)),sK57(U_769,U_767))),U_769)) )
& ! [U_768,U_762,U_766] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_766,U_766)),hAPP(hAPP(c_Product__Type_OPair(U_766,U_766),U_762),U_762)),U_768))
| ~ c_Relation_Oirrefl(U_766,U_768) ) ),
inference(definitional_conversion,[status(esa)],[f_117_4]) ).
cnf(f_117_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_766,U_766)),hAPP(hAPP(c_Product__Type_OPair(U_766,U_766),U_762),U_762)),U_768))
| ~ c_Relation_Oirrefl(U_766,U_768) ),
inference(clausify,[status(thm)],[f_117_5]) ).
cnf(f_117_7,plain,
( c_Relation_Oirrefl(U_767,U_769)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_767,U_767)),hAPP(hAPP(c_Product__Type_OPair(U_767,U_767),sK57(U_769,U_767)),sK57(U_769,U_767))),U_769)) ),
inference(clausify,[status(thm)],[f_117_5]) ).
fof(f_118_1,plain,
! [V_r_2,T_b,V_aa_2,T_a] :
( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_DomainE]) ).
fof(f_118_2,plain,
! [U_774,U_773,U_772,U_771] :
( ? [U_770] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_771,U_773)),hAPP(hAPP(c_Product__Type_OPair(U_771,U_773),U_772),U_770)),U_774))
| ~ hBOOL(hAPP(hAPP(c_member(U_771),U_772),c_Relation_ODomain(U_771,U_773,U_774))) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_774,U_773,U_772,U_771] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_771,U_773)),hAPP(hAPP(c_Product__Type_OPair(U_771,U_773),U_772),sK58(U_774,U_773,U_772,U_771))),U_774))
| ~ hBOOL(hAPP(hAPP(c_member(U_771),U_772),c_Relation_ODomain(U_771,U_773,U_774))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_770,sK58(U_774,U_773,U_772,U_771))],[f_118_2]) ).
fof(f_118_4,plain,
! [U_771,U_772,U_773,U_774] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_771,U_773)),hAPP(hAPP(c_Product__Type_OPair(U_771,U_773),U_772),sK58(U_774,U_773,U_772,U_771))),U_774))
| ~ hBOOL(hAPP(hAPP(c_member(U_771),U_772),c_Relation_ODomain(U_771,U_773,U_774))) ),
inference(definitional_conversion,[status(esa)],[f_118_3]) ).
cnf(f_118_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_771,U_773)),hAPP(hAPP(c_Product__Type_OPair(U_771,U_773),U_772),sK58(U_774,U_773,U_772,U_771))),U_774))
| ~ hBOOL(hAPP(hAPP(c_member(U_771),U_772),c_Relation_ODomain(U_771,U_773,U_774))) ),
inference(clausify,[status(thm)],[f_118_4]) ).
fof(f_119_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Relation_ORange(T_a,T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_RangeI]) ).
fof(f_119_2,plain,
! [U_779,U_778,U_777,U_776,U_775] :
( hBOOL(hAPP(hAPP(c_member(U_776),U_778),c_Relation_ORange(U_775,U_776,U_779)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_775,U_776)),hAPP(hAPP(c_Product__Type_OPair(U_775,U_776),U_777),U_778)),U_779)) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_775,U_776,U_777,U_778,U_779] :
( hBOOL(hAPP(hAPP(c_member(U_776),U_778),c_Relation_ORange(U_775,U_776,U_779)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_775,U_776)),hAPP(hAPP(c_Product__Type_OPair(U_775,U_776),U_777),U_778)),U_779)) ),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_776),U_778),c_Relation_ORange(U_775,U_776,U_779)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_775,U_776)),hAPP(hAPP(c_Product__Type_OPair(U_775,U_776),U_777),U_778)),U_779)) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [V_A_2,V_y_2,V_x_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| V_x_2 != V_y_2 )
& ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
& V_x_2 = V_y_2 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Id__on__iff]) ).
fof(f_120_2,plain,
! [U_783,U_782,U_781,U_780] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_780,U_780)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_780),U_781),U_782)),c_Relation_OId__on(U_780,U_783)))
| ~ hBOOL(hAPP(hAPP(c_member(U_780),U_781),U_783))
| U_781 != U_782 )
& ( ( hBOOL(hAPP(hAPP(c_member(U_780),U_781),U_783))
& U_781 = U_782 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_780,U_780)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_780),U_781),U_782)),c_Relation_OId__on(U_780,U_783))) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_791,U_789,U_787,U_785] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_785,U_785)),hAPP(hAPP(c_Product__Type_OPair(U_785,U_785),U_787),U_789)),c_Relation_OId__on(U_785,U_791)))
| ~ hBOOL(hAPP(hAPP(c_member(U_785),U_787),U_791))
| U_787 != U_789 )
& ! [U_790,U_788,U_786,U_784] :
( ( hBOOL(hAPP(hAPP(c_member(U_784),U_786),U_790))
& U_786 = U_788 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_784,U_784)),hAPP(hAPP(c_Product__Type_OPair(U_784,U_784),U_786),U_788)),c_Relation_OId__on(U_784,U_790))) ) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
fof(f_120_4,plain,
( ! [U_786,U_784,U_790,U_788] :
( hBOOL(hAPP(hAPP(c_member(U_784),U_786),U_790))
| ~ sP66(U_786,U_784,U_790,U_788) )
& ! [U_786,U_784,U_790,U_788] :
( U_786 = U_788
| ~ sP66(U_786,U_784,U_790,U_788) )
& ! [U_789,U_791,U_785,U_787] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_785,U_785)),hAPP(hAPP(c_Product__Type_OPair(U_785,U_785),U_787),U_789)),c_Relation_OId__on(U_785,U_791)))
| ~ hBOOL(hAPP(hAPP(c_member(U_785),U_787),U_791))
| U_787 != U_789 )
& ! [U_786,U_784,U_790,U_788] :
( sP66(U_786,U_784,U_790,U_788)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_784,U_784)),hAPP(hAPP(c_Product__Type_OPair(U_784,U_784),U_786),U_788)),c_Relation_OId__on(U_784,U_790))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_120_3]) ).
cnf(f_120_5,plain,
( sP66(U_786,U_784,U_790,U_788)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_784,U_784)),hAPP(hAPP(c_Product__Type_OPair(U_784,U_784),U_786),U_788)),c_Relation_OId__on(U_784,U_790))) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_785,U_785)),hAPP(hAPP(c_Product__Type_OPair(U_785,U_785),U_787),U_789)),c_Relation_OId__on(U_785,U_791)))
| ~ hBOOL(hAPP(hAPP(c_member(U_785),U_787),U_791))
| U_787 != U_789 ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_7,plain,
( U_786 = U_788
| ~ sP66(U_786,U_784,U_790,U_788) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_784),U_786),U_790))
| ~ sP66(U_786,U_784,U_790,U_788) ),
inference(clausify,[status(thm)],[f_120_4]) ).
fof(f_121_1,plain,
! [V_A_2,T_a,V_ba_2,V_aa_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Relation_OId__on(T_a,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
| V_aa_2 != V_ba_2 ),
inference(fof_nnf,[status(thm)],[fact_Id__on__eqI]) ).
fof(f_121_2,plain,
! [U_795,U_794,U_793,U_792] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_794,U_794)),hAPP(hAPP(c_Product__Type_OPair(U_794,U_794),U_792),U_793)),c_Relation_OId__on(U_794,U_795)))
| ~ hBOOL(hAPP(hAPP(c_member(U_794),U_792),U_795))
| U_792 != U_793 ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_792,U_793,U_794,U_795] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_794,U_794)),hAPP(hAPP(c_Product__Type_OPair(U_794,U_794),U_792),U_793)),c_Relation_OId__on(U_794,U_795)))
| ~ hBOOL(hAPP(hAPP(c_member(U_794),U_792),U_795))
| U_792 != U_793 ),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_794,U_794)),hAPP(hAPP(c_Product__Type_OPair(U_794,U_794),U_792),U_793)),c_Relation_OId__on(U_794,U_795)))
| ~ hBOOL(hAPP(hAPP(c_member(U_794),U_792),U_795))
| U_792 != U_793 ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [V_a2_2,V_a1_2,V_Fa_2,V_R_2,T_b,T_a] :
( ( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2),V_a2_2))
| ! [B_g] :
( ? [B_z] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(B_g,B_z)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_a1_2)),V_R_2)) )
| V_a2_2 != hAPP(hAPP(V_Fa_2,B_g),V_a1_2) ) )
& ( ? [B_g] :
( ! [B_z] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(B_g,B_z)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_a1_2)),V_R_2)) )
& V_a2_2 = hAPP(hAPP(V_Fa_2,B_g),V_a1_2) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2),V_a2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_wfrec__rel_Osimps]) ).
fof(f_122_2,plain,
! [U_805,U_804,U_803,U_802,U_801,U_800] :
( ( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_800,U_801,U_802,U_803,U_804),U_805))
| ! [U_799] :
( ? [U_798] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_800,U_801,U_802,U_803,U_798),hAPP(U_799,U_798)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_800,U_800)),hAPP(hAPP(c_Product__Type_OPair(U_800,U_800),U_798),U_804)),U_802)) )
| U_805 != hAPP(hAPP(U_803,U_799),U_804) ) )
& ( ? [U_797] :
( ! [U_796] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_800,U_801,U_802,U_803,U_796),hAPP(U_797,U_796)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_800,U_800)),hAPP(hAPP(c_Product__Type_OPair(U_800,U_800),U_796),U_804)),U_802)) )
& U_805 = hAPP(hAPP(U_803,U_797),U_804) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_800,U_801,U_802,U_803,U_804),U_805)) ) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_817,U_815,U_813,U_811,U_809,U_807] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,U_815),U_817))
| ! [U_799] :
( ? [U_798] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,U_798),hAPP(U_799,U_798)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_807,U_807)),hAPP(hAPP(c_Product__Type_OPair(U_807,U_807),U_798),U_815)),U_811)) )
| U_817 != hAPP(hAPP(U_813,U_799),U_815) ) )
& ! [U_816,U_814,U_812,U_810,U_808,U_806] :
( ? [U_797] :
( ! [U_796] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_796),hAPP(U_797,U_796)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_806,U_806)),hAPP(hAPP(c_Product__Type_OPair(U_806,U_806),U_796),U_814)),U_810)) )
& U_816 = hAPP(hAPP(U_812,U_797),U_814) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_814),U_816)) ) ),
inference(miniscope,[status(thm)],[f_122_2]) ).
fof(f_122_4,plain,
( ! [U_817,U_815,U_813,U_811,U_809,U_807] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,U_815),U_817))
| ! [U_799] :
( ? [U_798] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,U_798),hAPP(U_799,U_798)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_807,U_807)),hAPP(hAPP(c_Product__Type_OPair(U_807,U_807),U_798),U_815)),U_811)) )
| U_817 != hAPP(hAPP(U_813,U_799),U_815) ) )
& ! [U_816,U_814,U_812,U_810,U_808,U_806] :
( ( ! [U_796] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_796),hAPP(sK59(U_816,U_814,U_812,U_810,U_808,U_806),U_796)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_806,U_806)),hAPP(hAPP(c_Product__Type_OPair(U_806,U_806),U_796),U_814)),U_810)) )
& U_816 = hAPP(hAPP(U_812,sK59(U_816,U_814,U_812,U_810,U_808,U_806)),U_814) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_814),U_816)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_797,sK59(U_816,U_814,U_812,U_810,U_808,U_806))],[f_122_3]) ).
fof(f_122_5,plain,
( ! [U_817,U_815,U_813,U_811,U_809,U_807] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,U_815),U_817))
| ! [U_799] :
( ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799)),hAPP(U_799,sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_807,U_807)),hAPP(hAPP(c_Product__Type_OPair(U_807,U_807),sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799)),U_815)),U_811)) )
| U_817 != hAPP(hAPP(U_813,U_799),U_815) ) )
& ! [U_816,U_814,U_812,U_810,U_808,U_806] :
( ( ! [U_796] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_796),hAPP(sK59(U_816,U_814,U_812,U_810,U_808,U_806),U_796)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_806,U_806)),hAPP(hAPP(c_Product__Type_OPair(U_806,U_806),U_796),U_814)),U_810)) )
& U_816 = hAPP(hAPP(U_812,sK59(U_816,U_814,U_812,U_810,U_808,U_806)),U_814) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_814),U_816)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_798,sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799))],[f_122_4]) ).
fof(f_122_6,plain,
( ! [U_811,U_809,U_817,U_799,U_807,U_813,U_815] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799)),hAPP(U_799,sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799))))
| ~ sP68(U_811,U_809,U_817,U_799,U_807,U_813,U_815) )
& ! [U_811,U_809,U_817,U_799,U_807,U_813,U_815] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_807,U_807)),hAPP(hAPP(c_Product__Type_OPair(U_807,U_807),sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799)),U_815)),U_811))
| ~ sP68(U_811,U_809,U_817,U_799,U_807,U_813,U_815) )
& ! [U_814,U_796,U_806,U_810,U_808,U_812,U_816] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_796),hAPP(sK59(U_816,U_814,U_812,U_810,U_808,U_806),U_796)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_806,U_806)),hAPP(hAPP(c_Product__Type_OPair(U_806,U_806),U_796),U_814)),U_810))
| ~ sP67(U_814,U_796,U_806,U_810,U_808,U_812,U_816) )
& ! [U_814,U_796,U_806,U_810,U_808,U_812,U_816] :
( U_816 = hAPP(hAPP(U_812,sK59(U_816,U_814,U_812,U_810,U_808,U_806)),U_814)
| ~ sP67(U_814,U_796,U_806,U_810,U_808,U_812,U_816) )
& ! [U_811,U_809,U_817,U_799,U_807,U_813,U_815] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,U_815),U_817))
| sP68(U_811,U_809,U_817,U_799,U_807,U_813,U_815)
| U_817 != hAPP(hAPP(U_813,U_799),U_815) )
& ! [U_814,U_796,U_806,U_810,U_808,U_812,U_816] :
( sP67(U_814,U_796,U_806,U_810,U_808,U_812,U_816)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_814),U_816)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67,sP68])],[f_122_5]) ).
cnf(f_122_7,plain,
( sP67(U_814,U_796,U_806,U_810,U_808,U_812,U_816)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_814),U_816)) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_8,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,U_815),U_817))
| sP68(U_811,U_809,U_817,U_799,U_807,U_813,U_815)
| U_817 != hAPP(hAPP(U_813,U_799),U_815) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_9,plain,
( U_816 = hAPP(hAPP(U_812,sK59(U_816,U_814,U_812,U_810,U_808,U_806)),U_814)
| ~ sP67(U_814,U_796,U_806,U_810,U_808,U_812,U_816) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_10,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_806,U_808,U_810,U_812,U_796),hAPP(sK59(U_816,U_814,U_812,U_810,U_808,U_806),U_796)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_806,U_806)),hAPP(hAPP(c_Product__Type_OPair(U_806,U_806),U_796),U_814)),U_810))
| ~ sP67(U_814,U_796,U_806,U_810,U_808,U_812,U_816) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_807,U_807)),hAPP(hAPP(c_Product__Type_OPair(U_807,U_807),sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799)),U_815)),U_811))
| ~ sP68(U_811,U_809,U_817,U_799,U_807,U_813,U_815) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_12,plain,
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_807,U_809,U_811,U_813,sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799)),hAPP(U_799,sK60(U_817,U_815,U_813,U_811,U_809,U_807,U_799))))
| ~ sP68(U_811,U_809,U_817,U_799,U_807,U_813,U_815) ),
inference(clausify,[status(thm)],[f_122_6]) ).
fof(f_123_1,plain,
! [V_g_2,V_Fa_2,T_b,V_R_2,V_x_2,T_a] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2),hAPP(hAPP(V_Fa_2,V_g_2),V_x_2)))
| ? [B_z] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z),hAPP(V_g_2,B_z)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_wfrec__rel_Ointros]) ).
fof(f_123_2,plain,
! [U_824,U_823,U_822,U_821,U_820,U_819] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,U_820),hAPP(hAPP(U_823,U_824),U_820)))
| ? [U_818] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,U_818),hAPP(U_824,U_818)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_819,U_819)),hAPP(hAPP(c_Product__Type_OPair(U_819,U_819),U_818),U_820)),U_821)) ) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_824,U_823,U_822,U_821,U_820,U_819] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,U_820),hAPP(hAPP(U_823,U_824),U_820)))
| ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,sK61(U_824,U_823,U_822,U_821,U_820,U_819)),hAPP(U_824,sK61(U_824,U_823,U_822,U_821,U_820,U_819))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_819,U_819)),hAPP(hAPP(c_Product__Type_OPair(U_819,U_819),sK61(U_824,U_823,U_822,U_821,U_820,U_819)),U_820)),U_821)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_818,sK61(U_824,U_823,U_822,U_821,U_820,U_819))],[f_123_2]) ).
fof(f_123_4,plain,
( ! [U_819,U_821,U_822,U_823,U_820,U_824] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,sK61(U_824,U_823,U_822,U_821,U_820,U_819)),hAPP(U_824,sK61(U_824,U_823,U_822,U_821,U_820,U_819))))
| ~ sP69(U_819,U_821,U_822,U_823,U_820,U_824) )
& ! [U_819,U_821,U_822,U_823,U_820,U_824] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_819,U_819)),hAPP(hAPP(c_Product__Type_OPair(U_819,U_819),sK61(U_824,U_823,U_822,U_821,U_820,U_819)),U_820)),U_821))
| ~ sP69(U_819,U_821,U_822,U_823,U_820,U_824) )
& ! [U_819,U_821,U_822,U_823,U_820,U_824] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,U_820),hAPP(hAPP(U_823,U_824),U_820)))
| sP69(U_819,U_821,U_822,U_823,U_820,U_824) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_123_3]) ).
cnf(f_123_5,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,U_820),hAPP(hAPP(U_823,U_824),U_820)))
| sP69(U_819,U_821,U_822,U_823,U_820,U_824) ),
inference(clausify,[status(thm)],[f_123_4]) ).
cnf(f_123_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_819,U_819)),hAPP(hAPP(c_Product__Type_OPair(U_819,U_819),sK61(U_824,U_823,U_822,U_821,U_820,U_819)),U_820)),U_821))
| ~ sP69(U_819,U_821,U_822,U_823,U_820,U_824) ),
inference(clausify,[status(thm)],[f_123_4]) ).
cnf(f_123_7,plain,
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_819,U_822,U_821,U_823,sK61(U_824,U_823,U_822,U_821,U_820,U_819)),hAPP(U_824,sK61(U_824,U_823,U_822,U_821,U_820,U_819))))
| ~ sP69(U_819,U_821,U_822,U_823,U_820,U_824) ),
inference(clausify,[status(thm)],[f_123_4]) ).
fof(f_124_1,plain,
! [V_A_2,T_a] : c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Range__Id__on]) ).
fof(f_124_2,plain,
! [U_826,U_825] : c_Relation_ORange(U_825,U_825,c_Relation_OId__on(U_825,U_826)) = U_826,
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_825,U_826] : c_Relation_ORange(U_825,U_825,c_Relation_OId__on(U_825,U_826)) = U_826,
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
c_Relation_ORange(U_825,U_825,c_Relation_OId__on(U_825,U_826)) = U_826,
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [V_A_2,T_a] : c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Domain__Id__on]) ).
fof(f_125_2,plain,
! [U_828,U_827] : c_Relation_ODomain(U_827,U_827,c_Relation_OId__on(U_827,U_828)) = U_828,
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_828,U_827] : c_Relation_ODomain(U_827,U_827,c_Relation_OId__on(U_827,U_828)) = U_828,
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
c_Relation_ODomain(U_827,U_827,c_Relation_OId__on(U_827,U_828)) = U_828,
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_single__valued__Id__on]) ).
fof(f_126_2,plain,
! [U_830,U_829] : c_Relation_Osingle__valued(U_829,U_829,c_Relation_OId__on(U_829,U_830)),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_830,U_829] : c_Relation_Osingle__valued(U_829,U_829,c_Relation_OId__on(U_829,U_830)),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
c_Relation_Osingle__valued(U_829,U_829,c_Relation_OId__on(U_829,U_830)),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [V_r_2,T_b,V_aa_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ORange(T_b,T_a,V_r_2)))
| ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_aa_2)),V_r_2)) )
& ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_aa_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ORange(T_b,T_a,V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Range__iff]) ).
fof(f_127_2,plain,
! [U_836,U_835,U_834,U_833] :
( ( hBOOL(hAPP(hAPP(c_member(U_833),U_834),c_Relation_ORange(U_835,U_833,U_836)))
| ! [U_832] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_835,U_833)),hAPP(hAPP(c_Product__Type_OPair(U_835,U_833),U_832),U_834)),U_836)) )
& ( ? [U_831] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_835,U_833)),hAPP(hAPP(c_Product__Type_OPair(U_835,U_833),U_831),U_834)),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(U_833),U_834),c_Relation_ORange(U_835,U_833,U_836))) ) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( ! [U_844,U_842,U_840,U_838] :
( hBOOL(hAPP(hAPP(c_member(U_838),U_840),c_Relation_ORange(U_842,U_838,U_844)))
| ! [U_832] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_842,U_838)),hAPP(hAPP(c_Product__Type_OPair(U_842,U_838),U_832),U_840)),U_844)) )
& ! [U_843,U_841,U_839,U_837] :
( ? [U_831] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_841,U_837)),hAPP(hAPP(c_Product__Type_OPair(U_841,U_837),U_831),U_839)),U_843))
| ~ hBOOL(hAPP(hAPP(c_member(U_837),U_839),c_Relation_ORange(U_841,U_837,U_843))) ) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
fof(f_127_4,plain,
( ! [U_844,U_842,U_840,U_838] :
( hBOOL(hAPP(hAPP(c_member(U_838),U_840),c_Relation_ORange(U_842,U_838,U_844)))
| ! [U_832] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_842,U_838)),hAPP(hAPP(c_Product__Type_OPair(U_842,U_838),U_832),U_840)),U_844)) )
& ! [U_843,U_841,U_839,U_837] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_841,U_837)),hAPP(hAPP(c_Product__Type_OPair(U_841,U_837),sK62(U_843,U_841,U_839,U_837)),U_839)),U_843))
| ~ hBOOL(hAPP(hAPP(c_member(U_837),U_839),c_Relation_ORange(U_841,U_837,U_843))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_831,sK62(U_843,U_841,U_839,U_837))],[f_127_3]) ).
fof(f_127_5,plain,
( ! [U_832,U_838,U_840,U_842,U_844] :
( hBOOL(hAPP(hAPP(c_member(U_838),U_840),c_Relation_ORange(U_842,U_838,U_844)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_842,U_838)),hAPP(hAPP(c_Product__Type_OPair(U_842,U_838),U_832),U_840)),U_844)) )
& ! [U_839,U_843,U_837,U_841] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_841,U_837)),hAPP(hAPP(c_Product__Type_OPair(U_841,U_837),sK62(U_843,U_841,U_839,U_837)),U_839)),U_843))
| ~ hBOOL(hAPP(hAPP(c_member(U_837),U_839),c_Relation_ORange(U_841,U_837,U_843))) ) ),
inference(definitional_conversion,[status(esa)],[f_127_4]) ).
cnf(f_127_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_841,U_837)),hAPP(hAPP(c_Product__Type_OPair(U_841,U_837),sK62(U_843,U_841,U_839,U_837)),U_839)),U_843))
| ~ hBOOL(hAPP(hAPP(c_member(U_837),U_839),c_Relation_ORange(U_841,U_837,U_843))) ),
inference(clausify,[status(thm)],[f_127_5]) ).
cnf(f_127_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_838),U_840),c_Relation_ORange(U_842,U_838,U_844)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_842,U_838)),hAPP(hAPP(c_Product__Type_OPair(U_842,U_838),U_832),U_840)),U_844)) ),
inference(clausify,[status(thm)],[f_127_5]) ).
fof(f_128_1,plain,
! [V_x_2,V_r_2,T_b,T_a] :
( ( c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Relation_ORange(T_a,T_b,V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Relation_ORange(T_a,T_b,V_r_2)))
| ~ c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2) ) ),
inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq]) ).
fof(f_128_2,plain,
! [U_848,U_847,U_846,U_845] :
( ( c_Predicate_ORangeP(U_845,U_846,hAPP(hAPP(c_COMBC(U_845,tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_fun(U_846,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_846,tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_fun(U_846,tc_HOL_Obool)),U_845),c_COMBC(U_846,tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_846,tc_prod(U_845,U_846)),tc_fun(U_846,tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool)),U_845),hAPP(c_COMBB(tc_prod(U_845,U_846),tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool),U_846),c_member(tc_prod(U_845,U_846)))),c_Product__Type_OPair(U_845,U_846)))),U_847),U_848)
| ~ hBOOL(hAPP(hAPP(c_member(U_846),U_848),c_Relation_ORange(U_845,U_846,U_847))) )
& ( hBOOL(hAPP(hAPP(c_member(U_846),U_848),c_Relation_ORange(U_845,U_846,U_847)))
| ~ c_Predicate_ORangeP(U_845,U_846,hAPP(hAPP(c_COMBC(U_845,tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_fun(U_846,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_846,tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_fun(U_846,tc_HOL_Obool)),U_845),c_COMBC(U_846,tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_846,tc_prod(U_845,U_846)),tc_fun(U_846,tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool)),U_845),hAPP(c_COMBB(tc_prod(U_845,U_846),tc_fun(tc_fun(tc_prod(U_845,U_846),tc_HOL_Obool),tc_HOL_Obool),U_846),c_member(tc_prod(U_845,U_846)))),c_Product__Type_OPair(U_845,U_846)))),U_847),U_848) ) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_856,U_854,U_852,U_850] :
( c_Predicate_ORangeP(U_850,U_852,hAPP(hAPP(c_COMBC(U_850,tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_fun(U_852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_852,tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_fun(U_852,tc_HOL_Obool)),U_850),c_COMBC(U_852,tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_852,tc_prod(U_850,U_852)),tc_fun(U_852,tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),U_850),hAPP(c_COMBB(tc_prod(U_850,U_852),tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool),U_852),c_member(tc_prod(U_850,U_852)))),c_Product__Type_OPair(U_850,U_852)))),U_854),U_856)
| ~ hBOOL(hAPP(hAPP(c_member(U_852),U_856),c_Relation_ORange(U_850,U_852,U_854))) )
& ! [U_855,U_853,U_851,U_849] :
( hBOOL(hAPP(hAPP(c_member(U_851),U_855),c_Relation_ORange(U_849,U_851,U_853)))
| ~ c_Predicate_ORangeP(U_849,U_851,hAPP(hAPP(c_COMBC(U_849,tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_fun(U_851,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_851,tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_fun(U_851,tc_HOL_Obool)),U_849),c_COMBC(U_851,tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_851,tc_prod(U_849,U_851)),tc_fun(U_851,tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),U_849),hAPP(c_COMBB(tc_prod(U_849,U_851),tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool),U_851),c_member(tc_prod(U_849,U_851)))),c_Product__Type_OPair(U_849,U_851)))),U_853),U_855) ) ),
inference(miniscope,[status(thm)],[f_128_2]) ).
fof(f_128_4,plain,
( ! [U_850,U_852,U_856,U_854] :
( c_Predicate_ORangeP(U_850,U_852,hAPP(hAPP(c_COMBC(U_850,tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_fun(U_852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_852,tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_fun(U_852,tc_HOL_Obool)),U_850),c_COMBC(U_852,tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_852,tc_prod(U_850,U_852)),tc_fun(U_852,tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),U_850),hAPP(c_COMBB(tc_prod(U_850,U_852),tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool),U_852),c_member(tc_prod(U_850,U_852)))),c_Product__Type_OPair(U_850,U_852)))),U_854),U_856)
| ~ hBOOL(hAPP(hAPP(c_member(U_852),U_856),c_Relation_ORange(U_850,U_852,U_854))) )
& ! [U_855,U_851,U_849,U_853] :
( hBOOL(hAPP(hAPP(c_member(U_851),U_855),c_Relation_ORange(U_849,U_851,U_853)))
| ~ c_Predicate_ORangeP(U_849,U_851,hAPP(hAPP(c_COMBC(U_849,tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_fun(U_851,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_851,tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_fun(U_851,tc_HOL_Obool)),U_849),c_COMBC(U_851,tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_851,tc_prod(U_849,U_851)),tc_fun(U_851,tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),U_849),hAPP(c_COMBB(tc_prod(U_849,U_851),tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool),U_851),c_member(tc_prod(U_849,U_851)))),c_Product__Type_OPair(U_849,U_851)))),U_853),U_855) ) ),
inference(definitional_conversion,[status(esa)],[f_128_3]) ).
cnf(f_128_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_851),U_855),c_Relation_ORange(U_849,U_851,U_853)))
| ~ c_Predicate_ORangeP(U_849,U_851,hAPP(hAPP(c_COMBC(U_849,tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_fun(U_851,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_851,tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_fun(U_851,tc_HOL_Obool)),U_849),c_COMBC(U_851,tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_851,tc_prod(U_849,U_851)),tc_fun(U_851,tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool)),U_849),hAPP(c_COMBB(tc_prod(U_849,U_851),tc_fun(tc_fun(tc_prod(U_849,U_851),tc_HOL_Obool),tc_HOL_Obool),U_851),c_member(tc_prod(U_849,U_851)))),c_Product__Type_OPair(U_849,U_851)))),U_853),U_855) ),
inference(clausify,[status(thm)],[f_128_4]) ).
cnf(f_128_6,plain,
( c_Predicate_ORangeP(U_850,U_852,hAPP(hAPP(c_COMBC(U_850,tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_fun(U_852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_852,tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_fun(U_852,tc_HOL_Obool)),U_850),c_COMBC(U_852,tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_852,tc_prod(U_850,U_852)),tc_fun(U_852,tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool)),U_850),hAPP(c_COMBB(tc_prod(U_850,U_852),tc_fun(tc_fun(tc_prod(U_850,U_852),tc_HOL_Obool),tc_HOL_Obool),U_852),c_member(tc_prod(U_850,U_852)))),c_Product__Type_OPair(U_850,U_852)))),U_854),U_856)
| ~ hBOOL(hAPP(hAPP(c_member(U_852),U_856),c_Relation_ORange(U_850,U_852,U_854))) ),
inference(clausify,[status(thm)],[f_128_4]) ).
fof(f_129_1,plain,
! [V_A_2,V_ca_2,T_a] :
( ? [B_x] :
( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_Id__onE]) ).
fof(f_129_2,plain,
! [U_860,U_859,U_858] :
( ? [U_857] :
( U_859 = hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),U_857),U_857)
& hBOOL(hAPP(hAPP(c_member(U_858),U_857),U_860)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),U_859),c_Relation_OId__on(U_858,U_860))) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_860,U_859,U_858] :
( ( U_859 = hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),sK63(U_860,U_859,U_858)),sK63(U_860,U_859,U_858))
& hBOOL(hAPP(hAPP(c_member(U_858),sK63(U_860,U_859,U_858)),U_860)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),U_859),c_Relation_OId__on(U_858,U_860))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_857,sK63(U_860,U_859,U_858))],[f_129_2]) ).
fof(f_129_4,plain,
( ! [U_858,U_859,U_860] :
( U_859 = hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),sK63(U_860,U_859,U_858)),sK63(U_860,U_859,U_858))
| ~ sP70(U_858,U_859,U_860) )
& ! [U_858,U_859,U_860] :
( hBOOL(hAPP(hAPP(c_member(U_858),sK63(U_860,U_859,U_858)),U_860))
| ~ sP70(U_858,U_859,U_860) )
& ! [U_858,U_859,U_860] :
( sP70(U_858,U_859,U_860)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),U_859),c_Relation_OId__on(U_858,U_860))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_129_3]) ).
cnf(f_129_5,plain,
( sP70(U_858,U_859,U_860)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),U_859),c_Relation_OId__on(U_858,U_860))) ),
inference(clausify,[status(thm)],[f_129_4]) ).
cnf(f_129_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_858),sK63(U_860,U_859,U_858)),U_860))
| ~ sP70(U_858,U_859,U_860) ),
inference(clausify,[status(thm)],[f_129_4]) ).
cnf(f_129_7,plain,
( U_859 = hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),sK63(U_860,U_859,U_858)),sK63(U_860,U_859,U_858))
| ~ sP70(U_858,U_859,U_860) ),
inference(clausify,[status(thm)],[f_129_4]) ).
fof(f_130_1,plain,
! [V_r_2,T_b,V_ba_2,T_a] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_ba_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Relation_ORange(T_b,T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_RangeE]) ).
fof(f_130_2,plain,
! [U_865,U_864,U_863,U_862] :
( ? [U_861] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_864,U_862)),hAPP(hAPP(c_Product__Type_OPair(U_864,U_862),U_861),U_863)),U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_862),U_863),c_Relation_ORange(U_864,U_862,U_865))) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_865,U_864,U_863,U_862] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_864,U_862)),hAPP(hAPP(c_Product__Type_OPair(U_864,U_862),sK64(U_865,U_864,U_863,U_862)),U_863)),U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_862),U_863),c_Relation_ORange(U_864,U_862,U_865))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_861,sK64(U_865,U_864,U_863,U_862))],[f_130_2]) ).
fof(f_130_4,plain,
! [U_863,U_862,U_864,U_865] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_864,U_862)),hAPP(hAPP(c_Product__Type_OPair(U_864,U_862),sK64(U_865,U_864,U_863,U_862)),U_863)),U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_862),U_863),c_Relation_ORange(U_864,U_862,U_865))) ),
inference(definitional_conversion,[status(esa)],[f_130_3]) ).
cnf(f_130_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_864,U_862)),hAPP(hAPP(c_Product__Type_OPair(U_864,U_862),sK64(U_865,U_864,U_863,U_862)),U_863)),U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_862),U_863),c_Relation_ORange(U_864,U_862,U_865))) ),
inference(clausify,[status(thm)],[f_130_4]) ).
fof(f_131_1,plain,
! [V_g_2,V_A_2,V_f_2,T_b,T_a] :
( V_f_2 = V_g_2
| ? [B_x] :
( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_extensionalityI]) ).
fof(f_131_2,plain,
! [U_871,U_870,U_869,U_868,U_867] :
( U_869 = U_871
| ? [U_866] :
( hAPP(U_869,U_866) != hAPP(U_871,U_866)
& hBOOL(hAPP(hAPP(c_member(U_867),U_866),U_870)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_871),c_FuncSet_Oextensional(U_867,U_868,U_870)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_869),c_FuncSet_Oextensional(U_867,U_868,U_870))) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_871,U_870,U_869,U_868,U_867] :
( U_869 = U_871
| ( hAPP(U_869,sK65(U_871,U_870,U_869,U_868,U_867)) != hAPP(U_871,sK65(U_871,U_870,U_869,U_868,U_867))
& hBOOL(hAPP(hAPP(c_member(U_867),sK65(U_871,U_870,U_869,U_868,U_867)),U_870)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_871),c_FuncSet_Oextensional(U_867,U_868,U_870)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_869),c_FuncSet_Oextensional(U_867,U_868,U_870))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_866,sK65(U_871,U_870,U_869,U_868,U_867))],[f_131_2]) ).
fof(f_131_4,plain,
( ! [U_867,U_868,U_869,U_870,U_871] :
( hAPP(U_869,sK65(U_871,U_870,U_869,U_868,U_867)) != hAPP(U_871,sK65(U_871,U_870,U_869,U_868,U_867))
| ~ sP71(U_867,U_868,U_869,U_870,U_871) )
& ! [U_867,U_868,U_869,U_870,U_871] :
( hBOOL(hAPP(hAPP(c_member(U_867),sK65(U_871,U_870,U_869,U_868,U_867)),U_870))
| ~ sP71(U_867,U_868,U_869,U_870,U_871) )
& ! [U_867,U_868,U_869,U_870,U_871] :
( U_869 = U_871
| sP71(U_867,U_868,U_869,U_870,U_871)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_871),c_FuncSet_Oextensional(U_867,U_868,U_870)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_869),c_FuncSet_Oextensional(U_867,U_868,U_870))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_131_3]) ).
cnf(f_131_5,plain,
( U_869 = U_871
| sP71(U_867,U_868,U_869,U_870,U_871)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_871),c_FuncSet_Oextensional(U_867,U_868,U_870)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_867,U_868)),U_869),c_FuncSet_Oextensional(U_867,U_868,U_870))) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_867),sK65(U_871,U_870,U_869,U_868,U_867)),U_870))
| ~ sP71(U_867,U_868,U_869,U_870,U_871) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_7,plain,
( hAPP(U_869,sK65(U_871,U_870,U_869,U_868,U_867)) != hAPP(U_871,sK65(U_871,U_870,U_869,U_868,U_867))
| ~ sP71(U_867,U_868,U_869,U_870,U_871) ),
inference(clausify,[status(thm)],[f_131_4]) ).
fof(f_132_1,plain,
! [V_r_2,T_b,T_a] :
( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
| ? [B_x,B_y] :
( ? [B_z] :
( B_y != B_z
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_single__valuedI]) ).
fof(f_132_2,plain,
! [U_877,U_876,U_875] :
( c_Relation_Osingle__valued(U_875,U_876,U_877)
| ? [U_874,U_873] :
( ? [U_872] :
( U_873 != U_872
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),U_874),U_872)),U_877)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),U_874),U_873)),U_877)) ) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_877,U_876,U_875] :
( c_Relation_Osingle__valued(U_875,U_876,U_877)
| ? [U_873] :
( ? [U_872] :
( U_873 != U_872
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),U_872)),U_877)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),U_873)),U_877)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_874,sK66(U_877,U_876,U_875))],[f_132_2]) ).
fof(f_132_4,plain,
! [U_877,U_876,U_875] :
( c_Relation_Osingle__valued(U_875,U_876,U_877)
| ( ? [U_872] :
( sK67(U_877,U_876,U_875) != U_872
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),U_872)),U_877)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),sK67(U_877,U_876,U_875))),U_877)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_873,sK67(U_877,U_876,U_875))],[f_132_3]) ).
fof(f_132_5,plain,
! [U_877,U_876,U_875] :
( c_Relation_Osingle__valued(U_875,U_876,U_877)
| ( sK67(U_877,U_876,U_875) != sK68(U_877,U_876,U_875)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),sK68(U_877,U_876,U_875))),U_877))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),sK67(U_877,U_876,U_875))),U_877)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_872,sK68(U_877,U_876,U_875))],[f_132_4]) ).
fof(f_132_6,plain,
( ! [U_875,U_876,U_877] :
( sK67(U_877,U_876,U_875) != sK68(U_877,U_876,U_875)
| ~ sP72(U_875,U_876,U_877) )
& ! [U_875,U_876,U_877] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),sK68(U_877,U_876,U_875))),U_877))
| ~ sP72(U_875,U_876,U_877) )
& ! [U_875,U_876,U_877] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),sK67(U_877,U_876,U_875))),U_877))
| ~ sP72(U_875,U_876,U_877) )
& ! [U_875,U_876,U_877] :
( c_Relation_Osingle__valued(U_875,U_876,U_877)
| sP72(U_875,U_876,U_877) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_132_5]) ).
cnf(f_132_7,plain,
( c_Relation_Osingle__valued(U_875,U_876,U_877)
| sP72(U_875,U_876,U_877) ),
inference(clausify,[status(thm)],[f_132_6]) ).
cnf(f_132_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),sK67(U_877,U_876,U_875))),U_877))
| ~ sP72(U_875,U_876,U_877) ),
inference(clausify,[status(thm)],[f_132_6]) ).
cnf(f_132_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_875,U_876)),hAPP(hAPP(c_Product__Type_OPair(U_875,U_876),sK66(U_877,U_876,U_875)),sK68(U_877,U_876,U_875))),U_877))
| ~ sP72(U_875,U_876,U_877) ),
inference(clausify,[status(thm)],[f_132_6]) ).
cnf(f_132_10,plain,
( sK67(U_877,U_876,U_875) != sK68(U_877,U_876,U_875)
| ~ sP72(U_875,U_876,U_877) ),
inference(clausify,[status(thm)],[f_132_6]) ).
fof(f_133_1,plain,
! [V_T_2,V_S_2,T_b,T_a] : c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_S_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_T_2)),c_FuncSet_Oextensional(T_a,T_b,V_S_2)),
inference(fof_nnf,[status(thm)],[fact_extensional__funcset__def]) ).
fof(f_133_2,plain,
! [U_881,U_880,U_879,U_878] : c_FuncSet_Oextensional__funcset(U_878,U_879,U_880,U_881) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_878,U_879),tc_HOL_Obool),c_FuncSet_OPi(U_878,U_879,U_880,c_COMBK(tc_fun(U_879,tc_HOL_Obool),U_878,U_881)),c_FuncSet_Oextensional(U_878,U_879,U_880)),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_878,U_880,U_879,U_881] : c_FuncSet_Oextensional__funcset(U_878,U_879,U_880,U_881) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_878,U_879),tc_HOL_Obool),c_FuncSet_OPi(U_878,U_879,U_880,c_COMBK(tc_fun(U_879,tc_HOL_Obool),U_878,U_881)),c_FuncSet_Oextensional(U_878,U_879,U_880)),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
c_FuncSet_Oextensional__funcset(U_878,U_879,U_880,U_881) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_878,U_879),tc_HOL_Obool),c_FuncSet_OPi(U_878,U_879,U_880,c_COMBK(tc_fun(U_879,tc_HOL_Obool),U_878,U_881)),c_FuncSet_Oextensional(U_878,U_879,U_880)),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_ba_2)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_y)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) )
| V_aa_2 = V_ba_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtranclE]) ).
fof(f_134_2,plain,
! [U_886,U_885,U_884,U_883] :
( ? [U_882] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_882),U_885)),U_886))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),U_882)),c_Transitive__Closure_Ortrancl(U_883,U_886))) )
| U_884 = U_885
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),U_885)),c_Transitive__Closure_Ortrancl(U_883,U_886))) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_886,U_885,U_884,U_883] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),sK69(U_886,U_885,U_884,U_883)),U_885)),U_886))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),sK69(U_886,U_885,U_884,U_883))),c_Transitive__Closure_Ortrancl(U_883,U_886))) )
| U_884 = U_885
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),U_885)),c_Transitive__Closure_Ortrancl(U_883,U_886))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_882,sK69(U_886,U_885,U_884,U_883))],[f_134_2]) ).
fof(f_134_4,plain,
( ! [U_883,U_884,U_885,U_886] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),sK69(U_886,U_885,U_884,U_883)),U_885)),U_886))
| ~ sP73(U_883,U_884,U_885,U_886) )
& ! [U_883,U_884,U_885,U_886] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),sK69(U_886,U_885,U_884,U_883))),c_Transitive__Closure_Ortrancl(U_883,U_886)))
| ~ sP73(U_883,U_884,U_885,U_886) )
& ! [U_883,U_884,U_885,U_886] :
( sP73(U_883,U_884,U_885,U_886)
| U_884 = U_885
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),U_885)),c_Transitive__Closure_Ortrancl(U_883,U_886))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_134_3]) ).
cnf(f_134_5,plain,
( sP73(U_883,U_884,U_885,U_886)
| U_884 = U_885
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),U_885)),c_Transitive__Closure_Ortrancl(U_883,U_886))) ),
inference(clausify,[status(thm)],[f_134_4]) ).
cnf(f_134_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),U_884),sK69(U_886,U_885,U_884,U_883))),c_Transitive__Closure_Ortrancl(U_883,U_886)))
| ~ sP73(U_883,U_884,U_885,U_886) ),
inference(clausify,[status(thm)],[f_134_4]) ).
cnf(f_134_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_883,U_883)),hAPP(hAPP(c_Product__Type_OPair(U_883,U_883),sK69(U_886,U_885,U_884,U_883)),U_885)),U_886))
| ~ sP73(U_883,U_884,U_885,U_886) ),
inference(clausify,[status(thm)],[f_134_4]) ).
fof(f_135_1,plain,
! [T_a,V_B_2,V_x_2,V_A_2] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_135_2,plain,
! [U_890,U_889,U_888,U_887] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_890,tc_HOL_Obool),U_887,U_889),U_888))
| ~ hBOOL(hAPP(U_889,U_888))
| ~ hBOOL(hAPP(U_887,U_888)) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_890,U_889,U_887,U_888] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_890,tc_HOL_Obool),U_887,U_889),U_888))
| ~ hBOOL(hAPP(U_889,U_888))
| ~ hBOOL(hAPP(U_887,U_888)) ),
inference(definitional_conversion,[status(esa)],[f_135_2]) ).
cnf(f_135_4,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_890,tc_HOL_Obool),U_887,U_889),U_888))
| ~ hBOOL(hAPP(U_889,U_888))
| ~ hBOOL(hAPP(U_887,U_888)) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
! [V_x_2,V_B_2,V_A_2,T_a] :
( ( hBOOL(hAPP(V_B_2,V_x_2))
& hBOOL(hAPP(V_A_2,V_x_2)) )
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1E]) ).
fof(f_136_2,plain,
! [U_894,U_893,U_892,U_891] :
( ( hBOOL(hAPP(U_893,U_894))
& hBOOL(hAPP(U_892,U_894)) )
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_891,tc_HOL_Obool),U_892,U_893),U_894)) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_894,U_893,U_892] :
( ! [U_891] : ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_891,tc_HOL_Obool),U_892,U_893),U_894))
| ( hBOOL(hAPP(U_893,U_894))
& hBOOL(hAPP(U_892,U_894)) ) ),
inference(miniscope,[status(thm)],[f_136_2]) ).
fof(f_136_4,plain,
( ! [U_892,U_893,U_894] :
( hBOOL(hAPP(U_893,U_894))
| ~ sP74(U_892,U_893,U_894) )
& ! [U_892,U_893,U_894] :
( hBOOL(hAPP(U_892,U_894))
| ~ sP74(U_892,U_893,U_894) )
& ! [U_892,U_891,U_893,U_894] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_891,tc_HOL_Obool),U_892,U_893),U_894))
| sP74(U_892,U_893,U_894) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_136_3]) ).
cnf(f_136_5,plain,
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_891,tc_HOL_Obool),U_892,U_893),U_894))
| sP74(U_892,U_893,U_894) ),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_6,plain,
( hBOOL(hAPP(U_892,U_894))
| ~ sP74(U_892,U_893,U_894) ),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_7,plain,
( hBOOL(hAPP(U_893,U_894))
| ~ sP74(U_892,U_893,U_894) ),
inference(clausify,[status(thm)],[f_136_4]) ).
fof(f_137_1,plain,
! [T_b,T_a,V_ba_2,V_aa_2,V_r_2] :
( c_Predicate_ORangeP(T_a,T_b,V_r_2,V_ba_2)
| ~ hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros]) ).
fof(f_137_2,plain,
! [U_899,U_898,U_897,U_896,U_895] :
( c_Predicate_ORangeP(U_898,U_899,U_895,U_897)
| ~ hBOOL(hAPP(hAPP(U_895,U_896),U_897)) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_896,U_895,U_897,U_898,U_899] :
( c_Predicate_ORangeP(U_898,U_899,U_895,U_897)
| ~ hBOOL(hAPP(hAPP(U_895,U_896),U_897)) ),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
( c_Predicate_ORangeP(U_898,U_899,U_895,U_897)
| ~ hBOOL(hAPP(hAPP(U_895,U_896),U_897)) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_IntI]) ).
fof(f_138_2,plain,
! [U_903,U_902,U_901,U_900] :
( hBOOL(hAPP(hAPP(c_member(U_900),U_901),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool),U_902,U_903)))
| ~ hBOOL(hAPP(hAPP(c_member(U_900),U_901),U_903))
| ~ hBOOL(hAPP(hAPP(c_member(U_900),U_901),U_902)) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_900,U_901,U_902,U_903] :
( hBOOL(hAPP(hAPP(c_member(U_900),U_901),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool),U_902,U_903)))
| ~ hBOOL(hAPP(hAPP(c_member(U_900),U_901),U_903))
| ~ hBOOL(hAPP(hAPP(c_member(U_900),U_901),U_902)) ),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_900),U_901),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool),U_902,U_903)))
| ~ hBOOL(hAPP(hAPP(c_member(U_900),U_901),U_903))
| ~ hBOOL(hAPP(hAPP(c_member(U_900),U_901),U_902)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntE]) ).
fof(f_139_2,plain,
! [U_907,U_906,U_905,U_904] :
( ( hBOOL(hAPP(hAPP(c_member(U_904),U_905),U_907))
& hBOOL(hAPP(hAPP(c_member(U_904),U_905),U_906)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_904),U_905),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool),U_906,U_907))) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
( ! [U_904,U_905,U_906,U_907] :
( hBOOL(hAPP(hAPP(c_member(U_904),U_905),U_907))
| ~ sP75(U_904,U_905,U_906,U_907) )
& ! [U_904,U_905,U_906,U_907] :
( hBOOL(hAPP(hAPP(c_member(U_904),U_905),U_906))
| ~ sP75(U_904,U_905,U_906,U_907) )
& ! [U_904,U_905,U_906,U_907] :
( sP75(U_904,U_905,U_906,U_907)
| ~ hBOOL(hAPP(hAPP(c_member(U_904),U_905),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool),U_906,U_907))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_139_2]) ).
cnf(f_139_4,plain,
( sP75(U_904,U_905,U_906,U_907)
| ~ hBOOL(hAPP(hAPP(c_member(U_904),U_905),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool),U_906,U_907))) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_904),U_905),U_906))
| ~ sP75(U_904,U_905,U_906,U_907) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_904),U_905),U_907))
| ~ sP75(U_904,U_905,U_906,U_907) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_1,plain,
! [V_a2_2,V_r_2,T_b,T_a] :
( ( c_Predicate_ORangeP(T_a,T_b,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))
| ~ c_Predicate_ORangeP(T_a,T_b,V_r_2,V_a2_2) ) ),
inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations]) ).
fof(f_140_2,plain,
! [U_913,U_912,U_911,U_910] :
( ( c_Predicate_ORangeP(U_910,U_911,U_912,U_913)
| ! [U_909] : ~ hBOOL(hAPP(hAPP(U_912,U_909),U_913)) )
& ( ? [U_908] : hBOOL(hAPP(hAPP(U_912,U_908),U_913))
| ~ c_Predicate_ORangeP(U_910,U_911,U_912,U_913) ) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_921,U_919] :
( ! [U_917,U_915] : c_Predicate_ORangeP(U_915,U_917,U_919,U_921)
| ! [U_909] : ~ hBOOL(hAPP(hAPP(U_919,U_909),U_921)) )
& ! [U_920,U_918] :
( ! [U_916,U_914] : ~ c_Predicate_ORangeP(U_914,U_916,U_918,U_920)
| ? [U_908] : hBOOL(hAPP(hAPP(U_918,U_908),U_920)) ) ),
inference(miniscope,[status(thm)],[f_140_2]) ).
fof(f_140_4,plain,
( ! [U_921,U_919] :
( ! [U_917,U_915] : c_Predicate_ORangeP(U_915,U_917,U_919,U_921)
| ! [U_909] : ~ hBOOL(hAPP(hAPP(U_919,U_909),U_921)) )
& ! [U_920,U_918] :
( ! [U_916,U_914] : ~ c_Predicate_ORangeP(U_914,U_916,U_918,U_920)
| hBOOL(hAPP(hAPP(U_918,sK70(U_920,U_918)),U_920)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_908,sK70(U_920,U_918))],[f_140_3]) ).
fof(f_140_5,plain,
( ! [U_917,U_909,U_919,U_915,U_921] :
( c_Predicate_ORangeP(U_915,U_917,U_919,U_921)
| ~ hBOOL(hAPP(hAPP(U_919,U_909),U_921)) )
& ! [U_916,U_918,U_914,U_920] :
( ~ c_Predicate_ORangeP(U_914,U_916,U_918,U_920)
| hBOOL(hAPP(hAPP(U_918,sK70(U_920,U_918)),U_920)) ) ),
inference(definitional_conversion,[status(esa)],[f_140_4]) ).
cnf(f_140_6,plain,
( ~ c_Predicate_ORangeP(U_914,U_916,U_918,U_920)
| hBOOL(hAPP(hAPP(U_918,sK70(U_920,U_918)),U_920)) ),
inference(clausify,[status(thm)],[f_140_5]) ).
cnf(f_140_7,plain,
( c_Predicate_ORangeP(U_915,U_917,U_919,U_921)
| ~ hBOOL(hAPP(hAPP(U_919,U_909),U_921)) ),
inference(clausify,[status(thm)],[f_140_5]) ).
fof(f_141_1,plain,
! [V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Int__absorb]) ).
fof(f_141_2,plain,
! [U_923,U_922] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_922,tc_HOL_Obool),U_923,U_923) = U_923,
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_923,U_922] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_922,tc_HOL_Obool),U_923,U_923) = U_923,
inference(definitional_conversion,[status(esa)],[f_141_2]) ).
cnf(f_141_4,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_922,tc_HOL_Obool),U_923,U_923) = U_923,
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [V_B_2,V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),
inference(fof_nnf,[status(thm)],[fact_Int__commute]) ).
fof(f_142_2,plain,
! [U_926,U_925,U_924] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool),U_925,U_926) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool),U_926,U_925),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_924,U_925,U_926] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool),U_925,U_926) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool),U_926,U_925),
inference(definitional_conversion,[status(esa)],[f_142_2]) ).
cnf(f_142_4,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool),U_925,U_926) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool),U_926,U_925),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [V_B_2,V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),
inference(fof_nnf,[status(thm)],[fact_Int__left__absorb]) ).
fof(f_143_2,plain,
! [U_929,U_928,U_927] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,U_929)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,U_929),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_927,U_928,U_929] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,U_929)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,U_929),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,U_929)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool),U_928,U_929),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_1,plain,
! [V_C_2,V_B_2,V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__left__commute]) ).
fof(f_144_2,plain,
! [U_933,U_932,U_931,U_930] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_931,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_932,U_933)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_932,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_931,U_933)),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_930,U_931,U_932,U_933] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_931,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_932,U_933)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_932,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_931,U_933)),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_931,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_932,U_933)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_932,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_930,tc_HOL_Obool),U_931,U_933)),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [V_C_2,V_B_2,V_A_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__assoc]) ).
fof(f_145_2,plain,
! [U_937,U_936,U_935,U_934] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_935,U_936),U_937) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_935,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_936,U_937)),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_936,U_937,U_935,U_934] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_935,U_936),U_937) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_935,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_936,U_937)),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_935,U_936),U_937) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_935,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool),U_936,U_937)),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [V_x_2,V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D1]) ).
fof(f_146_2,plain,
! [U_941,U_940,U_939,U_938] :
( hBOOL(hAPP(U_939,U_941))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool),U_939,U_940),U_941)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_941,U_940,U_939] :
( ! [U_938] : ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool),U_939,U_940),U_941))
| hBOOL(hAPP(U_939,U_941)) ),
inference(miniscope,[status(thm)],[f_146_2]) ).
fof(f_146_4,plain,
! [U_938,U_939,U_940,U_941] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool),U_939,U_940),U_941))
| hBOOL(hAPP(U_939,U_941)) ),
inference(definitional_conversion,[status(esa)],[f_146_3]) ).
cnf(f_146_5,plain,
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool),U_939,U_940),U_941))
| hBOOL(hAPP(U_939,U_941)) ),
inference(clausify,[status(thm)],[f_146_4]) ).
fof(f_147_1,plain,
! [V_x_2,V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(V_B_2,V_x_2))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D2]) ).
fof(f_147_2,plain,
! [U_945,U_944,U_943,U_942] :
( hBOOL(hAPP(U_944,U_945))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool),U_943,U_944),U_945)) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_945,U_944] :
( ! [U_943,U_942] : ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool),U_943,U_944),U_945))
| hBOOL(hAPP(U_944,U_945)) ),
inference(miniscope,[status(thm)],[f_147_2]) ).
fof(f_147_4,plain,
! [U_942,U_943,U_944,U_945] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool),U_943,U_944),U_945))
| hBOOL(hAPP(U_944,U_945)) ),
inference(definitional_conversion,[status(esa)],[f_147_3]) ).
cnf(f_147_5,plain,
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool),U_943,U_944),U_945))
| hBOOL(hAPP(U_944,U_945)) ),
inference(clausify,[status(thm)],[f_147_4]) ).
fof(f_148_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
& ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).
fof(f_148_2,plain,
! [U_949,U_948,U_947,U_946] :
( ( hBOOL(hAPP(hAPP(c_member(U_946),U_947),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_946,tc_HOL_Obool),U_948,U_949)))
| ~ hBOOL(hAPP(hAPP(c_member(U_946),U_947),U_949))
| ~ hBOOL(hAPP(hAPP(c_member(U_946),U_947),U_948)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_946),U_947),U_949))
& hBOOL(hAPP(hAPP(c_member(U_946),U_947),U_948)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_946),U_947),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_946,tc_HOL_Obool),U_948,U_949))) ) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
( ! [U_957,U_955,U_953,U_951] :
( hBOOL(hAPP(hAPP(c_member(U_951),U_953),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_951,tc_HOL_Obool),U_955,U_957)))
| ~ hBOOL(hAPP(hAPP(c_member(U_951),U_953),U_957))
| ~ hBOOL(hAPP(hAPP(c_member(U_951),U_953),U_955)) )
& ! [U_956,U_954,U_952,U_950] :
( ( hBOOL(hAPP(hAPP(c_member(U_950),U_952),U_956))
& hBOOL(hAPP(hAPP(c_member(U_950),U_952),U_954)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_950),U_952),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_950,tc_HOL_Obool),U_954,U_956))) ) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
fof(f_148_4,plain,
( ! [U_950,U_954,U_956,U_952] :
( hBOOL(hAPP(hAPP(c_member(U_950),U_952),U_956))
| ~ sP76(U_950,U_954,U_956,U_952) )
& ! [U_950,U_954,U_956,U_952] :
( hBOOL(hAPP(hAPP(c_member(U_950),U_952),U_954))
| ~ sP76(U_950,U_954,U_956,U_952) )
& ! [U_955,U_951,U_957,U_953] :
( hBOOL(hAPP(hAPP(c_member(U_951),U_953),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_951,tc_HOL_Obool),U_955,U_957)))
| ~ hBOOL(hAPP(hAPP(c_member(U_951),U_953),U_957))
| ~ hBOOL(hAPP(hAPP(c_member(U_951),U_953),U_955)) )
& ! [U_950,U_954,U_956,U_952] :
( sP76(U_950,U_954,U_956,U_952)
| ~ hBOOL(hAPP(hAPP(c_member(U_950),U_952),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_950,tc_HOL_Obool),U_954,U_956))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_148_3]) ).
cnf(f_148_5,plain,
( sP76(U_950,U_954,U_956,U_952)
| ~ hBOOL(hAPP(hAPP(c_member(U_950),U_952),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_950,tc_HOL_Obool),U_954,U_956))) ),
inference(clausify,[status(thm)],[f_148_4]) ).
cnf(f_148_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_951),U_953),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_951,tc_HOL_Obool),U_955,U_957)))
| ~ hBOOL(hAPP(hAPP(c_member(U_951),U_953),U_957))
| ~ hBOOL(hAPP(hAPP(c_member(U_951),U_953),U_955)) ),
inference(clausify,[status(thm)],[f_148_4]) ).
cnf(f_148_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_950),U_952),U_954))
| ~ sP76(U_950,U_954,U_956,U_952) ),
inference(clausify,[status(thm)],[f_148_4]) ).
cnf(f_148_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_950),U_952),U_956))
| ~ sP76(U_950,U_954,U_956,U_952) ),
inference(clausify,[status(thm)],[f_148_4]) ).
fof(f_149_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD1]) ).
fof(f_149_2,plain,
! [U_961,U_960,U_959,U_958] :
( hBOOL(hAPP(hAPP(c_member(U_958),U_959),U_960))
| ~ hBOOL(hAPP(hAPP(c_member(U_958),U_959),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool),U_960,U_961))) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_958,U_961,U_960,U_959] :
( hBOOL(hAPP(hAPP(c_member(U_958),U_959),U_960))
| ~ hBOOL(hAPP(hAPP(c_member(U_958),U_959),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool),U_960,U_961))) ),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_958),U_959),U_960))
| ~ hBOOL(hAPP(hAPP(c_member(U_958),U_959),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool),U_960,U_961))) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD2]) ).
fof(f_150_2,plain,
! [U_965,U_964,U_963,U_962] :
( hBOOL(hAPP(hAPP(c_member(U_962),U_963),U_965))
| ~ hBOOL(hAPP(hAPP(c_member(U_962),U_963),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_962,tc_HOL_Obool),U_964,U_965))) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_962,U_963,U_964,U_965] :
( hBOOL(hAPP(hAPP(c_member(U_962),U_963),U_965))
| ~ hBOOL(hAPP(hAPP(c_member(U_962),U_963),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_962,tc_HOL_Obool),U_964,U_965))) ),
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_962),U_963),U_965))
| ~ hBOOL(hAPP(hAPP(c_member(U_962),U_963),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_962,tc_HOL_Obool),U_964,U_965))) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [V_x_2,V_S_2,V_R_2,T_a] :
( ( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq]) ).
fof(f_151_2,plain,
! [U_969,U_968,U_967,U_966] :
( ( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_966,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_966,tc_fun(U_966,tc_HOL_Obool),tc_HOL_Obool),c_member(U_966)),U_967),hAPP(hAPP(c_COMBC(U_966,tc_fun(U_966,tc_HOL_Obool),tc_HOL_Obool),c_member(U_966)),U_968)),U_969))
| ~ hBOOL(hAPP(hAPP(c_member(U_966),U_969),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_966,tc_HOL_Obool),U_967,U_968))) )
& ( hBOOL(hAPP(hAPP(c_member(U_966),U_969),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_966,tc_HOL_Obool),U_967,U_968)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_966,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_966,tc_fun(U_966,tc_HOL_Obool),tc_HOL_Obool),c_member(U_966)),U_967),hAPP(hAPP(c_COMBC(U_966,tc_fun(U_966,tc_HOL_Obool),tc_HOL_Obool),c_member(U_966)),U_968)),U_969)) ) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
( ! [U_977,U_975,U_973,U_971] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_971,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_971,tc_fun(U_971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_971)),U_973),hAPP(hAPP(c_COMBC(U_971,tc_fun(U_971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_971)),U_975)),U_977))
| ~ hBOOL(hAPP(hAPP(c_member(U_971),U_977),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_971,tc_HOL_Obool),U_973,U_975))) )
& ! [U_976,U_974,U_972,U_970] :
( hBOOL(hAPP(hAPP(c_member(U_970),U_976),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_970,tc_HOL_Obool),U_972,U_974)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_970,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_970,tc_fun(U_970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_970)),U_972),hAPP(hAPP(c_COMBC(U_970,tc_fun(U_970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_970)),U_974)),U_976)) ) ),
inference(miniscope,[status(thm)],[f_151_2]) ).
fof(f_151_4,plain,
( ! [U_973,U_971,U_975,U_977] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_971,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_971,tc_fun(U_971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_971)),U_973),hAPP(hAPP(c_COMBC(U_971,tc_fun(U_971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_971)),U_975)),U_977))
| ~ hBOOL(hAPP(hAPP(c_member(U_971),U_977),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_971,tc_HOL_Obool),U_973,U_975))) )
& ! [U_974,U_972,U_976,U_970] :
( hBOOL(hAPP(hAPP(c_member(U_970),U_976),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_970,tc_HOL_Obool),U_972,U_974)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_970,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_970,tc_fun(U_970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_970)),U_972),hAPP(hAPP(c_COMBC(U_970,tc_fun(U_970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_970)),U_974)),U_976)) ) ),
inference(definitional_conversion,[status(esa)],[f_151_3]) ).
cnf(f_151_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_970),U_976),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_970,tc_HOL_Obool),U_972,U_974)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_970,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_970,tc_fun(U_970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_970)),U_972),hAPP(hAPP(c_COMBC(U_970,tc_fun(U_970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_970)),U_974)),U_976)) ),
inference(clausify,[status(thm)],[f_151_4]) ).
cnf(f_151_6,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_971,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_971,tc_fun(U_971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_971)),U_973),hAPP(hAPP(c_COMBC(U_971,tc_fun(U_971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_971)),U_975)),U_977))
| ~ hBOOL(hAPP(hAPP(c_member(U_971),U_977),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_971,tc_HOL_Obool),U_973,U_975))) ),
inference(clausify,[status(thm)],[f_151_4]) ).
fof(f_152_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__fun__def]) ).
fof(f_152_2,plain,
! [U_982,U_981,U_980,U_979,U_978] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_979,U_978),U_980,U_981),U_982) = c_Lattices_Osemilattice__inf__class_Oinf(U_978,hAPP(U_980,U_982),hAPP(U_981,U_982))
| ~ class_Lattices_Olattice(U_978) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_979,U_978,U_980,U_981,U_982] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_979,U_978),U_980,U_981),U_982) = c_Lattices_Osemilattice__inf__class_Oinf(U_978,hAPP(U_980,U_982),hAPP(U_981,U_982))
| ~ class_Lattices_Olattice(U_978) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_979,U_978),U_980,U_981),U_982) = c_Lattices_Osemilattice__inf__class_Oinf(U_978,hAPP(U_980,U_982),hAPP(U_981,U_982))
| ~ class_Lattices_Olattice(U_978) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__apply]) ).
fof(f_153_2,plain,
! [U_987,U_986,U_985,U_984,U_983] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_984,U_983),U_985,U_986),U_987) = c_Lattices_Osemilattice__inf__class_Oinf(U_983,hAPP(U_985,U_987),hAPP(U_986,U_987))
| ~ class_Lattices_Olattice(U_983) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_984,U_983,U_985,U_986,U_987] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_984,U_983),U_985,U_986),U_987) = c_Lattices_Osemilattice__inf__class_Oinf(U_983,hAPP(U_985,U_987),hAPP(U_986,U_987))
| ~ class_Lattices_Olattice(U_983) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_984,U_983),U_985,U_986),U_987) = c_Lattices_Osemilattice__inf__class_Oinf(U_983,hAPP(U_985,U_987),hAPP(U_986,U_987))
| ~ class_Lattices_Olattice(U_983) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [V_Pa_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(V_Pa_2,V_ba_2))
| ? [B_y] :
( ? [B_z] :
( ~ hBOOL(hAPP(V_Pa_2,B_z))
& hBOOL(hAPP(V_Pa_2,B_y))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_z)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_y)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) )
| ~ hBOOL(hAPP(V_Pa_2,V_aa_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__induct]) ).
fof(f_154_2,plain,
! [U_994,U_993,U_992,U_991,U_990] :
( hBOOL(hAPP(U_994,U_992))
| ? [U_989] :
( ? [U_988] :
( ~ hBOOL(hAPP(U_994,U_988))
& hBOOL(hAPP(U_994,U_989))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_989),U_988)),U_993)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),U_989)),c_Transitive__Closure_Ortrancl(U_990,U_993))) )
| ~ hBOOL(hAPP(U_994,U_991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),U_992)),c_Transitive__Closure_Ortrancl(U_990,U_993))) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_994,U_993,U_992,U_991,U_990] :
( hBOOL(hAPP(U_994,U_992))
| ( ? [U_988] :
( ~ hBOOL(hAPP(U_994,U_988))
& hBOOL(hAPP(U_994,sK71(U_994,U_993,U_992,U_991,U_990)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),sK71(U_994,U_993,U_992,U_991,U_990)),U_988)),U_993)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),sK71(U_994,U_993,U_992,U_991,U_990))),c_Transitive__Closure_Ortrancl(U_990,U_993))) )
| ~ hBOOL(hAPP(U_994,U_991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),U_992)),c_Transitive__Closure_Ortrancl(U_990,U_993))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_989,sK71(U_994,U_993,U_992,U_991,U_990))],[f_154_2]) ).
fof(f_154_4,plain,
! [U_994,U_993,U_992,U_991,U_990] :
( hBOOL(hAPP(U_994,U_992))
| ( ~ hBOOL(hAPP(U_994,sK72(U_994,U_993,U_992,U_991,U_990)))
& hBOOL(hAPP(U_994,sK71(U_994,U_993,U_992,U_991,U_990)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),sK71(U_994,U_993,U_992,U_991,U_990)),sK72(U_994,U_993,U_992,U_991,U_990))),U_993))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),sK71(U_994,U_993,U_992,U_991,U_990))),c_Transitive__Closure_Ortrancl(U_990,U_993))) )
| ~ hBOOL(hAPP(U_994,U_991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),U_992)),c_Transitive__Closure_Ortrancl(U_990,U_993))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_988,sK72(U_994,U_993,U_992,U_991,U_990))],[f_154_3]) ).
fof(f_154_5,plain,
( ! [U_990,U_991,U_992,U_993,U_994] :
( ~ hBOOL(hAPP(U_994,sK72(U_994,U_993,U_992,U_991,U_990)))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) )
& ! [U_990,U_991,U_992,U_993,U_994] :
( hBOOL(hAPP(U_994,sK71(U_994,U_993,U_992,U_991,U_990)))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) )
& ! [U_990,U_991,U_992,U_993,U_994] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),sK71(U_994,U_993,U_992,U_991,U_990)),sK72(U_994,U_993,U_992,U_991,U_990))),U_993))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) )
& ! [U_990,U_991,U_992,U_993,U_994] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),sK71(U_994,U_993,U_992,U_991,U_990))),c_Transitive__Closure_Ortrancl(U_990,U_993)))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) )
& ! [U_990,U_991,U_992,U_993,U_994] :
( hBOOL(hAPP(U_994,U_992))
| sP77(U_990,U_991,U_992,U_993,U_994)
| ~ hBOOL(hAPP(U_994,U_991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),U_992)),c_Transitive__Closure_Ortrancl(U_990,U_993))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_154_4]) ).
cnf(f_154_6,plain,
( hBOOL(hAPP(U_994,U_992))
| sP77(U_990,U_991,U_992,U_993,U_994)
| ~ hBOOL(hAPP(U_994,U_991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),U_992)),c_Transitive__Closure_Ortrancl(U_990,U_993))) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),U_991),sK71(U_994,U_993,U_992,U_991,U_990))),c_Transitive__Closure_Ortrancl(U_990,U_993)))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_990,U_990)),hAPP(hAPP(c_Product__Type_OPair(U_990,U_990),sK71(U_994,U_993,U_992,U_991,U_990)),sK72(U_994,U_993,U_992,U_991,U_990))),U_993))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_9,plain,
( hBOOL(hAPP(U_994,sK71(U_994,U_993,U_992,U_991,U_990)))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_10,plain,
( ~ hBOOL(hAPP(U_994,sK72(U_994,U_993,U_992,U_991,U_990)))
| ~ sP77(U_990,U_991,U_992,U_993,U_994) ),
inference(clausify,[status(thm)],[f_154_5]) ).
fof(f_155_1,plain,
! [V_Pa_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(V_Pa_2,V_aa_2))
| ? [B_y,B_z] :
( ~ hBOOL(hAPP(V_Pa_2,B_y))
& hBOOL(hAPP(V_Pa_2,B_z))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_z)),V_r_2)) )
| ~ hBOOL(hAPP(V_Pa_2,V_ba_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct]) ).
fof(f_155_2,plain,
! [U_1001,U_1000,U_999,U_998,U_997] :
( hBOOL(hAPP(U_1001,U_998))
| ? [U_996,U_995] :
( ~ hBOOL(hAPP(U_1001,U_996))
& hBOOL(hAPP(U_1001,U_995))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_995),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_996),U_995)),U_1000)) )
| ~ hBOOL(hAPP(U_1001,U_999))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_998),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000))) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_1001,U_1000,U_999,U_998,U_997] :
( hBOOL(hAPP(U_1001,U_998))
| ? [U_995] :
( ~ hBOOL(hAPP(U_1001,sK73(U_1001,U_1000,U_999,U_998,U_997)))
& hBOOL(hAPP(U_1001,U_995))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_995),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),sK73(U_1001,U_1000,U_999,U_998,U_997)),U_995)),U_1000)) )
| ~ hBOOL(hAPP(U_1001,U_999))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_998),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_996,sK73(U_1001,U_1000,U_999,U_998,U_997))],[f_155_2]) ).
fof(f_155_4,plain,
! [U_1001,U_1000,U_999,U_998,U_997] :
( hBOOL(hAPP(U_1001,U_998))
| ( ~ hBOOL(hAPP(U_1001,sK73(U_1001,U_1000,U_999,U_998,U_997)))
& hBOOL(hAPP(U_1001,sK74(U_1001,U_1000,U_999,U_998,U_997)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),sK74(U_1001,U_1000,U_999,U_998,U_997)),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),sK73(U_1001,U_1000,U_999,U_998,U_997)),sK74(U_1001,U_1000,U_999,U_998,U_997))),U_1000)) )
| ~ hBOOL(hAPP(U_1001,U_999))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_998),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_995,sK74(U_1001,U_1000,U_999,U_998,U_997))],[f_155_3]) ).
fof(f_155_5,plain,
( ! [U_997,U_998,U_999,U_1000,U_1001] :
( ~ hBOOL(hAPP(U_1001,sK73(U_1001,U_1000,U_999,U_998,U_997)))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) )
& ! [U_997,U_998,U_999,U_1000,U_1001] :
( hBOOL(hAPP(U_1001,sK74(U_1001,U_1000,U_999,U_998,U_997)))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) )
& ! [U_997,U_998,U_999,U_1000,U_1001] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),sK74(U_1001,U_1000,U_999,U_998,U_997)),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000)))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) )
& ! [U_997,U_998,U_999,U_1000,U_1001] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),sK73(U_1001,U_1000,U_999,U_998,U_997)),sK74(U_1001,U_1000,U_999,U_998,U_997))),U_1000))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) )
& ! [U_997,U_998,U_999,U_1000,U_1001] :
( hBOOL(hAPP(U_1001,U_998))
| sP78(U_997,U_998,U_999,U_1000,U_1001)
| ~ hBOOL(hAPP(U_1001,U_999))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_998),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_155_4]) ).
cnf(f_155_6,plain,
( hBOOL(hAPP(U_1001,U_998))
| sP78(U_997,U_998,U_999,U_1000,U_1001)
| ~ hBOOL(hAPP(U_1001,U_999))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),U_998),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000))) ),
inference(clausify,[status(thm)],[f_155_5]) ).
cnf(f_155_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),sK73(U_1001,U_1000,U_999,U_998,U_997)),sK74(U_1001,U_1000,U_999,U_998,U_997))),U_1000))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) ),
inference(clausify,[status(thm)],[f_155_5]) ).
cnf(f_155_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_997,U_997)),hAPP(hAPP(c_Product__Type_OPair(U_997,U_997),sK74(U_1001,U_1000,U_999,U_998,U_997)),U_999)),c_Transitive__Closure_Ortrancl(U_997,U_1000)))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) ),
inference(clausify,[status(thm)],[f_155_5]) ).
cnf(f_155_9,plain,
( hBOOL(hAPP(U_1001,sK74(U_1001,U_1000,U_999,U_998,U_997)))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) ),
inference(clausify,[status(thm)],[f_155_5]) ).
cnf(f_155_10,plain,
( ~ hBOOL(hAPP(U_1001,sK73(U_1001,U_1000,U_999,U_998,U_997)))
| ~ sP78(U_997,U_998,U_999,U_1000,U_1001) ),
inference(clausify,[status(thm)],[f_155_5]) ).
fof(f_156_1,plain,
! [V_r_2,V_z_2,V_x_2,T_a] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_r_2)) )
| V_x_2 = V_z_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtranclE]) ).
fof(f_156_2,plain,
! [U_1006,U_1005,U_1004,U_1003] :
( ? [U_1002] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1002),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),U_1002)),U_1006)) )
| U_1004 = U_1005
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006))) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_1006,U_1005,U_1004,U_1003] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),sK75(U_1006,U_1005,U_1004,U_1003)),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),sK75(U_1006,U_1005,U_1004,U_1003))),U_1006)) )
| U_1004 = U_1005
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1002,sK75(U_1006,U_1005,U_1004,U_1003))],[f_156_2]) ).
fof(f_156_4,plain,
( ! [U_1003,U_1006,U_1004,U_1005] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),sK75(U_1006,U_1005,U_1004,U_1003)),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006)))
| ~ sP79(U_1003,U_1006,U_1004,U_1005) )
& ! [U_1003,U_1006,U_1004,U_1005] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),sK75(U_1006,U_1005,U_1004,U_1003))),U_1006))
| ~ sP79(U_1003,U_1006,U_1004,U_1005) )
& ! [U_1003,U_1006,U_1004,U_1005] :
( sP79(U_1003,U_1006,U_1004,U_1005)
| U_1004 = U_1005
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_156_3]) ).
cnf(f_156_5,plain,
( sP79(U_1003,U_1006,U_1004,U_1005)
| U_1004 = U_1005
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006))) ),
inference(clausify,[status(thm)],[f_156_4]) ).
cnf(f_156_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),U_1004),sK75(U_1006,U_1005,U_1004,U_1003))),U_1006))
| ~ sP79(U_1003,U_1006,U_1004,U_1005) ),
inference(clausify,[status(thm)],[f_156_4]) ).
cnf(f_156_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1003,U_1003)),hAPP(hAPP(c_Product__Type_OPair(U_1003,U_1003),sK75(U_1006,U_1005,U_1004,U_1003)),U_1005)),c_Transitive__Closure_Ortrancl(U_1003,U_1006)))
| ~ sP79(U_1003,U_1006,U_1004,U_1005) ),
inference(clausify,[status(thm)],[f_156_4]) ).
fof(f_157_1,plain,
! [V_r_2,V_A_2,T_a] :
( ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
| ? [B_x] :
( ? [B_xa] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2))
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) )
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2))
| B_x = B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
| ~ c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_total__on__def]) ).
fof(f_157_2,plain,
! [U_1013,U_1012,U_1011] :
( ( c_Relation_Ototal__on(U_1011,U_1012,U_1013)
| ? [U_1010] :
( ? [U_1009] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1011,U_1011)),hAPP(hAPP(c_Product__Type_OPair(U_1011,U_1011),U_1009),U_1010)),U_1013))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1011,U_1011)),hAPP(hAPP(c_Product__Type_OPair(U_1011,U_1011),U_1010),U_1009)),U_1013))
& U_1010 != U_1009
& hBOOL(hAPP(hAPP(c_member(U_1011),U_1009),U_1012)) )
& hBOOL(hAPP(hAPP(c_member(U_1011),U_1010),U_1012)) ) )
& ( ! [U_1008] :
( ! [U_1007] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1011,U_1011)),hAPP(hAPP(c_Product__Type_OPair(U_1011,U_1011),U_1007),U_1008)),U_1013))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1011,U_1011)),hAPP(hAPP(c_Product__Type_OPair(U_1011,U_1011),U_1008),U_1007)),U_1013))
| U_1008 = U_1007
| ~ hBOOL(hAPP(hAPP(c_member(U_1011),U_1007),U_1012)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1011),U_1008),U_1012)) )
| ~ c_Relation_Ototal__on(U_1011,U_1012,U_1013) ) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_1019,U_1017,U_1015] :
( c_Relation_Ototal__on(U_1015,U_1017,U_1019)
| ? [U_1010] :
( ? [U_1009] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),U_1009),U_1010)),U_1019))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),U_1010),U_1009)),U_1019))
& U_1010 != U_1009
& hBOOL(hAPP(hAPP(c_member(U_1015),U_1009),U_1017)) )
& hBOOL(hAPP(hAPP(c_member(U_1015),U_1010),U_1017)) ) )
& ! [U_1018,U_1016,U_1014] :
( ! [U_1008] :
( ! [U_1007] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1007),U_1008)),U_1018))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1008),U_1007)),U_1018))
| U_1008 = U_1007
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1007),U_1016)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1008),U_1016)) )
| ~ c_Relation_Ototal__on(U_1014,U_1016,U_1018) ) ),
inference(miniscope,[status(thm)],[f_157_2]) ).
fof(f_157_4,plain,
( ! [U_1019,U_1017,U_1015] :
( c_Relation_Ototal__on(U_1015,U_1017,U_1019)
| ( ? [U_1009] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),U_1009),sK76(U_1019,U_1017,U_1015))),U_1019))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),sK76(U_1019,U_1017,U_1015)),U_1009)),U_1019))
& sK76(U_1019,U_1017,U_1015) != U_1009
& hBOOL(hAPP(hAPP(c_member(U_1015),U_1009),U_1017)) )
& hBOOL(hAPP(hAPP(c_member(U_1015),sK76(U_1019,U_1017,U_1015)),U_1017)) ) )
& ! [U_1018,U_1016,U_1014] :
( ! [U_1008] :
( ! [U_1007] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1007),U_1008)),U_1018))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1008),U_1007)),U_1018))
| U_1008 = U_1007
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1007),U_1016)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1008),U_1016)) )
| ~ c_Relation_Ototal__on(U_1014,U_1016,U_1018) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1010,sK76(U_1019,U_1017,U_1015))],[f_157_3]) ).
fof(f_157_5,plain,
( ! [U_1019,U_1017,U_1015] :
( c_Relation_Ototal__on(U_1015,U_1017,U_1019)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),sK77(U_1019,U_1017,U_1015)),sK76(U_1019,U_1017,U_1015))),U_1019))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),sK76(U_1019,U_1017,U_1015)),sK77(U_1019,U_1017,U_1015))),U_1019))
& sK76(U_1019,U_1017,U_1015) != sK77(U_1019,U_1017,U_1015)
& hBOOL(hAPP(hAPP(c_member(U_1015),sK77(U_1019,U_1017,U_1015)),U_1017))
& hBOOL(hAPP(hAPP(c_member(U_1015),sK76(U_1019,U_1017,U_1015)),U_1017)) ) )
& ! [U_1018,U_1016,U_1014] :
( ! [U_1008] :
( ! [U_1007] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1007),U_1008)),U_1018))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1008),U_1007)),U_1018))
| U_1008 = U_1007
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1007),U_1016)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1008),U_1016)) )
| ~ c_Relation_Ototal__on(U_1014,U_1016,U_1018) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1009,sK77(U_1019,U_1017,U_1015))],[f_157_4]) ).
fof(f_157_6,plain,
( ! [U_1015,U_1017,U_1019] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),sK77(U_1019,U_1017,U_1015)),sK76(U_1019,U_1017,U_1015))),U_1019))
| ~ sP80(U_1015,U_1017,U_1019) )
& ! [U_1015,U_1017,U_1019] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),sK76(U_1019,U_1017,U_1015)),sK77(U_1019,U_1017,U_1015))),U_1019))
| ~ sP80(U_1015,U_1017,U_1019) )
& ! [U_1015,U_1017,U_1019] :
( sK76(U_1019,U_1017,U_1015) != sK77(U_1019,U_1017,U_1015)
| ~ sP80(U_1015,U_1017,U_1019) )
& ! [U_1015,U_1017,U_1019] :
( hBOOL(hAPP(hAPP(c_member(U_1015),sK77(U_1019,U_1017,U_1015)),U_1017))
| ~ sP80(U_1015,U_1017,U_1019) )
& ! [U_1015,U_1017,U_1019] :
( hBOOL(hAPP(hAPP(c_member(U_1015),sK76(U_1019,U_1017,U_1015)),U_1017))
| ~ sP80(U_1015,U_1017,U_1019) )
& ! [U_1015,U_1017,U_1019] :
( c_Relation_Ototal__on(U_1015,U_1017,U_1019)
| sP80(U_1015,U_1017,U_1019) )
& ! [U_1014,U_1007,U_1018,U_1008,U_1016] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1007),U_1008)),U_1018))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1008),U_1007)),U_1018))
| U_1008 = U_1007
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1007),U_1016))
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1008),U_1016))
| ~ c_Relation_Ototal__on(U_1014,U_1016,U_1018) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_157_5]) ).
cnf(f_157_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1007),U_1008)),U_1018))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1014,U_1014)),hAPP(hAPP(c_Product__Type_OPair(U_1014,U_1014),U_1008),U_1007)),U_1018))
| U_1008 = U_1007
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1007),U_1016))
| ~ hBOOL(hAPP(hAPP(c_member(U_1014),U_1008),U_1016))
| ~ c_Relation_Ototal__on(U_1014,U_1016,U_1018) ),
inference(clausify,[status(thm)],[f_157_6]) ).
cnf(f_157_8,plain,
( c_Relation_Ototal__on(U_1015,U_1017,U_1019)
| sP80(U_1015,U_1017,U_1019) ),
inference(clausify,[status(thm)],[f_157_6]) ).
cnf(f_157_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_1015),sK76(U_1019,U_1017,U_1015)),U_1017))
| ~ sP80(U_1015,U_1017,U_1019) ),
inference(clausify,[status(thm)],[f_157_6]) ).
cnf(f_157_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_1015),sK77(U_1019,U_1017,U_1015)),U_1017))
| ~ sP80(U_1015,U_1017,U_1019) ),
inference(clausify,[status(thm)],[f_157_6]) ).
cnf(f_157_11,plain,
( sK76(U_1019,U_1017,U_1015) != sK77(U_1019,U_1017,U_1015)
| ~ sP80(U_1015,U_1017,U_1019) ),
inference(clausify,[status(thm)],[f_157_6]) ).
cnf(f_157_12,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),sK76(U_1019,U_1017,U_1015)),sK77(U_1019,U_1017,U_1015))),U_1019))
| ~ sP80(U_1015,U_1017,U_1019) ),
inference(clausify,[status(thm)],[f_157_6]) ).
cnf(f_157_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),sK77(U_1019,U_1017,U_1015)),sK76(U_1019,U_1017,U_1015))),U_1019))
| ~ sP80(U_1015,U_1017,U_1019) ),
inference(clausify,[status(thm)],[f_157_6]) ).
fof(f_158_1,plain,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
( ( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2]) ).
fof(f_158_2,plain,
! [U_1025,U_1024,U_1023,U_1022,U_1021,U_1020] :
( ( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1020,tc_fun(U_1021,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1020,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),U_1020),c_COMBC(U_1021,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_prod(U_1020,U_1021)),tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),U_1020),hAPP(c_COMBB(tc_prod(U_1020,U_1021),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool),U_1021),c_member(tc_prod(U_1020,U_1021)))),c_Product__Type_OPair(U_1020,U_1021)))),U_1022),hAPP(hAPP(c_COMBC(U_1020,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),U_1020),c_COMBC(U_1021,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_prod(U_1020,U_1021)),tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),U_1020),hAPP(c_COMBB(tc_prod(U_1020,U_1021),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool),U_1021),c_member(tc_prod(U_1020,U_1021)))),c_Product__Type_OPair(U_1020,U_1021)))),U_1023)),U_1024),U_1025))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1020,U_1021)),hAPP(hAPP(c_Product__Type_OPair(U_1020,U_1021),U_1024),U_1025)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),U_1022,U_1023))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1020,U_1021)),hAPP(hAPP(c_Product__Type_OPair(U_1020,U_1021),U_1024),U_1025)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),U_1022,U_1023)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1020,tc_fun(U_1021,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1020,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),U_1020),c_COMBC(U_1021,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_prod(U_1020,U_1021)),tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),U_1020),hAPP(c_COMBB(tc_prod(U_1020,U_1021),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool),U_1021),c_member(tc_prod(U_1020,U_1021)))),c_Product__Type_OPair(U_1020,U_1021)))),U_1022),hAPP(hAPP(c_COMBC(U_1020,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_fun(U_1021,tc_HOL_Obool)),U_1020),c_COMBC(U_1021,tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1021,tc_prod(U_1020,U_1021)),tc_fun(U_1021,tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool)),U_1020),hAPP(c_COMBB(tc_prod(U_1020,U_1021),tc_fun(tc_fun(tc_prod(U_1020,U_1021),tc_HOL_Obool),tc_HOL_Obool),U_1021),c_member(tc_prod(U_1020,U_1021)))),c_Product__Type_OPair(U_1020,U_1021)))),U_1023)),U_1024),U_1025)) ) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
( ! [U_1037,U_1035,U_1033,U_1031,U_1029,U_1027] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1027,tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1027,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),U_1027),c_COMBC(U_1029,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_prod(U_1027,U_1029)),tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),U_1027),hAPP(c_COMBB(tc_prod(U_1027,U_1029),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool),U_1029),c_member(tc_prod(U_1027,U_1029)))),c_Product__Type_OPair(U_1027,U_1029)))),U_1031),hAPP(hAPP(c_COMBC(U_1027,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),U_1027),c_COMBC(U_1029,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_prod(U_1027,U_1029)),tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),U_1027),hAPP(c_COMBB(tc_prod(U_1027,U_1029),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool),U_1029),c_member(tc_prod(U_1027,U_1029)))),c_Product__Type_OPair(U_1027,U_1029)))),U_1033)),U_1035),U_1037))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1027,U_1029)),hAPP(hAPP(c_Product__Type_OPair(U_1027,U_1029),U_1035),U_1037)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),U_1031,U_1033))) )
& ! [U_1036,U_1034,U_1032,U_1030,U_1028,U_1026] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1026,U_1028)),hAPP(hAPP(c_Product__Type_OPair(U_1026,U_1028),U_1034),U_1036)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),U_1030,U_1032)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1026,tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1026,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),U_1026),c_COMBC(U_1028,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_prod(U_1026,U_1028)),tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),U_1026),hAPP(c_COMBB(tc_prod(U_1026,U_1028),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool),U_1028),c_member(tc_prod(U_1026,U_1028)))),c_Product__Type_OPair(U_1026,U_1028)))),U_1030),hAPP(hAPP(c_COMBC(U_1026,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),U_1026),c_COMBC(U_1028,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_prod(U_1026,U_1028)),tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),U_1026),hAPP(c_COMBB(tc_prod(U_1026,U_1028),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool),U_1028),c_member(tc_prod(U_1026,U_1028)))),c_Product__Type_OPair(U_1026,U_1028)))),U_1032)),U_1034),U_1036)) ) ),
inference(miniscope,[status(thm)],[f_158_2]) ).
fof(f_158_4,plain,
( ! [U_1027,U_1029,U_1031,U_1033,U_1035,U_1037] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1027,tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1027,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),U_1027),c_COMBC(U_1029,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_prod(U_1027,U_1029)),tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),U_1027),hAPP(c_COMBB(tc_prod(U_1027,U_1029),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool),U_1029),c_member(tc_prod(U_1027,U_1029)))),c_Product__Type_OPair(U_1027,U_1029)))),U_1031),hAPP(hAPP(c_COMBC(U_1027,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),U_1027),c_COMBC(U_1029,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_prod(U_1027,U_1029)),tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),U_1027),hAPP(c_COMBB(tc_prod(U_1027,U_1029),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool),U_1029),c_member(tc_prod(U_1027,U_1029)))),c_Product__Type_OPair(U_1027,U_1029)))),U_1033)),U_1035),U_1037))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1027,U_1029)),hAPP(hAPP(c_Product__Type_OPair(U_1027,U_1029),U_1035),U_1037)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),U_1031,U_1033))) )
& ! [U_1032,U_1030,U_1028,U_1026,U_1034,U_1036] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1026,U_1028)),hAPP(hAPP(c_Product__Type_OPair(U_1026,U_1028),U_1034),U_1036)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),U_1030,U_1032)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1026,tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1026,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),U_1026),c_COMBC(U_1028,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_prod(U_1026,U_1028)),tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),U_1026),hAPP(c_COMBB(tc_prod(U_1026,U_1028),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool),U_1028),c_member(tc_prod(U_1026,U_1028)))),c_Product__Type_OPair(U_1026,U_1028)))),U_1030),hAPP(hAPP(c_COMBC(U_1026,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),U_1026),c_COMBC(U_1028,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_prod(U_1026,U_1028)),tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),U_1026),hAPP(c_COMBB(tc_prod(U_1026,U_1028),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool),U_1028),c_member(tc_prod(U_1026,U_1028)))),c_Product__Type_OPair(U_1026,U_1028)))),U_1032)),U_1034),U_1036)) ) ),
inference(definitional_conversion,[status(esa)],[f_158_3]) ).
cnf(f_158_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1026,U_1028)),hAPP(hAPP(c_Product__Type_OPair(U_1026,U_1028),U_1034),U_1036)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),U_1030,U_1032)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1026,tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1026,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),U_1026),c_COMBC(U_1028,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_prod(U_1026,U_1028)),tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),U_1026),hAPP(c_COMBB(tc_prod(U_1026,U_1028),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool),U_1028),c_member(tc_prod(U_1026,U_1028)))),c_Product__Type_OPair(U_1026,U_1028)))),U_1030),hAPP(hAPP(c_COMBC(U_1026,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_fun(U_1028,tc_HOL_Obool)),U_1026),c_COMBC(U_1028,tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1028,tc_prod(U_1026,U_1028)),tc_fun(U_1028,tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool)),U_1026),hAPP(c_COMBB(tc_prod(U_1026,U_1028),tc_fun(tc_fun(tc_prod(U_1026,U_1028),tc_HOL_Obool),tc_HOL_Obool),U_1028),c_member(tc_prod(U_1026,U_1028)))),c_Product__Type_OPair(U_1026,U_1028)))),U_1032)),U_1034),U_1036)) ),
inference(clausify,[status(thm)],[f_158_4]) ).
cnf(f_158_6,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1027,tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1027,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),U_1027),c_COMBC(U_1029,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_prod(U_1027,U_1029)),tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),U_1027),hAPP(c_COMBB(tc_prod(U_1027,U_1029),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool),U_1029),c_member(tc_prod(U_1027,U_1029)))),c_Product__Type_OPair(U_1027,U_1029)))),U_1031),hAPP(hAPP(c_COMBC(U_1027,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_fun(U_1029,tc_HOL_Obool)),U_1027),c_COMBC(U_1029,tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1029,tc_prod(U_1027,U_1029)),tc_fun(U_1029,tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool)),U_1027),hAPP(c_COMBB(tc_prod(U_1027,U_1029),tc_fun(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),tc_HOL_Obool),U_1029),c_member(tc_prod(U_1027,U_1029)))),c_Product__Type_OPair(U_1027,U_1029)))),U_1033)),U_1035),U_1037))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1027,U_1029)),hAPP(hAPP(c_Product__Type_OPair(U_1027,U_1029),U_1035),U_1037)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1027,U_1029),tc_HOL_Obool),U_1031,U_1033))) ),
inference(clausify,[status(thm)],[f_158_4]) ).
fof(f_159_1,plain,
! [V_a,T_a] :
( 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_159_2,plain,
! [U_1039,U_1038] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1038,U_1039,U_1039) = U_1039
| ~ class_Lattices_Osemilattice__inf(U_1038) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_1039,U_1038] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1038,U_1039,U_1039) = U_1039
| ~ class_Lattices_Osemilattice__inf(U_1038) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1038,U_1039,U_1039) = U_1039
| ~ class_Lattices_Osemilattice__inf(U_1038) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
! [V_x,T_a] :
( 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_160_2,plain,
! [U_1041,U_1040] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1040,U_1041,U_1041) = U_1041
| ~ class_Lattices_Osemilattice__inf(U_1040) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_1041,U_1040] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1040,U_1041,U_1041) = U_1041
| ~ class_Lattices_Osemilattice__inf(U_1040) ),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1040,U_1041,U_1041) = U_1041
| ~ class_Lattices_Osemilattice__inf(U_1040) ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [V_b,V_a,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b) = 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_161_2,plain,
! [U_1044,U_1043,U_1042] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1042,U_1043,U_1044) = c_Lattices_Osemilattice__inf__class_Oinf(U_1042,U_1044,U_1043)
| ~ class_Lattices_Osemilattice__inf(U_1042) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_1043,U_1042,U_1044] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1042,U_1043,U_1044) = c_Lattices_Osemilattice__inf__class_Oinf(U_1042,U_1044,U_1043)
| ~ class_Lattices_Osemilattice__inf(U_1042) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1042,U_1043,U_1044) = c_Lattices_Osemilattice__inf__class_Oinf(U_1042,U_1044,U_1043)
| ~ class_Lattices_Osemilattice__inf(U_1042) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
! [V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = 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_162_2,plain,
! [U_1047,U_1046,U_1045] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1045,U_1046,U_1047) = c_Lattices_Osemilattice__inf__class_Oinf(U_1045,U_1047,U_1046)
| ~ class_Lattices_Olattice(U_1045) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_1046,U_1045,U_1047] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1045,U_1046,U_1047) = c_Lattices_Osemilattice__inf__class_Oinf(U_1045,U_1047,U_1046)
| ~ class_Lattices_Olattice(U_1045) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1045,U_1046,U_1047) = c_Lattices_Osemilattice__inf__class_Oinf(U_1045,U_1047,U_1046)
| ~ class_Lattices_Olattice(U_1045) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = 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_163_2,plain,
! [U_1050,U_1049,U_1048] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1048,U_1049,U_1050) = c_Lattices_Osemilattice__inf__class_Oinf(U_1048,U_1050,U_1049)
| ~ class_Lattices_Osemilattice__inf(U_1048) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_1048,U_1049,U_1050] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1048,U_1049,U_1050) = c_Lattices_Osemilattice__inf__class_Oinf(U_1048,U_1050,U_1049)
| ~ class_Lattices_Osemilattice__inf(U_1048) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1048,U_1049,U_1050) = c_Lattices_Osemilattice__inf__class_Oinf(U_1048,U_1050,U_1049)
| ~ class_Lattices_Osemilattice__inf(U_1048) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [V_b,V_a,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) = 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_164_2,plain,
! [U_1053,U_1052,U_1051] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,U_1053)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,U_1053)
| ~ class_Lattices_Osemilattice__inf(U_1051) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_1052,U_1051,U_1053] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,U_1053)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,U_1053)
| ~ class_Lattices_Osemilattice__inf(U_1051) ),
inference(definitional_conversion,[status(esa)],[f_164_2]) ).
cnf(f_164_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,U_1053)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1051,U_1052,U_1053)
| ~ class_Lattices_Osemilattice__inf(U_1051) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,plain,
! [V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = 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_165_2,plain,
! [U_1056,U_1055,U_1054] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,U_1056)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,U_1056)
| ~ class_Lattices_Olattice(U_1054) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_1054,U_1055,U_1056] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,U_1056)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,U_1056)
| ~ class_Lattices_Olattice(U_1054) ),
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,U_1056)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1054,U_1055,U_1056)
| ~ class_Lattices_Olattice(U_1054) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = 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_166_2,plain,
! [U_1059,U_1058,U_1057] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,U_1059)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,U_1059)
| ~ class_Lattices_Osemilattice__inf(U_1057) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_1058,U_1057,U_1059] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,U_1059)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,U_1059)
| ~ class_Lattices_Osemilattice__inf(U_1057) ),
inference(definitional_conversion,[status(esa)],[f_166_2]) ).
cnf(f_166_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,U_1059)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1057,U_1058,U_1059)
| ~ class_Lattices_Osemilattice__inf(U_1057) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,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_167_2,plain,
! [U_1063,U_1062,U_1061,U_1060] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1061,c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1062,U_1063)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1062,c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1061,U_1063))
| ~ class_Lattices_Osemilattice__inf(U_1060) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_1061,U_1060,U_1062,U_1063] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1061,c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1062,U_1063)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1062,c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1061,U_1063))
| ~ class_Lattices_Osemilattice__inf(U_1060) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1061,c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1062,U_1063)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1062,c_Lattices_Osemilattice__inf__class_Oinf(U_1060,U_1061,U_1063))
| ~ class_Lattices_Osemilattice__inf(U_1060) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,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_168_2,plain,
! [U_1067,U_1066,U_1065,U_1064] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1065,c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1066,U_1067)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1066,c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1065,U_1067))
| ~ class_Lattices_Olattice(U_1064) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_1064,U_1065,U_1066,U_1067] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1065,c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1066,U_1067)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1066,c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1065,U_1067))
| ~ class_Lattices_Olattice(U_1064) ),
inference(definitional_conversion,[status(esa)],[f_168_2]) ).
cnf(f_168_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1065,c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1066,U_1067)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1066,c_Lattices_Osemilattice__inf__class_Oinf(U_1064,U_1065,U_1067))
| ~ class_Lattices_Olattice(U_1064) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,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_169_2,plain,
! [U_1071,U_1070,U_1069,U_1068] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1069,c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1070,U_1071)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1070,c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1069,U_1071))
| ~ class_Lattices_Osemilattice__inf(U_1068) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_1069,U_1068,U_1070,U_1071] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1069,c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1070,U_1071)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1070,c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1069,U_1071))
| ~ class_Lattices_Osemilattice__inf(U_1068) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1069,c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1070,U_1071)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1070,c_Lattices_Osemilattice__inf__class_Oinf(U_1068,U_1069,U_1071))
| ~ class_Lattices_Osemilattice__inf(U_1068) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,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_170_2,plain,
! [U_1075,U_1074,U_1073,U_1072] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1072,c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1073,U_1074),U_1075) = c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1073,c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1074,U_1075))
| ~ class_Lattices_Osemilattice__inf(U_1072) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_1073,U_1072,U_1074,U_1075] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1072,c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1073,U_1074),U_1075) = c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1073,c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1074,U_1075))
| ~ class_Lattices_Osemilattice__inf(U_1072) ),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1072,c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1073,U_1074),U_1075) = c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1073,c_Lattices_Osemilattice__inf__class_Oinf(U_1072,U_1074,U_1075))
| ~ class_Lattices_Osemilattice__inf(U_1072) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,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_171_2,plain,
! [U_1079,U_1078,U_1077,U_1076] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1076,c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1077,U_1078),U_1079) = c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1077,c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1078,U_1079))
| ~ class_Lattices_Olattice(U_1076) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_1076,U_1077,U_1078,U_1079] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1076,c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1077,U_1078),U_1079) = c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1077,c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1078,U_1079))
| ~ class_Lattices_Olattice(U_1076) ),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1076,c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1077,U_1078),U_1079) = c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1077,c_Lattices_Osemilattice__inf__class_Oinf(U_1076,U_1078,U_1079))
| ~ class_Lattices_Olattice(U_1076) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,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_172_2,plain,
! [U_1083,U_1082,U_1081,U_1080] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1080,c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1081,U_1082),U_1083) = c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1081,c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1082,U_1083))
| ~ class_Lattices_Osemilattice__inf(U_1080) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_1081,U_1080,U_1082,U_1083] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1080,c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1081,U_1082),U_1083) = c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1081,c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1082,U_1083))
| ~ class_Lattices_Osemilattice__inf(U_1080) ),
inference(definitional_conversion,[status(esa)],[f_172_2]) ).
cnf(f_172_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1080,c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1081,U_1082),U_1083) = c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1081,c_Lattices_Osemilattice__inf__class_Oinf(U_1080,U_1082,U_1083))
| ~ class_Lattices_Osemilattice__inf(U_1080) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),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),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),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__inv__image]) ).
fof(f_173_2,plain,
! [U_1089,U_1088,U_1087,U_1086,U_1085,U_1084] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1084,U_1084)),hAPP(hAPP(c_Product__Type_OPair(U_1084,U_1084),U_1085),U_1086)),hAPP(hAPP(c_Relation_Oinv__image(U_1087,U_1084),U_1088),U_1089)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1087,U_1087)),hAPP(hAPP(c_Product__Type_OPair(U_1087,U_1087),hAPP(U_1089,U_1085)),hAPP(U_1089,U_1086))),U_1088)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1087,U_1087)),hAPP(hAPP(c_Product__Type_OPair(U_1087,U_1087),hAPP(U_1089,U_1085)),hAPP(U_1089,U_1086))),U_1088))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1084,U_1084)),hAPP(hAPP(c_Product__Type_OPair(U_1084,U_1084),U_1085),U_1086)),hAPP(hAPP(c_Relation_Oinv__image(U_1087,U_1084),U_1088),U_1089))) ) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
( ! [U_1101,U_1099,U_1097,U_1095,U_1093] :
( ! [U_1091] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1091,U_1091)),hAPP(hAPP(c_Product__Type_OPair(U_1091,U_1091),U_1093),U_1095)),hAPP(hAPP(c_Relation_Oinv__image(U_1097,U_1091),U_1099),U_1101)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1097,U_1097)),hAPP(hAPP(c_Product__Type_OPair(U_1097,U_1097),hAPP(U_1101,U_1093)),hAPP(U_1101,U_1095))),U_1099)) )
& ! [U_1100,U_1098,U_1096,U_1094,U_1092] :
( ! [U_1090] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1090,U_1090)),hAPP(hAPP(c_Product__Type_OPair(U_1090,U_1090),U_1092),U_1094)),hAPP(hAPP(c_Relation_Oinv__image(U_1096,U_1090),U_1098),U_1100)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1096,U_1096)),hAPP(hAPP(c_Product__Type_OPair(U_1096,U_1096),hAPP(U_1100,U_1092)),hAPP(U_1100,U_1094))),U_1098)) ) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
fof(f_173_4,plain,
( ! [U_1091,U_1093,U_1095,U_1097,U_1099,U_1101] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1091,U_1091)),hAPP(hAPP(c_Product__Type_OPair(U_1091,U_1091),U_1093),U_1095)),hAPP(hAPP(c_Relation_Oinv__image(U_1097,U_1091),U_1099),U_1101)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1097,U_1097)),hAPP(hAPP(c_Product__Type_OPair(U_1097,U_1097),hAPP(U_1101,U_1093)),hAPP(U_1101,U_1095))),U_1099)) )
& ! [U_1096,U_1092,U_1090,U_1094,U_1098,U_1100] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1090,U_1090)),hAPP(hAPP(c_Product__Type_OPair(U_1090,U_1090),U_1092),U_1094)),hAPP(hAPP(c_Relation_Oinv__image(U_1096,U_1090),U_1098),U_1100)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1096,U_1096)),hAPP(hAPP(c_Product__Type_OPair(U_1096,U_1096),hAPP(U_1100,U_1092)),hAPP(U_1100,U_1094))),U_1098)) ) ),
inference(definitional_conversion,[status(esa)],[f_173_3]) ).
cnf(f_173_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1090,U_1090)),hAPP(hAPP(c_Product__Type_OPair(U_1090,U_1090),U_1092),U_1094)),hAPP(hAPP(c_Relation_Oinv__image(U_1096,U_1090),U_1098),U_1100)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1096,U_1096)),hAPP(hAPP(c_Product__Type_OPair(U_1096,U_1096),hAPP(U_1100,U_1092)),hAPP(U_1100,U_1094))),U_1098)) ),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1091,U_1091)),hAPP(hAPP(c_Product__Type_OPair(U_1091,U_1091),U_1093),U_1095)),hAPP(hAPP(c_Relation_Oinv__image(U_1097,U_1091),U_1099),U_1101)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1097,U_1097)),hAPP(hAPP(c_Product__Type_OPair(U_1097,U_1097),hAPP(U_1101,U_1093)),hAPP(U_1101,U_1095))),U_1099)) ),
inference(clausify,[status(thm)],[f_173_4]) ).
fof(f_174_1,plain,
! [V_aa_2,V_r_2,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
| ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__onD]) ).
fof(f_174_2,plain,
! [U_1105,U_1104,U_1103,U_1102] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1102,U_1102)),hAPP(hAPP(c_Product__Type_OPair(U_1102,U_1102),U_1105),U_1105)),U_1104))
| ~ hBOOL(hAPP(hAPP(c_member(U_1102),U_1105),U_1103))
| ~ c_Relation_Orefl__on(U_1102,U_1103,U_1104) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_1102,U_1103,U_1104,U_1105] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1102,U_1102)),hAPP(hAPP(c_Product__Type_OPair(U_1102,U_1102),U_1105),U_1105)),U_1104))
| ~ hBOOL(hAPP(hAPP(c_member(U_1102),U_1105),U_1103))
| ~ c_Relation_Orefl__on(U_1102,U_1103,U_1104) ),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1102,U_1102)),hAPP(hAPP(c_Product__Type_OPair(U_1102,U_1102),U_1105),U_1105)),U_1104))
| ~ hBOOL(hAPP(hAPP(c_member(U_1102),U_1105),U_1103))
| ~ c_Relation_Orefl__on(U_1102,U_1103,U_1104) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
| ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__onD2]) ).
fof(f_175_2,plain,
! [U_1110,U_1109,U_1108,U_1107,U_1106] :
( hBOOL(hAPP(hAPP(c_member(U_1106),U_1110),U_1107))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1106,U_1106)),hAPP(hAPP(c_Product__Type_OPair(U_1106,U_1106),U_1109),U_1110)),U_1108))
| ~ c_Relation_Orefl__on(U_1106,U_1107,U_1108) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_1106,U_1107,U_1108,U_1109,U_1110] :
( hBOOL(hAPP(hAPP(c_member(U_1106),U_1110),U_1107))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1106,U_1106)),hAPP(hAPP(c_Product__Type_OPair(U_1106,U_1106),U_1109),U_1110)),U_1108))
| ~ c_Relation_Orefl__on(U_1106,U_1107,U_1108) ),
inference(definitional_conversion,[status(esa)],[f_175_2]) ).
cnf(f_175_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1106),U_1110),U_1107))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1106,U_1106)),hAPP(hAPP(c_Product__Type_OPair(U_1106,U_1106),U_1109),U_1110)),U_1108))
| ~ c_Relation_Orefl__on(U_1106,U_1107,U_1108) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
| ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__onD1]) ).
fof(f_176_2,plain,
! [U_1115,U_1114,U_1113,U_1112,U_1111] :
( hBOOL(hAPP(hAPP(c_member(U_1111),U_1114),U_1112))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1111,U_1111)),hAPP(hAPP(c_Product__Type_OPair(U_1111,U_1111),U_1114),U_1115)),U_1113))
| ~ c_Relation_Orefl__on(U_1111,U_1112,U_1113) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_1111,U_1112,U_1113,U_1114,U_1115] :
( hBOOL(hAPP(hAPP(c_member(U_1111),U_1114),U_1112))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1111,U_1111)),hAPP(hAPP(c_Product__Type_OPair(U_1111,U_1111),U_1114),U_1115)),U_1113))
| ~ c_Relation_Orefl__on(U_1111,U_1112,U_1113) ),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1111),U_1114),U_1112))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1111,U_1111)),hAPP(hAPP(c_Product__Type_OPair(U_1111,U_1111),U_1114),U_1115)),U_1113))
| ~ c_Relation_Orefl__on(U_1111,U_1112,U_1113) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl]) ).
fof(f_177_2,plain,
! [U_1119,U_1118,U_1117,U_1116] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1116,U_1116)),hAPP(hAPP(c_Product__Type_OPair(U_1116,U_1116),U_1117),U_1118)),c_Transitive__Closure_Ortrancl(U_1116,U_1119)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1116,U_1116)),hAPP(hAPP(c_Product__Type_OPair(U_1116,U_1116),U_1117),U_1118)),c_Transitive__Closure_Otrancl(U_1116,U_1119))) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_1116,U_1117,U_1118,U_1119] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1116,U_1116)),hAPP(hAPP(c_Product__Type_OPair(U_1116,U_1116),U_1117),U_1118)),c_Transitive__Closure_Ortrancl(U_1116,U_1119)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1116,U_1116)),hAPP(hAPP(c_Product__Type_OPair(U_1116,U_1116),U_1117),U_1118)),c_Transitive__Closure_Otrancl(U_1116,U_1119))) ),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1116,U_1116)),hAPP(hAPP(c_Product__Type_OPair(U_1116,U_1116),U_1117),U_1118)),c_Transitive__Closure_Ortrancl(U_1116,U_1119)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1116,U_1116)),hAPP(hAPP(c_Product__Type_OPair(U_1116,U_1116),U_1117),U_1118)),c_Transitive__Closure_Otrancl(U_1116,U_1119))) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [V_xa_2,V_x_2,V_r_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2),V_xa_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_xa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_xa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2),V_xa_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp__rtrancl__eq]) ).
fof(f_178_2,plain,
! [U_1123,U_1122,U_1121,U_1120] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1120,hAPP(hAPP(c_COMBC(U_1120,tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_fun(U_1120,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1120,tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_fun(U_1120,tc_HOL_Obool)),U_1120),c_COMBC(U_1120,tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1120,tc_prod(U_1120,U_1120)),tc_fun(U_1120,tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool)),U_1120),hAPP(c_COMBB(tc_prod(U_1120,U_1120),tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool),U_1120),c_member(tc_prod(U_1120,U_1120)))),c_Product__Type_OPair(U_1120,U_1120)))),U_1121)),U_1122),U_1123))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1120,U_1120)),hAPP(hAPP(c_Product__Type_OPair(U_1120,U_1120),U_1122),U_1123)),c_Transitive__Closure_Ortrancl(U_1120,U_1121))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1120,U_1120)),hAPP(hAPP(c_Product__Type_OPair(U_1120,U_1120),U_1122),U_1123)),c_Transitive__Closure_Ortrancl(U_1120,U_1121)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1120,hAPP(hAPP(c_COMBC(U_1120,tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_fun(U_1120,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1120,tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_fun(U_1120,tc_HOL_Obool)),U_1120),c_COMBC(U_1120,tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1120,tc_prod(U_1120,U_1120)),tc_fun(U_1120,tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool)),U_1120),hAPP(c_COMBB(tc_prod(U_1120,U_1120),tc_fun(tc_fun(tc_prod(U_1120,U_1120),tc_HOL_Obool),tc_HOL_Obool),U_1120),c_member(tc_prod(U_1120,U_1120)))),c_Product__Type_OPair(U_1120,U_1120)))),U_1121)),U_1122),U_1123)) ) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
( ! [U_1131,U_1129,U_1127,U_1125] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1125,hAPP(hAPP(c_COMBC(U_1125,tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_fun(U_1125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1125,tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_fun(U_1125,tc_HOL_Obool)),U_1125),c_COMBC(U_1125,tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1125,tc_prod(U_1125,U_1125)),tc_fun(U_1125,tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),U_1125),hAPP(c_COMBB(tc_prod(U_1125,U_1125),tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool),U_1125),c_member(tc_prod(U_1125,U_1125)))),c_Product__Type_OPair(U_1125,U_1125)))),U_1127)),U_1129),U_1131))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1125,U_1125)),hAPP(hAPP(c_Product__Type_OPair(U_1125,U_1125),U_1129),U_1131)),c_Transitive__Closure_Ortrancl(U_1125,U_1127))) )
& ! [U_1130,U_1128,U_1126,U_1124] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1124,U_1124)),hAPP(hAPP(c_Product__Type_OPair(U_1124,U_1124),U_1128),U_1130)),c_Transitive__Closure_Ortrancl(U_1124,U_1126)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1124,hAPP(hAPP(c_COMBC(U_1124,tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_fun(U_1124,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1124,tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_fun(U_1124,tc_HOL_Obool)),U_1124),c_COMBC(U_1124,tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1124,tc_prod(U_1124,U_1124)),tc_fun(U_1124,tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),U_1124),hAPP(c_COMBB(tc_prod(U_1124,U_1124),tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool),U_1124),c_member(tc_prod(U_1124,U_1124)))),c_Product__Type_OPair(U_1124,U_1124)))),U_1126)),U_1128),U_1130)) ) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
fof(f_178_4,plain,
( ! [U_1125,U_1127,U_1129,U_1131] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1125,hAPP(hAPP(c_COMBC(U_1125,tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_fun(U_1125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1125,tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_fun(U_1125,tc_HOL_Obool)),U_1125),c_COMBC(U_1125,tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1125,tc_prod(U_1125,U_1125)),tc_fun(U_1125,tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),U_1125),hAPP(c_COMBB(tc_prod(U_1125,U_1125),tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool),U_1125),c_member(tc_prod(U_1125,U_1125)))),c_Product__Type_OPair(U_1125,U_1125)))),U_1127)),U_1129),U_1131))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1125,U_1125)),hAPP(hAPP(c_Product__Type_OPair(U_1125,U_1125),U_1129),U_1131)),c_Transitive__Closure_Ortrancl(U_1125,U_1127))) )
& ! [U_1126,U_1128,U_1130,U_1124] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1124,U_1124)),hAPP(hAPP(c_Product__Type_OPair(U_1124,U_1124),U_1128),U_1130)),c_Transitive__Closure_Ortrancl(U_1124,U_1126)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1124,hAPP(hAPP(c_COMBC(U_1124,tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_fun(U_1124,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1124,tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_fun(U_1124,tc_HOL_Obool)),U_1124),c_COMBC(U_1124,tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1124,tc_prod(U_1124,U_1124)),tc_fun(U_1124,tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),U_1124),hAPP(c_COMBB(tc_prod(U_1124,U_1124),tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool),U_1124),c_member(tc_prod(U_1124,U_1124)))),c_Product__Type_OPair(U_1124,U_1124)))),U_1126)),U_1128),U_1130)) ) ),
inference(definitional_conversion,[status(esa)],[f_178_3]) ).
cnf(f_178_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1124,U_1124)),hAPP(hAPP(c_Product__Type_OPair(U_1124,U_1124),U_1128),U_1130)),c_Transitive__Closure_Ortrancl(U_1124,U_1126)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1124,hAPP(hAPP(c_COMBC(U_1124,tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_fun(U_1124,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1124,tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_fun(U_1124,tc_HOL_Obool)),U_1124),c_COMBC(U_1124,tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1124,tc_prod(U_1124,U_1124)),tc_fun(U_1124,tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool)),U_1124),hAPP(c_COMBB(tc_prod(U_1124,U_1124),tc_fun(tc_fun(tc_prod(U_1124,U_1124),tc_HOL_Obool),tc_HOL_Obool),U_1124),c_member(tc_prod(U_1124,U_1124)))),c_Product__Type_OPair(U_1124,U_1124)))),U_1126)),U_1128),U_1130)) ),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_6,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1125,hAPP(hAPP(c_COMBC(U_1125,tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_fun(U_1125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1125,tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_fun(U_1125,tc_HOL_Obool)),U_1125),c_COMBC(U_1125,tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1125,tc_prod(U_1125,U_1125)),tc_fun(U_1125,tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool)),U_1125),hAPP(c_COMBB(tc_prod(U_1125,U_1125),tc_fun(tc_fun(tc_prod(U_1125,U_1125),tc_HOL_Obool),tc_HOL_Obool),U_1125),c_member(tc_prod(U_1125,U_1125)))),c_Product__Type_OPair(U_1125,U_1125)))),U_1127)),U_1129),U_1131))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1125,U_1125)),hAPP(hAPP(c_Product__Type_OPair(U_1125,U_1125),U_1129),U_1131)),c_Transitive__Closure_Ortrancl(U_1125,U_1127))) ),
inference(clausify,[status(thm)],[f_178_4]) ).
fof(f_179_1,plain,
! [V_aa_2,V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_aa_2)),
inference(fof_nnf,[status(thm)],[fact_rtranclp_Ortrancl__refl]) ).
fof(f_179_2,plain,
! [U_1134,U_1133,U_1132] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1132,U_1133),U_1134),U_1134)),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_1132,U_1133,U_1134] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1132,U_1133),U_1134),U_1134)),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1132,U_1133),U_1134),U_1134)),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [T_a,V_y_2,V_x_2,V_r_2] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__into__rtranclp]) ).
fof(f_180_2,plain,
! [U_1138,U_1137,U_1136,U_1135] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1138,U_1135),U_1136),U_1137))
| ~ hBOOL(hAPP(hAPP(U_1135,U_1136),U_1137)) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_1135,U_1136,U_1137,U_1138] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1138,U_1135),U_1136),U_1137))
| ~ hBOOL(hAPP(hAPP(U_1135,U_1136),U_1137)) ),
inference(definitional_conversion,[status(esa)],[f_180_2]) ).
cnf(f_180_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1138,U_1135),U_1136),U_1137))
| ~ hBOOL(hAPP(hAPP(U_1135,U_1136),U_1137)) ),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_1,plain,
! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,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_181_2,plain,
! [U_1144,U_1143,U_1142,U_1141,U_1140,U_1139] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1143,tc_fun(U_1144,tc_HOL_Obool)),U_1139,U_1142),U_1140),U_1141))
| ~ hBOOL(hAPP(hAPP(U_1142,U_1140),U_1141))
| ~ hBOOL(hAPP(hAPP(U_1139,U_1140),U_1141)) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_1139,U_1140,U_1141,U_1142,U_1143,U_1144] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1143,tc_fun(U_1144,tc_HOL_Obool)),U_1139,U_1142),U_1140),U_1141))
| ~ hBOOL(hAPP(hAPP(U_1142,U_1140),U_1141))
| ~ hBOOL(hAPP(hAPP(U_1139,U_1140),U_1141)) ),
inference(definitional_conversion,[status(esa)],[f_181_2]) ).
cnf(f_181_4,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1143,tc_fun(U_1144,tc_HOL_Obool)),U_1139,U_1142),U_1140),U_1141))
| ~ hBOOL(hAPP(hAPP(U_1142,U_1140),U_1141))
| ~ hBOOL(hAPP(hAPP(U_1139,U_1140),U_1141)) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
( ( 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(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2E]) ).
fof(f_182_2,plain,
! [U_1150,U_1149,U_1148,U_1147,U_1146,U_1145] :
( ( hBOOL(hAPP(hAPP(U_1148,U_1149),U_1150))
& hBOOL(hAPP(hAPP(U_1147,U_1149),U_1150)) )
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_fun(U_1146,tc_HOL_Obool)),U_1147,U_1148),U_1149),U_1150)) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_1150,U_1149,U_1148,U_1147] :
( ! [U_1146,U_1145] : ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_fun(U_1146,tc_HOL_Obool)),U_1147,U_1148),U_1149),U_1150))
| ( hBOOL(hAPP(hAPP(U_1148,U_1149),U_1150))
& hBOOL(hAPP(hAPP(U_1147,U_1149),U_1150)) ) ),
inference(miniscope,[status(thm)],[f_182_2]) ).
fof(f_182_4,plain,
( ! [U_1147,U_1148,U_1149,U_1150] :
( hBOOL(hAPP(hAPP(U_1148,U_1149),U_1150))
| ~ sP81(U_1147,U_1148,U_1149,U_1150) )
& ! [U_1147,U_1148,U_1149,U_1150] :
( hBOOL(hAPP(hAPP(U_1147,U_1149),U_1150))
| ~ sP81(U_1147,U_1148,U_1149,U_1150) )
& ! [U_1146,U_1145,U_1147,U_1148,U_1149,U_1150] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_fun(U_1146,tc_HOL_Obool)),U_1147,U_1148),U_1149),U_1150))
| sP81(U_1147,U_1148,U_1149,U_1150) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_182_3]) ).
cnf(f_182_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_fun(U_1146,tc_HOL_Obool)),U_1147,U_1148),U_1149),U_1150))
| sP81(U_1147,U_1148,U_1149,U_1150) ),
inference(clausify,[status(thm)],[f_182_4]) ).
cnf(f_182_6,plain,
( hBOOL(hAPP(hAPP(U_1147,U_1149),U_1150))
| ~ sP81(U_1147,U_1148,U_1149,U_1150) ),
inference(clausify,[status(thm)],[f_182_4]) ).
cnf(f_182_7,plain,
( hBOOL(hAPP(hAPP(U_1148,U_1149),U_1150))
| ~ sP81(U_1147,U_1148,U_1149,U_1150) ),
inference(clausify,[status(thm)],[f_182_4]) ).
fof(f_183_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl]) ).
fof(f_183_2,plain,
! [U_1154,U_1153,U_1152,U_1151] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1151,U_1151)),hAPP(hAPP(c_Product__Type_OPair(U_1151,U_1151),U_1152),U_1153)),c_Transitive__Closure_Otrancl(U_1151,U_1154)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1151,U_1151)),hAPP(hAPP(c_Product__Type_OPair(U_1151,U_1151),U_1152),U_1153)),U_1154)) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_1151,U_1152,U_1153,U_1154] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1151,U_1151)),hAPP(hAPP(c_Product__Type_OPair(U_1151,U_1151),U_1152),U_1153)),c_Transitive__Closure_Otrancl(U_1151,U_1154)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1151,U_1151)),hAPP(hAPP(c_Product__Type_OPair(U_1151,U_1151),U_1152),U_1153)),U_1154)) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1151,U_1151)),hAPP(hAPP(c_Product__Type_OPair(U_1151,U_1151),U_1152),U_1153)),c_Transitive__Closure_Otrancl(U_1151,U_1154)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1151,U_1151)),hAPP(hAPP(c_Product__Type_OPair(U_1151,U_1151),U_1152),U_1153)),U_1154)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D1]) ).
fof(f_184_2,plain,
! [U_1160,U_1159,U_1158,U_1157,U_1156,U_1155] :
( hBOOL(hAPP(hAPP(U_1157,U_1159),U_1160))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1155,tc_fun(U_1156,tc_HOL_Obool)),U_1157,U_1158),U_1159),U_1160)) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
! [U_1160,U_1159,U_1158,U_1157] :
( ! [U_1156,U_1155] : ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1155,tc_fun(U_1156,tc_HOL_Obool)),U_1157,U_1158),U_1159),U_1160))
| hBOOL(hAPP(hAPP(U_1157,U_1159),U_1160)) ),
inference(miniscope,[status(thm)],[f_184_2]) ).
fof(f_184_4,plain,
! [U_1155,U_1156,U_1157,U_1158,U_1159,U_1160] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1155,tc_fun(U_1156,tc_HOL_Obool)),U_1157,U_1158),U_1159),U_1160))
| hBOOL(hAPP(hAPP(U_1157,U_1159),U_1160)) ),
inference(definitional_conversion,[status(esa)],[f_184_3]) ).
cnf(f_184_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1155,tc_fun(U_1156,tc_HOL_Obool)),U_1157,U_1158),U_1159),U_1160))
| hBOOL(hAPP(hAPP(U_1157,U_1159),U_1160)) ),
inference(clausify,[status(thm)],[f_184_4]) ).
fof(f_185_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D2]) ).
fof(f_185_2,plain,
! [U_1166,U_1165,U_1164,U_1163,U_1162,U_1161] :
( hBOOL(hAPP(hAPP(U_1164,U_1165),U_1166))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1161,tc_fun(U_1162,tc_HOL_Obool)),U_1163,U_1164),U_1165),U_1166)) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_1166,U_1165,U_1164] :
( ! [U_1163,U_1162,U_1161] : ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1161,tc_fun(U_1162,tc_HOL_Obool)),U_1163,U_1164),U_1165),U_1166))
| hBOOL(hAPP(hAPP(U_1164,U_1165),U_1166)) ),
inference(miniscope,[status(thm)],[f_185_2]) ).
fof(f_185_4,plain,
! [U_1161,U_1162,U_1163,U_1164,U_1165,U_1166] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1161,tc_fun(U_1162,tc_HOL_Obool)),U_1163,U_1164),U_1165),U_1166))
| hBOOL(hAPP(hAPP(U_1164,U_1165),U_1166)) ),
inference(definitional_conversion,[status(esa)],[f_185_3]) ).
cnf(f_185_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1161,tc_fun(U_1162,tc_HOL_Obool)),U_1163,U_1164),U_1165),U_1166))
| hBOOL(hAPP(hAPP(U_1164,U_1165),U_1166)) ),
inference(clausify,[status(thm)],[f_185_4]) ).
fof(f_186_1,plain,
! [V_r_2,T_a] : c_Transitive__Closure_Ortranclp(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_r_2,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(T_a,V_r_2),
inference(fof_nnf,[status(thm)],[fact_rtranclp__r__diff__Id]) ).
fof(f_186_2,plain,
! [U_1168,U_1167] : c_Transitive__Closure_Ortranclp(U_1167,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1167,tc_fun(U_1167,tc_HOL_Obool)),U_1168,hAPP(hAPP(c_COMBB(tc_fun(U_1167,tc_HOL_Obool),tc_fun(U_1167,tc_HOL_Obool),U_1167),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_1167),c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(U_1167,U_1168),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_1167,U_1168] : c_Transitive__Closure_Ortranclp(U_1167,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1167,tc_fun(U_1167,tc_HOL_Obool)),U_1168,hAPP(hAPP(c_COMBB(tc_fun(U_1167,tc_HOL_Obool),tc_fun(U_1167,tc_HOL_Obool),U_1167),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_1167),c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(U_1167,U_1168),
inference(definitional_conversion,[status(esa)],[f_186_2]) ).
cnf(f_186_4,plain,
c_Transitive__Closure_Ortranclp(U_1167,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1167,tc_fun(U_1167,tc_HOL_Obool)),U_1168,hAPP(hAPP(c_COMBB(tc_fun(U_1167,tc_HOL_Obool),tc_fun(U_1167,tc_HOL_Obool),U_1167),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_1167),c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(U_1167,U_1168),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_1,plain,
! [V_r_2,T_a] : c_Transitive__Closure_Ortranclp(T_a,c_Transitive__Closure_Ortranclp(T_a,V_r_2)) = c_Transitive__Closure_Ortranclp(T_a,V_r_2),
inference(fof_nnf,[status(thm)],[fact_rtranclp__idemp]) ).
fof(f_187_2,plain,
! [U_1170,U_1169] : c_Transitive__Closure_Ortranclp(U_1169,c_Transitive__Closure_Ortranclp(U_1169,U_1170)) = c_Transitive__Closure_Ortranclp(U_1169,U_1170),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_1169,U_1170] : c_Transitive__Closure_Ortranclp(U_1169,c_Transitive__Closure_Ortranclp(U_1169,U_1170)) = c_Transitive__Closure_Ortranclp(U_1169,U_1170),
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
c_Transitive__Closure_Ortranclp(U_1169,c_Transitive__Closure_Ortranclp(U_1169,U_1170)) = c_Transitive__Closure_Ortranclp(U_1169,U_1170),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_1,plain,
! [V_aa_2,V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_aa_2)),
inference(fof_nnf,[status(thm)],[fact_rtranclp_Oequations_I1_J]) ).
fof(f_188_2,plain,
! [U_1173,U_1172,U_1171] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1171,U_1172),U_1173),U_1173)),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_1171,U_1172,U_1173] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1171,U_1172),U_1173),U_1173)),
inference(definitional_conversion,[status(esa)],[f_188_2]) ).
cnf(f_188_4,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1171,U_1172),U_1173),U_1173)),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [V_a3_2,V_a1_2,V_r_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),V_a3_2))
| ( ! [B_b] :
( ~ hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),B_b)) )
& V_a3_2 != V_a1_2 ) )
& ( ? [B_b] :
( hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),B_b)) )
| V_a3_2 = V_a1_2
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),V_a3_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp_Oequations_I2_J]) ).
fof(f_189_2,plain,
! [U_1179,U_1178,U_1177,U_1176] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1176,U_1177),U_1178),U_1179))
| ( ! [U_1175] :
( ~ hBOOL(hAPP(hAPP(U_1177,U_1175),U_1179))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1176,U_1177),U_1178),U_1175)) )
& U_1179 != U_1178 ) )
& ( ? [U_1174] :
( hBOOL(hAPP(hAPP(U_1177,U_1174),U_1179))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1176,U_1177),U_1178),U_1174)) )
| U_1179 = U_1178
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1176,U_1177),U_1178),U_1179)) ) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( ! [U_1187,U_1185,U_1183,U_1181] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1187))
| ( ! [U_1175] :
( ~ hBOOL(hAPP(hAPP(U_1183,U_1175),U_1187))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1175)) )
& U_1187 != U_1185 ) )
& ! [U_1186,U_1184,U_1182,U_1180] :
( ? [U_1174] :
( hBOOL(hAPP(hAPP(U_1182,U_1174),U_1186))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),U_1174)) )
| U_1186 = U_1184
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),U_1186)) ) ),
inference(miniscope,[status(thm)],[f_189_2]) ).
fof(f_189_4,plain,
( ! [U_1187,U_1185,U_1183,U_1181] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1187))
| ( ! [U_1175] :
( ~ hBOOL(hAPP(hAPP(U_1183,U_1175),U_1187))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1175)) )
& U_1187 != U_1185 ) )
& ! [U_1186,U_1184,U_1182,U_1180] :
( ( hBOOL(hAPP(hAPP(U_1182,sK78(U_1186,U_1184,U_1182,U_1180)),U_1186))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),sK78(U_1186,U_1184,U_1182,U_1180))) )
| U_1186 = U_1184
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),U_1186)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1174,sK78(U_1186,U_1184,U_1182,U_1180))],[f_189_3]) ).
fof(f_189_5,plain,
( ! [U_1185,U_1175,U_1183,U_1181,U_1187] :
( ~ hBOOL(hAPP(hAPP(U_1183,U_1175),U_1187))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1175))
| ~ sP83(U_1185,U_1175,U_1183,U_1181,U_1187) )
& ! [U_1185,U_1175,U_1183,U_1181,U_1187] :
( U_1187 != U_1185
| ~ sP83(U_1185,U_1175,U_1183,U_1181,U_1187) )
& ! [U_1184,U_1182,U_1180,U_1186] :
( hBOOL(hAPP(hAPP(U_1182,sK78(U_1186,U_1184,U_1182,U_1180)),U_1186))
| ~ sP82(U_1184,U_1182,U_1180,U_1186) )
& ! [U_1184,U_1182,U_1180,U_1186] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),sK78(U_1186,U_1184,U_1182,U_1180)))
| ~ sP82(U_1184,U_1182,U_1180,U_1186) )
& ! [U_1185,U_1175,U_1183,U_1181,U_1187] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1187))
| sP83(U_1185,U_1175,U_1183,U_1181,U_1187) )
& ! [U_1184,U_1182,U_1180,U_1186] :
( sP82(U_1184,U_1182,U_1180,U_1186)
| U_1186 = U_1184
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),U_1186)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82,sP83])],[f_189_4]) ).
cnf(f_189_6,plain,
( sP82(U_1184,U_1182,U_1180,U_1186)
| U_1186 = U_1184
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),U_1186)) ),
inference(clausify,[status(thm)],[f_189_5]) ).
cnf(f_189_7,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1187))
| sP83(U_1185,U_1175,U_1183,U_1181,U_1187) ),
inference(clausify,[status(thm)],[f_189_5]) ).
cnf(f_189_8,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1180,U_1182),U_1184),sK78(U_1186,U_1184,U_1182,U_1180)))
| ~ sP82(U_1184,U_1182,U_1180,U_1186) ),
inference(clausify,[status(thm)],[f_189_5]) ).
cnf(f_189_9,plain,
( hBOOL(hAPP(hAPP(U_1182,sK78(U_1186,U_1184,U_1182,U_1180)),U_1186))
| ~ sP82(U_1184,U_1182,U_1180,U_1186) ),
inference(clausify,[status(thm)],[f_189_5]) ).
cnf(f_189_10,plain,
( U_1187 != U_1185
| ~ sP83(U_1185,U_1175,U_1183,U_1181,U_1187) ),
inference(clausify,[status(thm)],[f_189_5]) ).
cnf(f_189_11,plain,
( ~ hBOOL(hAPP(hAPP(U_1183,U_1175),U_1187))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1181,U_1183),U_1185),U_1175))
| ~ sP83(U_1185,U_1175,U_1183,U_1181,U_1187) ),
inference(clausify,[status(thm)],[f_189_5]) ).
fof(f_190_1,plain,
! [V_ca_2,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtranclp__into__rtranclp]) ).
fof(f_190_2,plain,
! [U_1192,U_1191,U_1190,U_1189,U_1188] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1191,U_1188),U_1189),U_1192))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1191,U_1188),U_1190),U_1192))
| ~ hBOOL(hAPP(hAPP(U_1188,U_1189),U_1190)) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_1190,U_1191,U_1188,U_1192,U_1189] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1191,U_1188),U_1189),U_1192))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1191,U_1188),U_1190),U_1192))
| ~ hBOOL(hAPP(hAPP(U_1188,U_1189),U_1190)) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1191,U_1188),U_1189),U_1192))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1191,U_1188),U_1190),U_1192))
| ~ hBOOL(hAPP(hAPP(U_1188,U_1189),U_1190)) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp_Ortrancl__into__rtrancl]) ).
fof(f_191_2,plain,
! [U_1197,U_1196,U_1195,U_1194,U_1193] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1193,U_1194),U_1195),U_1197))
| ~ hBOOL(hAPP(hAPP(U_1194,U_1196),U_1197))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1193,U_1194),U_1195),U_1196)) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_1193,U_1194,U_1195,U_1196,U_1197] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1193,U_1194),U_1195),U_1197))
| ~ hBOOL(hAPP(hAPP(U_1194,U_1196),U_1197))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1193,U_1194),U_1195),U_1196)) ),
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1193,U_1194),U_1195),U_1197))
| ~ hBOOL(hAPP(hAPP(U_1194,U_1196),U_1197))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1193,U_1194),U_1195),U_1196)) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_1,plain,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp__trans]) ).
fof(f_192_2,plain,
! [U_1202,U_1201,U_1200,U_1199,U_1198] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1200),U_1202))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1201),U_1202))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1200),U_1201)) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_1198,U_1199,U_1200,U_1201,U_1202] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1200),U_1202))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1201),U_1202))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1200),U_1201)) ),
inference(definitional_conversion,[status(esa)],[f_192_2]) ).
cnf(f_192_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1200),U_1202))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1201),U_1202))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1198,U_1199),U_1200),U_1201)) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [V_r_2,V_p_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H]) ).
fof(f_193_2,plain,
! [U_1205,U_1204,U_1203] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1203,U_1203)),U_1204),c_Transitive__Closure_Otrancl(U_1203,U_1205)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1203,U_1203)),U_1204),U_1205)) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_1203,U_1204,U_1205] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1203,U_1203)),U_1204),c_Transitive__Closure_Otrancl(U_1203,U_1205)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1203,U_1203)),U_1204),U_1205)) ),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1203,U_1203)),U_1204),c_Transitive__Closure_Otrancl(U_1203,U_1205)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1203,U_1203)),U_1204),U_1205)) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__absorb]) ).
fof(f_194_2,plain,
! [U_1207,U_1206] : c_Transitive__Closure_Otrancl(U_1206,c_Transitive__Closure_Ortrancl(U_1206,U_1207)) = c_Transitive__Closure_Ortrancl(U_1206,U_1207),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_1206,U_1207] : c_Transitive__Closure_Otrancl(U_1206,c_Transitive__Closure_Ortrancl(U_1206,U_1207)) = c_Transitive__Closure_Ortrancl(U_1206,U_1207),
inference(definitional_conversion,[status(esa)],[f_194_2]) ).
cnf(f_194_4,plain,
c_Transitive__Closure_Otrancl(U_1206,c_Transitive__Closure_Ortrancl(U_1206,U_1207)) = c_Transitive__Closure_Ortrancl(U_1206,U_1207),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__absorb]) ).
fof(f_195_2,plain,
! [U_1209,U_1208] : c_Transitive__Closure_Ortrancl(U_1208,c_Transitive__Closure_Otrancl(U_1208,U_1209)) = c_Transitive__Closure_Ortrancl(U_1208,U_1209),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_1208,U_1209] : c_Transitive__Closure_Ortrancl(U_1208,c_Transitive__Closure_Otrancl(U_1208,U_1209)) = c_Transitive__Closure_Ortrancl(U_1208,U_1209),
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
c_Transitive__Closure_Ortrancl(U_1208,c_Transitive__Closure_Otrancl(U_1208,U_1209)) = c_Transitive__Closure_Ortrancl(U_1208,U_1209),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [V_r_2,T_a] : c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ODomain(T_a,T_a,V_r_2),
inference(fof_nnf,[status(thm)],[fact_trancl__domain]) ).
fof(f_196_2,plain,
! [U_1211,U_1210] : c_Relation_ODomain(U_1210,U_1210,c_Transitive__Closure_Otrancl(U_1210,U_1211)) = c_Relation_ODomain(U_1210,U_1210,U_1211),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
! [U_1210,U_1211] : c_Relation_ODomain(U_1210,U_1210,c_Transitive__Closure_Otrancl(U_1210,U_1211)) = c_Relation_ODomain(U_1210,U_1210,U_1211),
inference(definitional_conversion,[status(esa)],[f_196_2]) ).
cnf(f_196_4,plain,
c_Relation_ODomain(U_1210,U_1210,c_Transitive__Closure_Otrancl(U_1210,U_1211)) = c_Relation_ODomain(U_1210,U_1210,U_1211),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_1,plain,
! [V_r_2,T_a] : c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ORange(T_a,T_a,V_r_2),
inference(fof_nnf,[status(thm)],[fact_trancl__range]) ).
fof(f_197_2,plain,
! [U_1213,U_1212] : c_Relation_ORange(U_1212,U_1212,c_Transitive__Closure_Otrancl(U_1212,U_1213)) = c_Relation_ORange(U_1212,U_1212,U_1213),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_1212,U_1213] : c_Relation_ORange(U_1212,U_1212,c_Transitive__Closure_Otrancl(U_1212,U_1213)) = c_Relation_ORange(U_1212,U_1212,U_1213),
inference(definitional_conversion,[status(esa)],[f_197_2]) ).
cnf(f_197_4,plain,
c_Relation_ORange(U_1212,U_1212,c_Transitive__Closure_Otrancl(U_1212,U_1213)) = c_Relation_ORange(U_1212,U_1212,U_1213),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_1,plain,
! [V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_aa_2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) ),
inference(fof_nnf,[status(thm)],[fact_accp__downwards]) ).
fof(f_198_2,plain,
! [U_1217,U_1216,U_1215,U_1214] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1214,U_1215),U_1217))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1214,U_1215),U_1217),U_1216))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1214,U_1215),U_1216)) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_1214,U_1215,U_1216,U_1217] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1214,U_1215),U_1217))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1214,U_1215),U_1217),U_1216))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1214,U_1215),U_1216)) ),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1214,U_1215),U_1217))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1214,U_1215),U_1217),U_1216))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1214,U_1215),U_1216)) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [V_aa_2,V_ba_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_aa_2)) ),
inference(fof_nnf,[status(thm)],[fact_accp__downwards__aux]) ).
fof(f_199_2,plain,
! [U_1221,U_1220,U_1219,U_1218] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1218,U_1219),U_1220))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1218,U_1219),U_1221))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1218,U_1219),U_1220),U_1221)) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_1218,U_1219,U_1220,U_1221] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1218,U_1219),U_1220))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1218,U_1219),U_1221))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1218,U_1219),U_1220),U_1221)) ),
inference(definitional_conversion,[status(esa)],[f_199_2]) ).
cnf(f_199_4,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1218,U_1219),U_1220))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1218,U_1219),U_1221))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1218,U_1219),U_1220),U_1221)) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,plain,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
( c_Relation_Orefl__on(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))
| ~ c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
| ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__on__Int]) ).
fof(f_200_2,plain,
! [U_1226,U_1225,U_1224,U_1223,U_1222] :
( c_Relation_Orefl__on(U_1222,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1222,tc_HOL_Obool),U_1223,U_1225),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1222,U_1222),tc_HOL_Obool),U_1224,U_1226))
| ~ c_Relation_Orefl__on(U_1222,U_1225,U_1226)
| ~ c_Relation_Orefl__on(U_1222,U_1223,U_1224) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_1223,U_1222,U_1224,U_1225,U_1226] :
( c_Relation_Orefl__on(U_1222,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1222,tc_HOL_Obool),U_1223,U_1225),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1222,U_1222),tc_HOL_Obool),U_1224,U_1226))
| ~ c_Relation_Orefl__on(U_1222,U_1225,U_1226)
| ~ c_Relation_Orefl__on(U_1222,U_1223,U_1224) ),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
( c_Relation_Orefl__on(U_1222,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1222,tc_HOL_Obool),U_1223,U_1225),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1222,U_1222),tc_HOL_Obool),U_1224,U_1226))
| ~ c_Relation_Orefl__on(U_1222,U_1225,U_1226)
| ~ c_Relation_Orefl__on(U_1222,U_1223,U_1224) ),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_1,plain,
! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_refl__on__Id__on]) ).
fof(f_201_2,plain,
! [U_1228,U_1227] : c_Relation_Orefl__on(U_1227,U_1228,c_Relation_OId__on(U_1227,U_1228)),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_1228,U_1227] : c_Relation_Orefl__on(U_1227,U_1228,c_Relation_OId__on(U_1227,U_1228)),
inference(definitional_conversion,[status(esa)],[f_201_2]) ).
cnf(f_201_4,plain,
c_Relation_Orefl__on(U_1227,U_1228,c_Relation_OId__on(U_1227,U_1228)),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_1,plain,
! [V_ca_2,V_R_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl]) ).
fof(f_202_2,plain,
! [U_1233,U_1232,U_1231,U_1230,U_1229] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1230),U_1233)),c_Transitive__Closure_Otrancl(U_1229,U_1232)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1231),U_1233)),U_1232))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1230),U_1231)),U_1232)) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_1229,U_1230,U_1231,U_1232,U_1233] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1230),U_1233)),c_Transitive__Closure_Otrancl(U_1229,U_1232)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1231),U_1233)),U_1232))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1230),U_1231)),U_1232)) ),
inference(definitional_conversion,[status(esa)],[f_202_2]) ).
cnf(f_202_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1230),U_1233)),c_Transitive__Closure_Otrancl(U_1229,U_1232)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1231),U_1233)),U_1232))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),hAPP(hAPP(c_Product__Type_OPair(U_1229,U_1229),U_1230),U_1231)),U_1232)) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2]) ).
fof(f_203_2,plain,
! [U_1238,U_1237,U_1236,U_1235,U_1234] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1235),U_1238)),c_Transitive__Closure_Otrancl(U_1234,U_1237)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1236),U_1238)),c_Transitive__Closure_Otrancl(U_1234,U_1237)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1235),U_1236)),U_1237)) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_1234,U_1235,U_1236,U_1237,U_1238] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1235),U_1238)),c_Transitive__Closure_Otrancl(U_1234,U_1237)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1236),U_1238)),c_Transitive__Closure_Otrancl(U_1234,U_1237)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1235),U_1236)),U_1237)) ),
inference(definitional_conversion,[status(esa)],[f_203_2]) ).
cnf(f_203_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1235),U_1238)),c_Transitive__Closure_Otrancl(U_1234,U_1237)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1236),U_1238)),c_Transitive__Closure_Otrancl(U_1234,U_1237)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1234,U_1234)),hAPP(hAPP(c_Product__Type_OPair(U_1234,U_1234),U_1235),U_1236)),U_1237)) ),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl]) ).
fof(f_204_2,plain,
! [U_1243,U_1242,U_1241,U_1240,U_1239] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1240),U_1243)),c_Transitive__Closure_Otrancl(U_1239,U_1242)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1241),U_1243)),U_1242))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1240),U_1241)),c_Transitive__Closure_Otrancl(U_1239,U_1242))) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_1239,U_1240,U_1241,U_1242,U_1243] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1240),U_1243)),c_Transitive__Closure_Otrancl(U_1239,U_1242)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1241),U_1243)),U_1242))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1240),U_1241)),c_Transitive__Closure_Otrancl(U_1239,U_1242))) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1240),U_1243)),c_Transitive__Closure_Otrancl(U_1239,U_1242)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1241),U_1243)),U_1242))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1239,U_1239)),hAPP(hAPP(c_Product__Type_OPair(U_1239,U_1239),U_1240),U_1241)),c_Transitive__Closure_Otrancl(U_1239,U_1242))) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__trans]) ).
fof(f_205_2,plain,
! [U_1248,U_1247,U_1246,U_1245,U_1244] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1245),U_1248)),c_Transitive__Closure_Otrancl(U_1244,U_1247)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1246),U_1248)),c_Transitive__Closure_Otrancl(U_1244,U_1247)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1245),U_1246)),c_Transitive__Closure_Otrancl(U_1244,U_1247))) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_1246,U_1247,U_1248,U_1244,U_1245] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1245),U_1248)),c_Transitive__Closure_Otrancl(U_1244,U_1247)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1246),U_1248)),c_Transitive__Closure_Otrancl(U_1244,U_1247)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1245),U_1246)),c_Transitive__Closure_Otrancl(U_1244,U_1247))) ),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1245),U_1248)),c_Transitive__Closure_Otrancl(U_1244,U_1247)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1246),U_1248)),c_Transitive__Closure_Otrancl(U_1244,U_1247)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1244,U_1244)),hAPP(hAPP(c_Product__Type_OPair(U_1244,U_1244),U_1245),U_1246)),c_Transitive__Closure_Otrancl(U_1244,U_1247))) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_1,plain,
! [V_R_2,V_y_2,V_x_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
| V_x_2 = V_y_2 )
& V_x_2 != V_y_2 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
& V_x_2 != V_y_2 )
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl]) ).
fof(f_206_2,plain,
! [U_1252,U_1251,U_1250,U_1249] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1249,U_1249)),hAPP(hAPP(c_Product__Type_OPair(U_1249,U_1249),U_1250),U_1251)),c_Transitive__Closure_Ortrancl(U_1249,U_1252)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1249,U_1249)),hAPP(hAPP(c_Product__Type_OPair(U_1249,U_1249),U_1250),U_1251)),c_Transitive__Closure_Otrancl(U_1249,U_1252)))
| U_1250 = U_1251 )
& U_1250 != U_1251 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1249,U_1249)),hAPP(hAPP(c_Product__Type_OPair(U_1249,U_1249),U_1250),U_1251)),c_Transitive__Closure_Otrancl(U_1249,U_1252)))
& U_1250 != U_1251 )
| U_1250 = U_1251
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1249,U_1249)),hAPP(hAPP(c_Product__Type_OPair(U_1249,U_1249),U_1250),U_1251)),c_Transitive__Closure_Ortrancl(U_1249,U_1252))) ) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
( ! [U_1260,U_1258,U_1256,U_1254] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1256),U_1258)),c_Transitive__Closure_Ortrancl(U_1254,U_1260)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1256),U_1258)),c_Transitive__Closure_Otrancl(U_1254,U_1260)))
| U_1256 = U_1258 )
& U_1256 != U_1258 ) )
& ! [U_1259,U_1257,U_1255,U_1253] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1253,U_1253)),hAPP(hAPP(c_Product__Type_OPair(U_1253,U_1253),U_1255),U_1257)),c_Transitive__Closure_Otrancl(U_1253,U_1259)))
& U_1255 != U_1257 )
| U_1255 = U_1257
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1253,U_1253)),hAPP(hAPP(c_Product__Type_OPair(U_1253,U_1253),U_1255),U_1257)),c_Transitive__Closure_Ortrancl(U_1253,U_1259))) ) ),
inference(miniscope,[status(thm)],[f_206_2]) ).
fof(f_206_4,plain,
( ! [U_1256,U_1254,U_1258,U_1260] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1256),U_1258)),c_Transitive__Closure_Otrancl(U_1254,U_1260)))
| U_1256 = U_1258
| ~ sP85(U_1256,U_1254,U_1258,U_1260) )
& ! [U_1256,U_1254,U_1258,U_1260] :
( U_1256 != U_1258
| ~ sP85(U_1256,U_1254,U_1258,U_1260) )
& ! [U_1255,U_1253,U_1259,U_1257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1253,U_1253)),hAPP(hAPP(c_Product__Type_OPair(U_1253,U_1253),U_1255),U_1257)),c_Transitive__Closure_Otrancl(U_1253,U_1259)))
| ~ sP84(U_1255,U_1253,U_1259,U_1257) )
& ! [U_1255,U_1253,U_1259,U_1257] :
( U_1255 != U_1257
| ~ sP84(U_1255,U_1253,U_1259,U_1257) )
& ! [U_1256,U_1254,U_1258,U_1260] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1256),U_1258)),c_Transitive__Closure_Ortrancl(U_1254,U_1260)))
| sP85(U_1256,U_1254,U_1258,U_1260) )
& ! [U_1255,U_1253,U_1259,U_1257] :
( sP84(U_1255,U_1253,U_1259,U_1257)
| U_1255 = U_1257
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1253,U_1253)),hAPP(hAPP(c_Product__Type_OPair(U_1253,U_1253),U_1255),U_1257)),c_Transitive__Closure_Ortrancl(U_1253,U_1259))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84,sP85])],[f_206_3]) ).
cnf(f_206_5,plain,
( sP84(U_1255,U_1253,U_1259,U_1257)
| U_1255 = U_1257
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1253,U_1253)),hAPP(hAPP(c_Product__Type_OPair(U_1253,U_1253),U_1255),U_1257)),c_Transitive__Closure_Ortrancl(U_1253,U_1259))) ),
inference(clausify,[status(thm)],[f_206_4]) ).
cnf(f_206_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1256),U_1258)),c_Transitive__Closure_Ortrancl(U_1254,U_1260)))
| sP85(U_1256,U_1254,U_1258,U_1260) ),
inference(clausify,[status(thm)],[f_206_4]) ).
cnf(f_206_7,plain,
( U_1255 != U_1257
| ~ sP84(U_1255,U_1253,U_1259,U_1257) ),
inference(clausify,[status(thm)],[f_206_4]) ).
cnf(f_206_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1253,U_1253)),hAPP(hAPP(c_Product__Type_OPair(U_1253,U_1253),U_1255),U_1257)),c_Transitive__Closure_Otrancl(U_1253,U_1259)))
| ~ sP84(U_1255,U_1253,U_1259,U_1257) ),
inference(clausify,[status(thm)],[f_206_4]) ).
cnf(f_206_9,plain,
( U_1256 != U_1258
| ~ sP85(U_1256,U_1254,U_1258,U_1260) ),
inference(clausify,[status(thm)],[f_206_4]) ).
cnf(f_206_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1256),U_1258)),c_Transitive__Closure_Otrancl(U_1254,U_1260)))
| U_1256 = U_1258
| ~ sP85(U_1256,U_1254,U_1258,U_1260) ),
inference(clausify,[status(thm)],[f_206_4]) ).
fof(f_207_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2]) ).
fof(f_207_2,plain,
! [U_1265,U_1264,U_1263,U_1262,U_1261] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1262),U_1265)),c_Transitive__Closure_Otrancl(U_1261,U_1264)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1263),U_1265)),c_Transitive__Closure_Ortrancl(U_1261,U_1264)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1262),U_1263)),U_1264)) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_1261,U_1262,U_1263,U_1264,U_1265] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1262),U_1265)),c_Transitive__Closure_Otrancl(U_1261,U_1264)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1263),U_1265)),c_Transitive__Closure_Ortrancl(U_1261,U_1264)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1262),U_1263)),U_1264)) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1262),U_1265)),c_Transitive__Closure_Otrancl(U_1261,U_1264)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1263),U_1265)),c_Transitive__Closure_Ortrancl(U_1261,U_1264)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1261,U_1261)),hAPP(hAPP(c_Product__Type_OPair(U_1261,U_1261),U_1262),U_1263)),U_1264)) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_1,plain,
! [V_R_2,V_ba_2,V_aa_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
& V_aa_2 != V_ba_2 )
| V_aa_2 = V_ba_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtranclD]) ).
fof(f_208_2,plain,
! [U_1269,U_1268,U_1267,U_1266] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1266,U_1266)),hAPP(hAPP(c_Product__Type_OPair(U_1266,U_1266),U_1267),U_1268)),c_Transitive__Closure_Otrancl(U_1266,U_1269)))
& U_1267 != U_1268 )
| U_1267 = U_1268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1266,U_1266)),hAPP(hAPP(c_Product__Type_OPair(U_1266,U_1266),U_1267),U_1268)),c_Transitive__Closure_Ortrancl(U_1266,U_1269))) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
( ! [U_1266,U_1267,U_1268,U_1269] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1266,U_1266)),hAPP(hAPP(c_Product__Type_OPair(U_1266,U_1266),U_1267),U_1268)),c_Transitive__Closure_Otrancl(U_1266,U_1269)))
| ~ sP86(U_1266,U_1267,U_1268,U_1269) )
& ! [U_1266,U_1267,U_1268,U_1269] :
( U_1267 != U_1268
| ~ sP86(U_1266,U_1267,U_1268,U_1269) )
& ! [U_1266,U_1267,U_1268,U_1269] :
( sP86(U_1266,U_1267,U_1268,U_1269)
| U_1267 = U_1268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1266,U_1266)),hAPP(hAPP(c_Product__Type_OPair(U_1266,U_1266),U_1267),U_1268)),c_Transitive__Closure_Ortrancl(U_1266,U_1269))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_208_2]) ).
cnf(f_208_4,plain,
( sP86(U_1266,U_1267,U_1268,U_1269)
| U_1267 = U_1268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1266,U_1266)),hAPP(hAPP(c_Product__Type_OPair(U_1266,U_1266),U_1267),U_1268)),c_Transitive__Closure_Ortrancl(U_1266,U_1269))) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_5,plain,
( U_1267 != U_1268
| ~ sP86(U_1266,U_1267,U_1268,U_1269) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1266,U_1266)),hAPP(hAPP(c_Product__Type_OPair(U_1266,U_1266),U_1267),U_1268)),c_Transitive__Closure_Otrancl(U_1266,U_1269)))
| ~ sP86(U_1266,U_1267,U_1268,U_1269) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1]) ).
fof(f_209_2,plain,
! [U_1274,U_1273,U_1272,U_1271,U_1270] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1271),U_1274)),c_Transitive__Closure_Otrancl(U_1270,U_1273)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1272),U_1274)),U_1273))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1271),U_1272)),c_Transitive__Closure_Ortrancl(U_1270,U_1273))) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_1270,U_1271,U_1272,U_1273,U_1274] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1271),U_1274)),c_Transitive__Closure_Otrancl(U_1270,U_1273)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1272),U_1274)),U_1273))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1271),U_1272)),c_Transitive__Closure_Ortrancl(U_1270,U_1273))) ),
inference(definitional_conversion,[status(esa)],[f_209_2]) ).
cnf(f_209_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1271),U_1274)),c_Transitive__Closure_Otrancl(U_1270,U_1273)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1272),U_1274)),U_1273))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1270,U_1270)),hAPP(hAPP(c_Product__Type_OPair(U_1270,U_1270),U_1271),U_1272)),c_Transitive__Closure_Ortrancl(U_1270,U_1273))) ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_1,plain,
! [V_ca_2,V_r_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl]) ).
fof(f_210_2,plain,
! [U_1279,U_1278,U_1277,U_1276,U_1275] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1276),U_1279)),c_Transitive__Closure_Otrancl(U_1275,U_1278)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1277),U_1279)),c_Transitive__Closure_Ortrancl(U_1275,U_1278)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1276),U_1277)),c_Transitive__Closure_Otrancl(U_1275,U_1278))) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_1275,U_1276,U_1277,U_1278,U_1279] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1276),U_1279)),c_Transitive__Closure_Otrancl(U_1275,U_1278)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1277),U_1279)),c_Transitive__Closure_Ortrancl(U_1275,U_1278)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1276),U_1277)),c_Transitive__Closure_Otrancl(U_1275,U_1278))) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1276),U_1279)),c_Transitive__Closure_Otrancl(U_1275,U_1278)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1277),U_1279)),c_Transitive__Closure_Ortrancl(U_1275,U_1278)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1275,U_1275)),hAPP(hAPP(c_Product__Type_OPair(U_1275,U_1275),U_1276),U_1277)),c_Transitive__Closure_Otrancl(U_1275,U_1278))) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl]) ).
fof(f_211_2,plain,
! [U_1284,U_1283,U_1282,U_1281,U_1280] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1281),U_1284)),c_Transitive__Closure_Otrancl(U_1280,U_1283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1282),U_1284)),c_Transitive__Closure_Otrancl(U_1280,U_1283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1281),U_1282)),c_Transitive__Closure_Ortrancl(U_1280,U_1283))) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_1281,U_1280,U_1282,U_1283,U_1284] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1281),U_1284)),c_Transitive__Closure_Otrancl(U_1280,U_1283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1282),U_1284)),c_Transitive__Closure_Otrancl(U_1280,U_1283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1281),U_1282)),c_Transitive__Closure_Ortrancl(U_1280,U_1283))) ),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1281),U_1284)),c_Transitive__Closure_Otrancl(U_1280,U_1283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1282),U_1284)),c_Transitive__Closure_Otrancl(U_1280,U_1283)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1280,U_1280)),hAPP(hAPP(c_Product__Type_OPair(U_1280,U_1280),U_1281),U_1282)),c_Transitive__Closure_Ortrancl(U_1280,U_1283))) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_1,plain,
! [V_R_2,V_y_2,V_x_2,T_a] :
( ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_tranclD2]) ).
fof(f_212_2,plain,
! [U_1289,U_1288,U_1287,U_1286] :
( ? [U_1285] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1285),U_1288)),U_1289))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),U_1285)),c_Transitive__Closure_Ortrancl(U_1286,U_1289))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),U_1288)),c_Transitive__Closure_Otrancl(U_1286,U_1289))) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_1289,U_1288,U_1287,U_1286] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),sK79(U_1289,U_1288,U_1287,U_1286)),U_1288)),U_1289))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),sK79(U_1289,U_1288,U_1287,U_1286))),c_Transitive__Closure_Ortrancl(U_1286,U_1289))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),U_1288)),c_Transitive__Closure_Otrancl(U_1286,U_1289))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1285,sK79(U_1289,U_1288,U_1287,U_1286))],[f_212_2]) ).
fof(f_212_4,plain,
( ! [U_1286,U_1287,U_1288,U_1289] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),sK79(U_1289,U_1288,U_1287,U_1286)),U_1288)),U_1289))
| ~ sP87(U_1286,U_1287,U_1288,U_1289) )
& ! [U_1286,U_1287,U_1288,U_1289] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),sK79(U_1289,U_1288,U_1287,U_1286))),c_Transitive__Closure_Ortrancl(U_1286,U_1289)))
| ~ sP87(U_1286,U_1287,U_1288,U_1289) )
& ! [U_1286,U_1287,U_1288,U_1289] :
( sP87(U_1286,U_1287,U_1288,U_1289)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),U_1288)),c_Transitive__Closure_Otrancl(U_1286,U_1289))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_212_3]) ).
cnf(f_212_5,plain,
( sP87(U_1286,U_1287,U_1288,U_1289)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),U_1288)),c_Transitive__Closure_Otrancl(U_1286,U_1289))) ),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),U_1287),sK79(U_1289,U_1288,U_1287,U_1286))),c_Transitive__Closure_Ortrancl(U_1286,U_1289)))
| ~ sP87(U_1286,U_1287,U_1288,U_1289) ),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1286,U_1286)),hAPP(hAPP(c_Product__Type_OPair(U_1286,U_1286),sK79(U_1289,U_1288,U_1287,U_1286)),U_1288)),U_1289))
| ~ sP87(U_1286,U_1287,U_1288,U_1289) ),
inference(clausify,[status(thm)],[f_212_4]) ).
fof(f_213_1,plain,
! [V_R_2,V_y_2,V_x_2,T_a] :
( ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_tranclD]) ).
fof(f_213_2,plain,
! [U_1294,U_1293,U_1292,U_1291] :
( ? [U_1290] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1290),U_1293)),c_Transitive__Closure_Ortrancl(U_1291,U_1294)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),U_1290)),U_1294)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),U_1293)),c_Transitive__Closure_Otrancl(U_1291,U_1294))) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_1294,U_1293,U_1292,U_1291] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),sK80(U_1294,U_1293,U_1292,U_1291)),U_1293)),c_Transitive__Closure_Ortrancl(U_1291,U_1294)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),sK80(U_1294,U_1293,U_1292,U_1291))),U_1294)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),U_1293)),c_Transitive__Closure_Otrancl(U_1291,U_1294))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1290,sK80(U_1294,U_1293,U_1292,U_1291))],[f_213_2]) ).
fof(f_213_4,plain,
( ! [U_1291,U_1292,U_1293,U_1294] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),sK80(U_1294,U_1293,U_1292,U_1291)),U_1293)),c_Transitive__Closure_Ortrancl(U_1291,U_1294)))
| ~ sP88(U_1291,U_1292,U_1293,U_1294) )
& ! [U_1291,U_1292,U_1293,U_1294] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),sK80(U_1294,U_1293,U_1292,U_1291))),U_1294))
| ~ sP88(U_1291,U_1292,U_1293,U_1294) )
& ! [U_1291,U_1292,U_1293,U_1294] :
( sP88(U_1291,U_1292,U_1293,U_1294)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),U_1293)),c_Transitive__Closure_Otrancl(U_1291,U_1294))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_213_3]) ).
cnf(f_213_5,plain,
( sP88(U_1291,U_1292,U_1293,U_1294)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),U_1293)),c_Transitive__Closure_Otrancl(U_1291,U_1294))) ),
inference(clausify,[status(thm)],[f_213_4]) ).
cnf(f_213_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),U_1292),sK80(U_1294,U_1293,U_1292,U_1291))),U_1294))
| ~ sP88(U_1291,U_1292,U_1293,U_1294) ),
inference(clausify,[status(thm)],[f_213_4]) ).
cnf(f_213_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1291,U_1291)),hAPP(hAPP(c_Product__Type_OPair(U_1291,U_1291),sK80(U_1294,U_1293,U_1292,U_1291)),U_1293)),c_Transitive__Closure_Ortrancl(U_1291,U_1294)))
| ~ sP88(U_1291,U_1292,U_1293,U_1294) ),
inference(clausify,[status(thm)],[f_213_4]) ).
fof(f_214_1,plain,
! [V_r_2,T_a] :
( ( c_Wellfounded_Oacyclic(T_a,V_r_2)
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) )
& ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__def]) ).
fof(f_214_2,plain,
! [U_1298,U_1297] :
( ( c_Wellfounded_Oacyclic(U_1297,U_1298)
| ? [U_1296] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1296),U_1296)),c_Transitive__Closure_Otrancl(U_1297,U_1298))) )
& ( ! [U_1295] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1295),U_1295)),c_Transitive__Closure_Otrancl(U_1297,U_1298)))
| ~ c_Wellfounded_Oacyclic(U_1297,U_1298) ) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
( ! [U_1302,U_1300] :
( c_Wellfounded_Oacyclic(U_1300,U_1302)
| ? [U_1296] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1300,U_1300)),hAPP(hAPP(c_Product__Type_OPair(U_1300,U_1300),U_1296),U_1296)),c_Transitive__Closure_Otrancl(U_1300,U_1302))) )
& ! [U_1301,U_1299] :
( ! [U_1295] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1299,U_1299)),hAPP(hAPP(c_Product__Type_OPair(U_1299,U_1299),U_1295),U_1295)),c_Transitive__Closure_Otrancl(U_1299,U_1301)))
| ~ c_Wellfounded_Oacyclic(U_1299,U_1301) ) ),
inference(miniscope,[status(thm)],[f_214_2]) ).
fof(f_214_4,plain,
( ! [U_1302,U_1300] :
( c_Wellfounded_Oacyclic(U_1300,U_1302)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1300,U_1300)),hAPP(hAPP(c_Product__Type_OPair(U_1300,U_1300),sK81(U_1302,U_1300)),sK81(U_1302,U_1300))),c_Transitive__Closure_Otrancl(U_1300,U_1302))) )
& ! [U_1301,U_1299] :
( ! [U_1295] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1299,U_1299)),hAPP(hAPP(c_Product__Type_OPair(U_1299,U_1299),U_1295),U_1295)),c_Transitive__Closure_Otrancl(U_1299,U_1301)))
| ~ c_Wellfounded_Oacyclic(U_1299,U_1301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_1296,sK81(U_1302,U_1300))],[f_214_3]) ).
fof(f_214_5,plain,
( ! [U_1300,U_1302] :
( c_Wellfounded_Oacyclic(U_1300,U_1302)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1300,U_1300)),hAPP(hAPP(c_Product__Type_OPair(U_1300,U_1300),sK81(U_1302,U_1300)),sK81(U_1302,U_1300))),c_Transitive__Closure_Otrancl(U_1300,U_1302))) )
& ! [U_1301,U_1295,U_1299] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1299,U_1299)),hAPP(hAPP(c_Product__Type_OPair(U_1299,U_1299),U_1295),U_1295)),c_Transitive__Closure_Otrancl(U_1299,U_1301)))
| ~ c_Wellfounded_Oacyclic(U_1299,U_1301) ) ),
inference(definitional_conversion,[status(esa)],[f_214_4]) ).
cnf(f_214_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1299,U_1299)),hAPP(hAPP(c_Product__Type_OPair(U_1299,U_1299),U_1295),U_1295)),c_Transitive__Closure_Otrancl(U_1299,U_1301)))
| ~ c_Wellfounded_Oacyclic(U_1299,U_1301) ),
inference(clausify,[status(thm)],[f_214_5]) ).
cnf(f_214_7,plain,
( c_Wellfounded_Oacyclic(U_1300,U_1302)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1300,U_1300)),hAPP(hAPP(c_Product__Type_OPair(U_1300,U_1300),sK81(U_1302,U_1300)),sK81(U_1302,U_1300))),c_Transitive__Closure_Otrancl(U_1300,U_1302))) ),
inference(clausify,[status(thm)],[f_214_5]) ).
fof(f_215_1,plain,
! [V_y_2,V_x_2,V_r_2,T_a] :
( V_x_2 != V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_irrefl__trancl__rD]) ).
fof(f_215_2,plain,
! [U_1307,U_1306,U_1305,U_1304] :
( U_1306 != U_1307
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),U_1306),U_1307)),U_1305))
| ? [U_1303] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),U_1303),U_1303)),c_Transitive__Closure_Otrancl(U_1304,U_1305))) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_1307,U_1306,U_1305,U_1304] :
( U_1306 != U_1307
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),U_1306),U_1307)),U_1305))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),sK82(U_1307,U_1306,U_1305,U_1304)),sK82(U_1307,U_1306,U_1305,U_1304))),c_Transitive__Closure_Otrancl(U_1304,U_1305))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_1303,sK82(U_1307,U_1306,U_1305,U_1304))],[f_215_2]) ).
fof(f_215_4,plain,
! [U_1304,U_1305,U_1306,U_1307] :
( U_1306 != U_1307
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),U_1306),U_1307)),U_1305))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),sK82(U_1307,U_1306,U_1305,U_1304)),sK82(U_1307,U_1306,U_1305,U_1304))),c_Transitive__Closure_Otrancl(U_1304,U_1305))) ),
inference(definitional_conversion,[status(esa)],[f_215_3]) ).
cnf(f_215_5,plain,
( U_1306 != U_1307
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),U_1306),U_1307)),U_1305))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1304,U_1304)),hAPP(hAPP(c_Product__Type_OPair(U_1304,U_1304),sK82(U_1307,U_1306,U_1305,U_1304)),sK82(U_1307,U_1306,U_1305,U_1304))),c_Transitive__Closure_Otrancl(U_1304,U_1305))) ),
inference(clausify,[status(thm)],[f_215_4]) ).
fof(f_216_1,plain,
! [V_r_2,V_z_2,V_x_2,T_a] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_r_2)) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_converse__tranclE]) ).
fof(f_216_2,plain,
! [U_1312,U_1311,U_1310,U_1309] :
( ? [U_1308] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1308),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1308)),U_1312)) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),U_1312))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312))) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_1312,U_1311,U_1310,U_1309] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),sK83(U_1312,U_1311,U_1310,U_1309)),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),sK83(U_1312,U_1311,U_1310,U_1309))),U_1312)) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),U_1312))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_1308,sK83(U_1312,U_1311,U_1310,U_1309))],[f_216_2]) ).
fof(f_216_4,plain,
( ! [U_1309,U_1310,U_1311,U_1312] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),sK83(U_1312,U_1311,U_1310,U_1309)),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312)))
| ~ sP89(U_1309,U_1310,U_1311,U_1312) )
& ! [U_1309,U_1310,U_1311,U_1312] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),sK83(U_1312,U_1311,U_1310,U_1309))),U_1312))
| ~ sP89(U_1309,U_1310,U_1311,U_1312) )
& ! [U_1309,U_1310,U_1311,U_1312] :
( sP89(U_1309,U_1310,U_1311,U_1312)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),U_1312))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_216_3]) ).
cnf(f_216_5,plain,
( sP89(U_1309,U_1310,U_1311,U_1312)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),U_1312))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312))) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),U_1310),sK83(U_1312,U_1311,U_1310,U_1309))),U_1312))
| ~ sP89(U_1309,U_1310,U_1311,U_1312) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1309,U_1309)),hAPP(hAPP(c_Product__Type_OPair(U_1309,U_1309),sK83(U_1312,U_1311,U_1310,U_1309)),U_1311)),c_Transitive__Closure_Otrancl(U_1309,U_1312)))
| ~ sP89(U_1309,U_1310,U_1311,U_1312) ),
inference(clausify,[status(thm)],[f_216_4]) ).
fof(f_217_1,plain,
! [V_r_2,T_a] :
( c_Wellfounded_Oacyclic(T_a,V_r_2)
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acyclicI]) ).
fof(f_217_2,plain,
! [U_1315,U_1314] :
( c_Wellfounded_Oacyclic(U_1314,U_1315)
| ? [U_1313] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1314,U_1314)),hAPP(hAPP(c_Product__Type_OPair(U_1314,U_1314),U_1313),U_1313)),c_Transitive__Closure_Otrancl(U_1314,U_1315))) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_1315,U_1314] :
( c_Wellfounded_Oacyclic(U_1314,U_1315)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1314,U_1314)),hAPP(hAPP(c_Product__Type_OPair(U_1314,U_1314),sK84(U_1315,U_1314)),sK84(U_1315,U_1314))),c_Transitive__Closure_Otrancl(U_1314,U_1315))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_1313,sK84(U_1315,U_1314))],[f_217_2]) ).
fof(f_217_4,plain,
! [U_1314,U_1315] :
( c_Wellfounded_Oacyclic(U_1314,U_1315)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1314,U_1314)),hAPP(hAPP(c_Product__Type_OPair(U_1314,U_1314),sK84(U_1315,U_1314)),sK84(U_1315,U_1314))),c_Transitive__Closure_Otrancl(U_1314,U_1315))) ),
inference(definitional_conversion,[status(esa)],[f_217_3]) ).
cnf(f_217_5,plain,
( c_Wellfounded_Oacyclic(U_1314,U_1315)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1314,U_1314)),hAPP(hAPP(c_Product__Type_OPair(U_1314,U_1314),sK84(U_1315,U_1314)),sK84(U_1315,U_1314))),c_Transitive__Closure_Otrancl(U_1314,U_1315))) ),
inference(clausify,[status(thm)],[f_217_4]) ).
fof(f_218_1,plain,
! [V_r_2,V_x_2,V_y_2,T_a] :
( ( c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ c_Wellfounded_Oacyclic(T_a,V_r_2) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
& c_Wellfounded_Oacyclic(T_a,V_r_2) )
| ~ c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__insert]) ).
fof(f_218_2,plain,
! [U_1319,U_1318,U_1317,U_1316] :
( ( c_Wellfounded_Oacyclic(U_1316,c_Set_Oinsert(tc_prod(U_1316,U_1316),hAPP(hAPP(c_Product__Type_OPair(U_1316,U_1316),U_1317),U_1318),U_1319))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1316,U_1316)),hAPP(hAPP(c_Product__Type_OPair(U_1316,U_1316),U_1318),U_1317)),c_Transitive__Closure_Ortrancl(U_1316,U_1319)))
| ~ c_Wellfounded_Oacyclic(U_1316,U_1319) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1316,U_1316)),hAPP(hAPP(c_Product__Type_OPair(U_1316,U_1316),U_1318),U_1317)),c_Transitive__Closure_Ortrancl(U_1316,U_1319)))
& c_Wellfounded_Oacyclic(U_1316,U_1319) )
| ~ c_Wellfounded_Oacyclic(U_1316,c_Set_Oinsert(tc_prod(U_1316,U_1316),hAPP(hAPP(c_Product__Type_OPair(U_1316,U_1316),U_1317),U_1318),U_1319)) ) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
( ! [U_1327,U_1325,U_1323,U_1321] :
( c_Wellfounded_Oacyclic(U_1321,c_Set_Oinsert(tc_prod(U_1321,U_1321),hAPP(hAPP(c_Product__Type_OPair(U_1321,U_1321),U_1323),U_1325),U_1327))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1321,U_1321)),hAPP(hAPP(c_Product__Type_OPair(U_1321,U_1321),U_1325),U_1323)),c_Transitive__Closure_Ortrancl(U_1321,U_1327)))
| ~ c_Wellfounded_Oacyclic(U_1321,U_1327) )
& ! [U_1326,U_1324,U_1322,U_1320] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1324),U_1322)),c_Transitive__Closure_Ortrancl(U_1320,U_1326)))
& c_Wellfounded_Oacyclic(U_1320,U_1326) )
| ~ c_Wellfounded_Oacyclic(U_1320,c_Set_Oinsert(tc_prod(U_1320,U_1320),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1322),U_1324),U_1326)) ) ),
inference(miniscope,[status(thm)],[f_218_2]) ).
fof(f_218_4,plain,
( ! [U_1320,U_1322,U_1324,U_1326] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1324),U_1322)),c_Transitive__Closure_Ortrancl(U_1320,U_1326)))
| ~ sP90(U_1320,U_1322,U_1324,U_1326) )
& ! [U_1320,U_1322,U_1324,U_1326] :
( c_Wellfounded_Oacyclic(U_1320,U_1326)
| ~ sP90(U_1320,U_1322,U_1324,U_1326) )
& ! [U_1321,U_1323,U_1327,U_1325] :
( c_Wellfounded_Oacyclic(U_1321,c_Set_Oinsert(tc_prod(U_1321,U_1321),hAPP(hAPP(c_Product__Type_OPair(U_1321,U_1321),U_1323),U_1325),U_1327))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1321,U_1321)),hAPP(hAPP(c_Product__Type_OPair(U_1321,U_1321),U_1325),U_1323)),c_Transitive__Closure_Ortrancl(U_1321,U_1327)))
| ~ c_Wellfounded_Oacyclic(U_1321,U_1327) )
& ! [U_1320,U_1322,U_1324,U_1326] :
( sP90(U_1320,U_1322,U_1324,U_1326)
| ~ c_Wellfounded_Oacyclic(U_1320,c_Set_Oinsert(tc_prod(U_1320,U_1320),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1322),U_1324),U_1326)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_218_3]) ).
cnf(f_218_5,plain,
( sP90(U_1320,U_1322,U_1324,U_1326)
| ~ c_Wellfounded_Oacyclic(U_1320,c_Set_Oinsert(tc_prod(U_1320,U_1320),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1322),U_1324),U_1326)) ),
inference(clausify,[status(thm)],[f_218_4]) ).
cnf(f_218_6,plain,
( c_Wellfounded_Oacyclic(U_1321,c_Set_Oinsert(tc_prod(U_1321,U_1321),hAPP(hAPP(c_Product__Type_OPair(U_1321,U_1321),U_1323),U_1325),U_1327))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1321,U_1321)),hAPP(hAPP(c_Product__Type_OPair(U_1321,U_1321),U_1325),U_1323)),c_Transitive__Closure_Ortrancl(U_1321,U_1327)))
| ~ c_Wellfounded_Oacyclic(U_1321,U_1327) ),
inference(clausify,[status(thm)],[f_218_4]) ).
cnf(f_218_7,plain,
( c_Wellfounded_Oacyclic(U_1320,U_1326)
| ~ sP90(U_1320,U_1322,U_1324,U_1326) ),
inference(clausify,[status(thm)],[f_218_4]) ).
cnf(f_218_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1324),U_1322)),c_Transitive__Closure_Ortrancl(U_1320,U_1326)))
| ~ sP90(U_1320,U_1322,U_1324,U_1326) ),
inference(clausify,[status(thm)],[f_218_4]) ).
fof(f_219_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_a] :
( ? [B_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_c),V_ba_2)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_c)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_tranclE]) ).
fof(f_219_2,plain,
! [U_1332,U_1331,U_1330,U_1329] :
( ? [U_1328] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1328),U_1331)),U_1332))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1328)),c_Transitive__Closure_Otrancl(U_1329,U_1332))) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),U_1332))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),c_Transitive__Closure_Otrancl(U_1329,U_1332))) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_1332,U_1331,U_1330,U_1329] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),sK85(U_1332,U_1331,U_1330,U_1329)),U_1331)),U_1332))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),sK85(U_1332,U_1331,U_1330,U_1329))),c_Transitive__Closure_Otrancl(U_1329,U_1332))) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),U_1332))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),c_Transitive__Closure_Otrancl(U_1329,U_1332))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_1328,sK85(U_1332,U_1331,U_1330,U_1329))],[f_219_2]) ).
fof(f_219_4,plain,
( ! [U_1329,U_1330,U_1331,U_1332] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),sK85(U_1332,U_1331,U_1330,U_1329)),U_1331)),U_1332))
| ~ sP91(U_1329,U_1330,U_1331,U_1332) )
& ! [U_1329,U_1330,U_1331,U_1332] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),sK85(U_1332,U_1331,U_1330,U_1329))),c_Transitive__Closure_Otrancl(U_1329,U_1332)))
| ~ sP91(U_1329,U_1330,U_1331,U_1332) )
& ! [U_1329,U_1330,U_1331,U_1332] :
( sP91(U_1329,U_1330,U_1331,U_1332)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),U_1332))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),c_Transitive__Closure_Otrancl(U_1329,U_1332))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_219_3]) ).
cnf(f_219_5,plain,
( sP91(U_1329,U_1330,U_1331,U_1332)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),U_1332))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),U_1331)),c_Transitive__Closure_Otrancl(U_1329,U_1332))) ),
inference(clausify,[status(thm)],[f_219_4]) ).
cnf(f_219_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1330),sK85(U_1332,U_1331,U_1330,U_1329))),c_Transitive__Closure_Otrancl(U_1329,U_1332)))
| ~ sP91(U_1329,U_1330,U_1331,U_1332) ),
inference(clausify,[status(thm)],[f_219_4]) ).
cnf(f_219_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),sK85(U_1332,U_1331,U_1330,U_1329)),U_1331)),U_1332))
| ~ sP91(U_1329,U_1330,U_1331,U_1332) ),
inference(clausify,[status(thm)],[f_219_4]) ).
fof(f_220_1,plain,
! [V_xa_2,V_x_2,V_r_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2),V_xa_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_xa_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_xa_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2),V_xa_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_tranclp__trancl__eq]) ).
fof(f_220_2,plain,
! [U_1336,U_1335,U_1334,U_1333] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1333,hAPP(hAPP(c_COMBC(U_1333,tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_fun(U_1333,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1333,tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_fun(U_1333,tc_HOL_Obool)),U_1333),c_COMBC(U_1333,tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1333,tc_prod(U_1333,U_1333)),tc_fun(U_1333,tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool)),U_1333),hAPP(c_COMBB(tc_prod(U_1333,U_1333),tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool),U_1333),c_member(tc_prod(U_1333,U_1333)))),c_Product__Type_OPair(U_1333,U_1333)))),U_1334)),U_1335),U_1336))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1333,U_1333)),hAPP(hAPP(c_Product__Type_OPair(U_1333,U_1333),U_1335),U_1336)),c_Transitive__Closure_Otrancl(U_1333,U_1334))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1333,U_1333)),hAPP(hAPP(c_Product__Type_OPair(U_1333,U_1333),U_1335),U_1336)),c_Transitive__Closure_Otrancl(U_1333,U_1334)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1333,hAPP(hAPP(c_COMBC(U_1333,tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_fun(U_1333,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1333,tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_fun(U_1333,tc_HOL_Obool)),U_1333),c_COMBC(U_1333,tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1333,tc_prod(U_1333,U_1333)),tc_fun(U_1333,tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool)),U_1333),hAPP(c_COMBB(tc_prod(U_1333,U_1333),tc_fun(tc_fun(tc_prod(U_1333,U_1333),tc_HOL_Obool),tc_HOL_Obool),U_1333),c_member(tc_prod(U_1333,U_1333)))),c_Product__Type_OPair(U_1333,U_1333)))),U_1334)),U_1335),U_1336)) ) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
( ! [U_1344,U_1342,U_1340,U_1338] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1338,hAPP(hAPP(c_COMBC(U_1338,tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_fun(U_1338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1338,tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_fun(U_1338,tc_HOL_Obool)),U_1338),c_COMBC(U_1338,tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1338,tc_prod(U_1338,U_1338)),tc_fun(U_1338,tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),U_1338),hAPP(c_COMBB(tc_prod(U_1338,U_1338),tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool),U_1338),c_member(tc_prod(U_1338,U_1338)))),c_Product__Type_OPair(U_1338,U_1338)))),U_1340)),U_1342),U_1344))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1338,U_1338)),hAPP(hAPP(c_Product__Type_OPair(U_1338,U_1338),U_1342),U_1344)),c_Transitive__Closure_Otrancl(U_1338,U_1340))) )
& ! [U_1343,U_1341,U_1339,U_1337] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1337,U_1337)),hAPP(hAPP(c_Product__Type_OPair(U_1337,U_1337),U_1341),U_1343)),c_Transitive__Closure_Otrancl(U_1337,U_1339)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1337,hAPP(hAPP(c_COMBC(U_1337,tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_fun(U_1337,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1337,tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_fun(U_1337,tc_HOL_Obool)),U_1337),c_COMBC(U_1337,tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1337,tc_prod(U_1337,U_1337)),tc_fun(U_1337,tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),U_1337),hAPP(c_COMBB(tc_prod(U_1337,U_1337),tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool),U_1337),c_member(tc_prod(U_1337,U_1337)))),c_Product__Type_OPair(U_1337,U_1337)))),U_1339)),U_1341),U_1343)) ) ),
inference(miniscope,[status(thm)],[f_220_2]) ).
fof(f_220_4,plain,
( ! [U_1338,U_1340,U_1342,U_1344] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1338,hAPP(hAPP(c_COMBC(U_1338,tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_fun(U_1338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1338,tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_fun(U_1338,tc_HOL_Obool)),U_1338),c_COMBC(U_1338,tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1338,tc_prod(U_1338,U_1338)),tc_fun(U_1338,tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),U_1338),hAPP(c_COMBB(tc_prod(U_1338,U_1338),tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool),U_1338),c_member(tc_prod(U_1338,U_1338)))),c_Product__Type_OPair(U_1338,U_1338)))),U_1340)),U_1342),U_1344))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1338,U_1338)),hAPP(hAPP(c_Product__Type_OPair(U_1338,U_1338),U_1342),U_1344)),c_Transitive__Closure_Otrancl(U_1338,U_1340))) )
& ! [U_1343,U_1339,U_1337,U_1341] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1337,U_1337)),hAPP(hAPP(c_Product__Type_OPair(U_1337,U_1337),U_1341),U_1343)),c_Transitive__Closure_Otrancl(U_1337,U_1339)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1337,hAPP(hAPP(c_COMBC(U_1337,tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_fun(U_1337,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1337,tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_fun(U_1337,tc_HOL_Obool)),U_1337),c_COMBC(U_1337,tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1337,tc_prod(U_1337,U_1337)),tc_fun(U_1337,tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),U_1337),hAPP(c_COMBB(tc_prod(U_1337,U_1337),tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool),U_1337),c_member(tc_prod(U_1337,U_1337)))),c_Product__Type_OPair(U_1337,U_1337)))),U_1339)),U_1341),U_1343)) ) ),
inference(definitional_conversion,[status(esa)],[f_220_3]) ).
cnf(f_220_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1337,U_1337)),hAPP(hAPP(c_Product__Type_OPair(U_1337,U_1337),U_1341),U_1343)),c_Transitive__Closure_Otrancl(U_1337,U_1339)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1337,hAPP(hAPP(c_COMBC(U_1337,tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_fun(U_1337,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1337,tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_fun(U_1337,tc_HOL_Obool)),U_1337),c_COMBC(U_1337,tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1337,tc_prod(U_1337,U_1337)),tc_fun(U_1337,tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool)),U_1337),hAPP(c_COMBB(tc_prod(U_1337,U_1337),tc_fun(tc_fun(tc_prod(U_1337,U_1337),tc_HOL_Obool),tc_HOL_Obool),U_1337),c_member(tc_prod(U_1337,U_1337)))),c_Product__Type_OPair(U_1337,U_1337)))),U_1339)),U_1341),U_1343)) ),
inference(clausify,[status(thm)],[f_220_4]) ).
cnf(f_220_6,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1338,hAPP(hAPP(c_COMBC(U_1338,tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_fun(U_1338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1338,tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_fun(U_1338,tc_HOL_Obool)),U_1338),c_COMBC(U_1338,tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1338,tc_prod(U_1338,U_1338)),tc_fun(U_1338,tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool)),U_1338),hAPP(c_COMBB(tc_prod(U_1338,U_1338),tc_fun(tc_fun(tc_prod(U_1338,U_1338),tc_HOL_Obool),tc_HOL_Obool),U_1338),c_member(tc_prod(U_1338,U_1338)))),c_Product__Type_OPair(U_1338,U_1338)))),U_1340)),U_1342),U_1344))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1338,U_1338)),hAPP(hAPP(c_Product__Type_OPair(U_1338,U_1338),U_1342),U_1344)),c_Transitive__Closure_Otrancl(U_1338,U_1340))) ),
inference(clausify,[status(thm)],[f_220_4]) ).
fof(f_221_1,plain,
! [T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_tranclp_Or__into__trancl]) ).
fof(f_221_2,plain,
! [U_1348,U_1347,U_1346,U_1345] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1348,U_1345),U_1346),U_1347))
| ~ hBOOL(hAPP(hAPP(U_1345,U_1346),U_1347)) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_1345,U_1346,U_1348,U_1347] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1348,U_1345),U_1346),U_1347))
| ~ hBOOL(hAPP(hAPP(U_1345,U_1346),U_1347)) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1348,U_1345),U_1346),U_1347))
| ~ hBOOL(hAPP(hAPP(U_1345,U_1346),U_1347)) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [V_A_2,V_ba_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
| V_aa_2 = V_ba_2
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_insertE]) ).
fof(f_222_2,plain,
! [U_1352,U_1351,U_1350,U_1349] :
( hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),U_1352))
| U_1350 = U_1351
| ~ hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),c_Set_Oinsert(U_1349,U_1351,U_1352))) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_1349,U_1350,U_1351,U_1352] :
( hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),U_1352))
| U_1350 = U_1351
| ~ hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),c_Set_Oinsert(U_1349,U_1351,U_1352))) ),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),U_1352))
| U_1350 = U_1351
| ~ hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),c_Set_Oinsert(U_1349,U_1351,U_1352))) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [V_ba_2,V_B_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2)))
| ( V_aa_2 != V_ba_2
& ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insertCI]) ).
fof(f_223_2,plain,
! [U_1356,U_1355,U_1354,U_1353] :
( hBOOL(hAPP(hAPP(c_member(U_1353),U_1354),c_Set_Oinsert(U_1353,U_1356,U_1355)))
| ( U_1354 != U_1356
& ~ hBOOL(hAPP(hAPP(c_member(U_1353),U_1354),U_1355)) ) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
( ! [U_1353,U_1354,U_1355,U_1356] :
( U_1354 != U_1356
| ~ sP92(U_1353,U_1354,U_1355,U_1356) )
& ! [U_1353,U_1354,U_1355,U_1356] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1353),U_1354),U_1355))
| ~ sP92(U_1353,U_1354,U_1355,U_1356) )
& ! [U_1353,U_1354,U_1355,U_1356] :
( hBOOL(hAPP(hAPP(c_member(U_1353),U_1354),c_Set_Oinsert(U_1353,U_1356,U_1355)))
| sP92(U_1353,U_1354,U_1355,U_1356) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_223_2]) ).
cnf(f_223_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1353),U_1354),c_Set_Oinsert(U_1353,U_1356,U_1355)))
| sP92(U_1353,U_1354,U_1355,U_1356) ),
inference(clausify,[status(thm)],[f_223_3]) ).
cnf(f_223_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1353),U_1354),U_1355))
| ~ sP92(U_1353,U_1354,U_1355,U_1356) ),
inference(clausify,[status(thm)],[f_223_3]) ).
cnf(f_223_6,plain,
( U_1354 != U_1356
| ~ sP92(U_1353,U_1354,U_1355,U_1356) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [V_B_2,V_A_2,V_aa_2,T_a] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)),
inference(fof_nnf,[status(thm)],[fact_insert__inter__insert]) ).
fof(f_224_2,plain,
! [U_1360,U_1359,U_1358,U_1357] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1357,tc_HOL_Obool),c_Set_Oinsert(U_1357,U_1358,U_1359),c_Set_Oinsert(U_1357,U_1358,U_1360)) = c_Set_Oinsert(U_1357,U_1358,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1357,tc_HOL_Obool),U_1359,U_1360)),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_1359,U_1357,U_1358,U_1360] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1357,tc_HOL_Obool),c_Set_Oinsert(U_1357,U_1358,U_1359),c_Set_Oinsert(U_1357,U_1358,U_1360)) = c_Set_Oinsert(U_1357,U_1358,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1357,tc_HOL_Obool),U_1359,U_1360)),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1357,tc_HOL_Obool),c_Set_Oinsert(U_1357,U_1358,U_1359),c_Set_Oinsert(U_1357,U_1358,U_1360)) = c_Set_Oinsert(U_1357,U_1358,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1357,tc_HOL_Obool),U_1359,U_1360)),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [V_A_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2),
inference(fof_nnf,[status(thm)],[fact_insert__absorb2]) ).
fof(f_225_2,plain,
! [U_1363,U_1362,U_1361] : c_Set_Oinsert(U_1361,U_1362,c_Set_Oinsert(U_1361,U_1362,U_1363)) = c_Set_Oinsert(U_1361,U_1362,U_1363),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_1362,U_1361,U_1363] : c_Set_Oinsert(U_1361,U_1362,c_Set_Oinsert(U_1361,U_1362,U_1363)) = c_Set_Oinsert(U_1361,U_1362,U_1363),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
c_Set_Oinsert(U_1361,U_1362,c_Set_Oinsert(U_1361,U_1362,U_1363)) = c_Set_Oinsert(U_1361,U_1362,U_1363),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [V_A_2,V_y_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_insert__commute]) ).
fof(f_226_2,plain,
! [U_1367,U_1366,U_1365,U_1364] : c_Set_Oinsert(U_1364,U_1365,c_Set_Oinsert(U_1364,U_1366,U_1367)) = c_Set_Oinsert(U_1364,U_1366,c_Set_Oinsert(U_1364,U_1365,U_1367)),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_1365,U_1364,U_1366,U_1367] : c_Set_Oinsert(U_1364,U_1365,c_Set_Oinsert(U_1364,U_1366,U_1367)) = c_Set_Oinsert(U_1364,U_1366,c_Set_Oinsert(U_1364,U_1365,U_1367)),
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
c_Set_Oinsert(U_1364,U_1365,c_Set_Oinsert(U_1364,U_1366,U_1367)) = c_Set_Oinsert(U_1364,U_1366,c_Set_Oinsert(U_1364,U_1365,U_1367)),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [V_x_2,V_A_2,V_y_2,T_a] :
( ( hBOOL(hAPP(c_Set_Oinsert(T_a,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(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__code]) ).
fof(f_227_2,plain,
! [U_1371,U_1370,U_1369,U_1368] :
( ( hBOOL(hAPP(c_Set_Oinsert(U_1368,U_1369,U_1370),U_1371))
| ( ~ hBOOL(hAPP(U_1370,U_1371))
& U_1369 != U_1371 ) )
& ( hBOOL(hAPP(U_1370,U_1371))
| U_1369 = U_1371
| ~ hBOOL(hAPP(c_Set_Oinsert(U_1368,U_1369,U_1370),U_1371)) ) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
( ! [U_1379,U_1377,U_1375] :
( ! [U_1373] : hBOOL(hAPP(c_Set_Oinsert(U_1373,U_1375,U_1377),U_1379))
| ( ~ hBOOL(hAPP(U_1377,U_1379))
& U_1375 != U_1379 ) )
& ! [U_1378,U_1376,U_1374] :
( ! [U_1372] : ~ hBOOL(hAPP(c_Set_Oinsert(U_1372,U_1374,U_1376),U_1378))
| hBOOL(hAPP(U_1376,U_1378))
| U_1374 = U_1378 ) ),
inference(miniscope,[status(thm)],[f_227_2]) ).
fof(f_227_4,plain,
( ! [U_1379,U_1375,U_1377] :
( ~ hBOOL(hAPP(U_1377,U_1379))
| ~ sP93(U_1379,U_1375,U_1377) )
& ! [U_1379,U_1375,U_1377] :
( U_1375 != U_1379
| ~ sP93(U_1379,U_1375,U_1377) )
& ! [U_1379,U_1375,U_1373,U_1377] :
( hBOOL(hAPP(c_Set_Oinsert(U_1373,U_1375,U_1377),U_1379))
| sP93(U_1379,U_1375,U_1377) )
& ! [U_1376,U_1374,U_1372,U_1378] :
( ~ hBOOL(hAPP(c_Set_Oinsert(U_1372,U_1374,U_1376),U_1378))
| hBOOL(hAPP(U_1376,U_1378))
| U_1374 = U_1378 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_227_3]) ).
cnf(f_227_5,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(U_1372,U_1374,U_1376),U_1378))
| hBOOL(hAPP(U_1376,U_1378))
| U_1374 = U_1378 ),
inference(clausify,[status(thm)],[f_227_4]) ).
cnf(f_227_6,plain,
( hBOOL(hAPP(c_Set_Oinsert(U_1373,U_1375,U_1377),U_1379))
| sP93(U_1379,U_1375,U_1377) ),
inference(clausify,[status(thm)],[f_227_4]) ).
cnf(f_227_7,plain,
( U_1375 != U_1379
| ~ sP93(U_1379,U_1375,U_1377) ),
inference(clausify,[status(thm)],[f_227_4]) ).
cnf(f_227_8,plain,
( ~ hBOOL(hAPP(U_1377,U_1379))
| ~ sP93(U_1379,U_1375,U_1377) ),
inference(clausify,[status(thm)],[f_227_4]) ).
fof(f_228_1,plain,
! [V_a2_2,V_a1_2,V_r_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),V_a2_2))
| ( ! [B_b] :
( ~ hBOOL(hAPP(hAPP(V_r_2,B_b),V_a2_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),B_b)) )
& ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) )
& ( ? [B_b] :
( hBOOL(hAPP(hAPP(V_r_2,B_b),V_a2_2))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),B_b)) )
| hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),V_a2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_tranclp_Oequations_I1_J]) ).
fof(f_228_2,plain,
! [U_1385,U_1384,U_1383,U_1382] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1382,U_1383),U_1384),U_1385))
| ( ! [U_1381] :
( ~ hBOOL(hAPP(hAPP(U_1383,U_1381),U_1385))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1382,U_1383),U_1384),U_1381)) )
& ~ hBOOL(hAPP(hAPP(U_1383,U_1384),U_1385)) ) )
& ( ? [U_1380] :
( hBOOL(hAPP(hAPP(U_1383,U_1380),U_1385))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1382,U_1383),U_1384),U_1380)) )
| hBOOL(hAPP(hAPP(U_1383,U_1384),U_1385))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1382,U_1383),U_1384),U_1385)) ) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
( ! [U_1393,U_1391,U_1389,U_1387] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1393))
| ( ! [U_1381] :
( ~ hBOOL(hAPP(hAPP(U_1389,U_1381),U_1393))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1381)) )
& ~ hBOOL(hAPP(hAPP(U_1389,U_1391),U_1393)) ) )
& ! [U_1392,U_1390,U_1388,U_1386] :
( ? [U_1380] :
( hBOOL(hAPP(hAPP(U_1388,U_1380),U_1392))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),U_1380)) )
| hBOOL(hAPP(hAPP(U_1388,U_1390),U_1392))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),U_1392)) ) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
fof(f_228_4,plain,
( ! [U_1393,U_1391,U_1389,U_1387] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1393))
| ( ! [U_1381] :
( ~ hBOOL(hAPP(hAPP(U_1389,U_1381),U_1393))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1381)) )
& ~ hBOOL(hAPP(hAPP(U_1389,U_1391),U_1393)) ) )
& ! [U_1392,U_1390,U_1388,U_1386] :
( ( hBOOL(hAPP(hAPP(U_1388,sK86(U_1392,U_1390,U_1388,U_1386)),U_1392))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),sK86(U_1392,U_1390,U_1388,U_1386))) )
| hBOOL(hAPP(hAPP(U_1388,U_1390),U_1392))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),U_1392)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_1380,sK86(U_1392,U_1390,U_1388,U_1386))],[f_228_3]) ).
fof(f_228_5,plain,
( ! [U_1391,U_1381,U_1393,U_1389,U_1387] :
( ~ hBOOL(hAPP(hAPP(U_1389,U_1381),U_1393))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1381))
| ~ sP95(U_1391,U_1381,U_1393,U_1389,U_1387) )
& ! [U_1391,U_1381,U_1393,U_1389,U_1387] :
( ~ hBOOL(hAPP(hAPP(U_1389,U_1391),U_1393))
| ~ sP95(U_1391,U_1381,U_1393,U_1389,U_1387) )
& ! [U_1390,U_1386,U_1388,U_1392] :
( hBOOL(hAPP(hAPP(U_1388,sK86(U_1392,U_1390,U_1388,U_1386)),U_1392))
| ~ sP94(U_1390,U_1386,U_1388,U_1392) )
& ! [U_1390,U_1386,U_1388,U_1392] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),sK86(U_1392,U_1390,U_1388,U_1386)))
| ~ sP94(U_1390,U_1386,U_1388,U_1392) )
& ! [U_1391,U_1381,U_1393,U_1389,U_1387] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1393))
| sP95(U_1391,U_1381,U_1393,U_1389,U_1387) )
& ! [U_1390,U_1386,U_1388,U_1392] :
( sP94(U_1390,U_1386,U_1388,U_1392)
| hBOOL(hAPP(hAPP(U_1388,U_1390),U_1392))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),U_1392)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94,sP95])],[f_228_4]) ).
cnf(f_228_6,plain,
( sP94(U_1390,U_1386,U_1388,U_1392)
| hBOOL(hAPP(hAPP(U_1388,U_1390),U_1392))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),U_1392)) ),
inference(clausify,[status(thm)],[f_228_5]) ).
cnf(f_228_7,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1393))
| sP95(U_1391,U_1381,U_1393,U_1389,U_1387) ),
inference(clausify,[status(thm)],[f_228_5]) ).
cnf(f_228_8,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1386,U_1388),U_1390),sK86(U_1392,U_1390,U_1388,U_1386)))
| ~ sP94(U_1390,U_1386,U_1388,U_1392) ),
inference(clausify,[status(thm)],[f_228_5]) ).
cnf(f_228_9,plain,
( hBOOL(hAPP(hAPP(U_1388,sK86(U_1392,U_1390,U_1388,U_1386)),U_1392))
| ~ sP94(U_1390,U_1386,U_1388,U_1392) ),
inference(clausify,[status(thm)],[f_228_5]) ).
cnf(f_228_10,plain,
( ~ hBOOL(hAPP(hAPP(U_1389,U_1391),U_1393))
| ~ sP95(U_1391,U_1381,U_1393,U_1389,U_1387) ),
inference(clausify,[status(thm)],[f_228_5]) ).
cnf(f_228_11,plain,
( ~ hBOOL(hAPP(hAPP(U_1389,U_1381),U_1393))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1387,U_1389),U_1391),U_1381))
| ~ sP95(U_1391,U_1381,U_1393,U_1389,U_1387) ),
inference(clausify,[status(thm)],[f_228_5]) ).
fof(f_229_1,plain,
! [V_a3_2,V_a1_2,V_r_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),V_a3_2))
| ( ! [B_b] :
( ~ hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),B_b)) )
& ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a3_2)) ) )
& ( ? [B_b] :
( hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),B_b)) )
| hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a3_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_a1_2),V_a3_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_tranclp_Oequations_I2_J]) ).
fof(f_229_2,plain,
! [U_1399,U_1398,U_1397,U_1396] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1396,U_1397),U_1398),U_1399))
| ( ! [U_1395] :
( ~ hBOOL(hAPP(hAPP(U_1397,U_1395),U_1399))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1396,U_1397),U_1398),U_1395)) )
& ~ hBOOL(hAPP(hAPP(U_1397,U_1398),U_1399)) ) )
& ( ? [U_1394] :
( hBOOL(hAPP(hAPP(U_1397,U_1394),U_1399))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1396,U_1397),U_1398),U_1394)) )
| hBOOL(hAPP(hAPP(U_1397,U_1398),U_1399))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1396,U_1397),U_1398),U_1399)) ) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
( ! [U_1407,U_1405,U_1403,U_1401] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1407))
| ( ! [U_1395] :
( ~ hBOOL(hAPP(hAPP(U_1403,U_1395),U_1407))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1395)) )
& ~ hBOOL(hAPP(hAPP(U_1403,U_1405),U_1407)) ) )
& ! [U_1406,U_1404,U_1402,U_1400] :
( ? [U_1394] :
( hBOOL(hAPP(hAPP(U_1402,U_1394),U_1406))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),U_1394)) )
| hBOOL(hAPP(hAPP(U_1402,U_1404),U_1406))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),U_1406)) ) ),
inference(miniscope,[status(thm)],[f_229_2]) ).
fof(f_229_4,plain,
( ! [U_1407,U_1405,U_1403,U_1401] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1407))
| ( ! [U_1395] :
( ~ hBOOL(hAPP(hAPP(U_1403,U_1395),U_1407))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1395)) )
& ~ hBOOL(hAPP(hAPP(U_1403,U_1405),U_1407)) ) )
& ! [U_1406,U_1404,U_1402,U_1400] :
( ( hBOOL(hAPP(hAPP(U_1402,sK87(U_1406,U_1404,U_1402,U_1400)),U_1406))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),sK87(U_1406,U_1404,U_1402,U_1400))) )
| hBOOL(hAPP(hAPP(U_1402,U_1404),U_1406))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),U_1406)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_1394,sK87(U_1406,U_1404,U_1402,U_1400))],[f_229_3]) ).
fof(f_229_5,plain,
( ! [U_1407,U_1395,U_1405,U_1403,U_1401] :
( ~ hBOOL(hAPP(hAPP(U_1403,U_1395),U_1407))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1395))
| ~ sP97(U_1407,U_1395,U_1405,U_1403,U_1401) )
& ! [U_1407,U_1395,U_1405,U_1403,U_1401] :
( ~ hBOOL(hAPP(hAPP(U_1403,U_1405),U_1407))
| ~ sP97(U_1407,U_1395,U_1405,U_1403,U_1401) )
& ! [U_1404,U_1400,U_1402,U_1406] :
( hBOOL(hAPP(hAPP(U_1402,sK87(U_1406,U_1404,U_1402,U_1400)),U_1406))
| ~ sP96(U_1404,U_1400,U_1402,U_1406) )
& ! [U_1404,U_1400,U_1402,U_1406] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),sK87(U_1406,U_1404,U_1402,U_1400)))
| ~ sP96(U_1404,U_1400,U_1402,U_1406) )
& ! [U_1407,U_1395,U_1405,U_1403,U_1401] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1407))
| sP97(U_1407,U_1395,U_1405,U_1403,U_1401) )
& ! [U_1404,U_1400,U_1402,U_1406] :
( sP96(U_1404,U_1400,U_1402,U_1406)
| hBOOL(hAPP(hAPP(U_1402,U_1404),U_1406))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),U_1406)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96,sP97])],[f_229_4]) ).
cnf(f_229_6,plain,
( sP96(U_1404,U_1400,U_1402,U_1406)
| hBOOL(hAPP(hAPP(U_1402,U_1404),U_1406))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),U_1406)) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_7,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1407))
| sP97(U_1407,U_1395,U_1405,U_1403,U_1401) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_8,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1400,U_1402),U_1404),sK87(U_1406,U_1404,U_1402,U_1400)))
| ~ sP96(U_1404,U_1400,U_1402,U_1406) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_9,plain,
( hBOOL(hAPP(hAPP(U_1402,sK87(U_1406,U_1404,U_1402,U_1400)),U_1406))
| ~ sP96(U_1404,U_1400,U_1402,U_1406) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_10,plain,
( ~ hBOOL(hAPP(hAPP(U_1403,U_1405),U_1407))
| ~ sP97(U_1407,U_1395,U_1405,U_1403,U_1401) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_11,plain,
( ~ hBOOL(hAPP(hAPP(U_1403,U_1395),U_1407))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1401,U_1403),U_1405),U_1395))
| ~ sP97(U_1407,U_1395,U_1405,U_1403,U_1401) ),
inference(clausify,[status(thm)],[f_229_5]) ).
fof(f_230_1,plain,
! [V_ca_2,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_ba_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_tranclp__into__tranclp2]) ).
fof(f_230_2,plain,
! [U_1412,U_1411,U_1410,U_1409,U_1408] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1411,U_1408),U_1409),U_1412))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1411,U_1408),U_1410),U_1412))
| ~ hBOOL(hAPP(hAPP(U_1408,U_1409),U_1410)) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_1410,U_1411,U_1408,U_1409,U_1412] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1411,U_1408),U_1409),U_1412))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1411,U_1408),U_1410),U_1412))
| ~ hBOOL(hAPP(hAPP(U_1408,U_1409),U_1410)) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1411,U_1408),U_1409),U_1412))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1411,U_1408),U_1410),U_1412))
| ~ hBOOL(hAPP(hAPP(U_1408,U_1409),U_1410)) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_tranclp_Otrancl__into__trancl]) ).
fof(f_231_2,plain,
! [U_1417,U_1416,U_1415,U_1414,U_1413] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1413,U_1414),U_1415),U_1417))
| ~ hBOOL(hAPP(hAPP(U_1414,U_1416),U_1417))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1413,U_1414),U_1415),U_1416)) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_1414,U_1413,U_1415,U_1416,U_1417] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1413,U_1414),U_1415),U_1417))
| ~ hBOOL(hAPP(hAPP(U_1414,U_1416),U_1417))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1413,U_1414),U_1415),U_1416)) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1413,U_1414),U_1415),U_1417))
| ~ hBOOL(hAPP(hAPP(U_1414,U_1416),U_1417))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1413,U_1414),U_1415),U_1416)) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_tranclp__trans]) ).
fof(f_232_2,plain,
! [U_1422,U_1421,U_1420,U_1419,U_1418] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1420),U_1422))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1421),U_1422))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1420),U_1421)) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_1418,U_1419,U_1420,U_1421,U_1422] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1420),U_1422))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1421),U_1422))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1420),U_1421)) ),
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1420),U_1422))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1421),U_1422))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1418,U_1419),U_1420),U_1421)) ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [V_A_2,V_aa_2,T_a] :
( c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__absorb]) ).
fof(f_233_2,plain,
! [U_1425,U_1424,U_1423] :
( c_Set_Oinsert(U_1423,U_1424,U_1425) = U_1425
| ~ hBOOL(hAPP(hAPP(c_member(U_1423),U_1424),U_1425)) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_1425,U_1424,U_1423] :
( c_Set_Oinsert(U_1423,U_1424,U_1425) = U_1425
| ~ hBOOL(hAPP(hAPP(c_member(U_1423),U_1424),U_1425)) ),
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
( c_Set_Oinsert(U_1423,U_1424,U_1425) = U_1425
| ~ hBOOL(hAPP(hAPP(c_member(U_1423),U_1424),U_1425)) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_1,plain,
! [V_ba_2,V_B_2,V_aa_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_insertI2]) ).
fof(f_234_2,plain,
! [U_1429,U_1428,U_1427,U_1426] :
( hBOOL(hAPP(hAPP(c_member(U_1426),U_1427),c_Set_Oinsert(U_1426,U_1429,U_1428)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1426),U_1427),U_1428)) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_1426,U_1427,U_1428,U_1429] :
( hBOOL(hAPP(hAPP(c_member(U_1426),U_1427),c_Set_Oinsert(U_1426,U_1429,U_1428)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1426),U_1427),U_1428)) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1426),U_1427),c_Set_Oinsert(U_1426,U_1429,U_1428)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1426),U_1427),U_1428)) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [V_B_2,V_A_2,V_x_2,T_a] :
( ( ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| c_Set_Oinsert(T_a,V_x_2,V_A_2) != c_Set_Oinsert(T_a,V_x_2,V_B_2) ) )
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__ident]) ).
fof(f_235_2,plain,
! [U_1433,U_1432,U_1431,U_1430] :
( ( ( c_Set_Oinsert(U_1430,U_1431,U_1432) = c_Set_Oinsert(U_1430,U_1431,U_1433)
| U_1432 != U_1433 )
& ( U_1432 = U_1433
| c_Set_Oinsert(U_1430,U_1431,U_1432) != c_Set_Oinsert(U_1430,U_1431,U_1433) ) )
| hBOOL(hAPP(hAPP(c_member(U_1430),U_1431),U_1433))
| hBOOL(hAPP(hAPP(c_member(U_1430),U_1431),U_1432)) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
( ! [U_1430,U_1431,U_1432,U_1433] :
( c_Set_Oinsert(U_1430,U_1431,U_1432) = c_Set_Oinsert(U_1430,U_1431,U_1433)
| U_1432 != U_1433
| ~ sP98(U_1430,U_1431,U_1432,U_1433) )
& ! [U_1430,U_1431,U_1432,U_1433] :
( U_1432 = U_1433
| c_Set_Oinsert(U_1430,U_1431,U_1432) != c_Set_Oinsert(U_1430,U_1431,U_1433)
| ~ sP98(U_1430,U_1431,U_1432,U_1433) )
& ! [U_1430,U_1431,U_1432,U_1433] :
( sP98(U_1430,U_1431,U_1432,U_1433)
| hBOOL(hAPP(hAPP(c_member(U_1430),U_1431),U_1433))
| hBOOL(hAPP(hAPP(c_member(U_1430),U_1431),U_1432)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_235_2]) ).
cnf(f_235_4,plain,
( sP98(U_1430,U_1431,U_1432,U_1433)
| hBOOL(hAPP(hAPP(c_member(U_1430),U_1431),U_1433))
| hBOOL(hAPP(hAPP(c_member(U_1430),U_1431),U_1432)) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_5,plain,
( U_1432 = U_1433
| c_Set_Oinsert(U_1430,U_1431,U_1432) != c_Set_Oinsert(U_1430,U_1431,U_1433)
| ~ sP98(U_1430,U_1431,U_1432,U_1433) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_6,plain,
( c_Set_Oinsert(U_1430,U_1431,U_1432) = c_Set_Oinsert(U_1430,U_1431,U_1433)
| U_1432 != U_1433
| ~ sP98(U_1430,U_1431,U_1432,U_1433) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [V_A_2,V_ba_2,V_aa_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
& V_aa_2 != V_ba_2 ) )
& ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
| V_aa_2 = V_ba_2
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__iff]) ).
fof(f_236_2,plain,
! [U_1437,U_1436,U_1435,U_1434] :
( ( hBOOL(hAPP(hAPP(c_member(U_1434),U_1435),c_Set_Oinsert(U_1434,U_1436,U_1437)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_1434),U_1435),U_1437))
& U_1435 != U_1436 ) )
& ( hBOOL(hAPP(hAPP(c_member(U_1434),U_1435),U_1437))
| U_1435 = U_1436
| ~ hBOOL(hAPP(hAPP(c_member(U_1434),U_1435),c_Set_Oinsert(U_1434,U_1436,U_1437))) ) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
( ! [U_1445,U_1443,U_1441,U_1439] :
( hBOOL(hAPP(hAPP(c_member(U_1439),U_1441),c_Set_Oinsert(U_1439,U_1443,U_1445)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_1439),U_1441),U_1445))
& U_1441 != U_1443 ) )
& ! [U_1444,U_1442,U_1440,U_1438] :
( hBOOL(hAPP(hAPP(c_member(U_1438),U_1440),U_1444))
| U_1440 = U_1442
| ~ hBOOL(hAPP(hAPP(c_member(U_1438),U_1440),c_Set_Oinsert(U_1438,U_1442,U_1444))) ) ),
inference(miniscope,[status(thm)],[f_236_2]) ).
fof(f_236_4,plain,
( ! [U_1441,U_1443,U_1445,U_1439] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1439),U_1441),U_1445))
| ~ sP99(U_1441,U_1443,U_1445,U_1439) )
& ! [U_1441,U_1443,U_1445,U_1439] :
( U_1441 != U_1443
| ~ sP99(U_1441,U_1443,U_1445,U_1439) )
& ! [U_1441,U_1443,U_1445,U_1439] :
( hBOOL(hAPP(hAPP(c_member(U_1439),U_1441),c_Set_Oinsert(U_1439,U_1443,U_1445)))
| sP99(U_1441,U_1443,U_1445,U_1439) )
& ! [U_1442,U_1438,U_1440,U_1444] :
( hBOOL(hAPP(hAPP(c_member(U_1438),U_1440),U_1444))
| U_1440 = U_1442
| ~ hBOOL(hAPP(hAPP(c_member(U_1438),U_1440),c_Set_Oinsert(U_1438,U_1442,U_1444))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_236_3]) ).
cnf(f_236_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_1438),U_1440),U_1444))
| U_1440 = U_1442
| ~ hBOOL(hAPP(hAPP(c_member(U_1438),U_1440),c_Set_Oinsert(U_1438,U_1442,U_1444))) ),
inference(clausify,[status(thm)],[f_236_4]) ).
cnf(f_236_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1439),U_1441),c_Set_Oinsert(U_1439,U_1443,U_1445)))
| sP99(U_1441,U_1443,U_1445,U_1439) ),
inference(clausify,[status(thm)],[f_236_4]) ).
cnf(f_236_7,plain,
( U_1441 != U_1443
| ~ sP99(U_1441,U_1443,U_1445,U_1439) ),
inference(clausify,[status(thm)],[f_236_4]) ).
cnf(f_236_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1439),U_1441),U_1445))
| ~ sP99(U_1441,U_1443,U_1445,U_1439) ),
inference(clausify,[status(thm)],[f_236_4]) ).
fof(f_237_1,plain,
! [V_B_2,V_aa_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))),
inference(fof_nnf,[status(thm)],[fact_insertI1]) ).
fof(f_237_2,plain,
! [U_1448,U_1447,U_1446] : hBOOL(hAPP(hAPP(c_member(U_1446),U_1447),c_Set_Oinsert(U_1446,U_1447,U_1448))),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_1447,U_1448,U_1446] : hBOOL(hAPP(hAPP(c_member(U_1446),U_1447),c_Set_Oinsert(U_1446,U_1447,U_1448))),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
hBOOL(hAPP(hAPP(c_member(U_1446),U_1447),c_Set_Oinsert(U_1446,U_1447,U_1448))),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_a,T_b] : c_Relation_ORange(T_b,T_a,c_Set_Oinsert(tc_prod(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_aa_2),V_ba_2),V_r_2)) = c_Set_Oinsert(T_a,V_ba_2,c_Relation_ORange(T_b,T_a,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Range__insert]) ).
fof(f_238_2,plain,
! [U_1453,U_1452,U_1451,U_1450,U_1449] : c_Relation_ORange(U_1449,U_1450,c_Set_Oinsert(tc_prod(U_1449,U_1450),hAPP(hAPP(c_Product__Type_OPair(U_1449,U_1450),U_1451),U_1452),U_1453)) = c_Set_Oinsert(U_1450,U_1452,c_Relation_ORange(U_1449,U_1450,U_1453)),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_1449,U_1450,U_1451,U_1452,U_1453] : c_Relation_ORange(U_1449,U_1450,c_Set_Oinsert(tc_prod(U_1449,U_1450),hAPP(hAPP(c_Product__Type_OPair(U_1449,U_1450),U_1451),U_1452),U_1453)) = c_Set_Oinsert(U_1450,U_1452,c_Relation_ORange(U_1449,U_1450,U_1453)),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
c_Relation_ORange(U_1449,U_1450,c_Set_Oinsert(tc_prod(U_1449,U_1450),hAPP(hAPP(c_Product__Type_OPair(U_1449,U_1450),U_1451),U_1452),U_1453)) = c_Set_Oinsert(U_1450,U_1452,c_Relation_ORange(U_1449,U_1450,U_1453)),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
! [V_r_2,V_ba_2,V_aa_2,T_b,T_a] : c_Relation_ODomain(T_a,T_b,c_Set_Oinsert(tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2),V_r_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Domain__insert]) ).
fof(f_239_2,plain,
! [U_1458,U_1457,U_1456,U_1455,U_1454] : c_Relation_ODomain(U_1454,U_1455,c_Set_Oinsert(tc_prod(U_1454,U_1455),hAPP(hAPP(c_Product__Type_OPair(U_1454,U_1455),U_1456),U_1457),U_1458)) = c_Set_Oinsert(U_1454,U_1456,c_Relation_ODomain(U_1454,U_1455,U_1458)),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_1455,U_1454,U_1456,U_1457,U_1458] : c_Relation_ODomain(U_1454,U_1455,c_Set_Oinsert(tc_prod(U_1454,U_1455),hAPP(hAPP(c_Product__Type_OPair(U_1454,U_1455),U_1456),U_1457),U_1458)) = c_Set_Oinsert(U_1454,U_1456,c_Relation_ODomain(U_1454,U_1455,U_1458)),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
c_Relation_ODomain(U_1454,U_1455,c_Set_Oinsert(tc_prod(U_1454,U_1455),hAPP(hAPP(c_Product__Type_OPair(U_1454,U_1455),U_1456),U_1457),U_1458)) = c_Set_Oinsert(U_1454,U_1456,c_Relation_ODomain(U_1454,U_1455,U_1458)),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
! [V_ca_2,T_a,V_ba_2,V_aa_2,V_r_2] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp__into__tranclp2]) ).
fof(f_240_2,plain,
! [U_1463,U_1462,U_1461,U_1460,U_1459] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1462,U_1459),U_1460),U_1463))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1462,U_1459),U_1461),U_1463))
| ~ hBOOL(hAPP(hAPP(U_1459,U_1460),U_1461)) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_1459,U_1460,U_1461,U_1462,U_1463] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1462,U_1459),U_1460),U_1463))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1462,U_1459),U_1461),U_1463))
| ~ hBOOL(hAPP(hAPP(U_1459,U_1460),U_1461)) ),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1462,U_1459),U_1460),U_1463))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1462,U_1459),U_1461),U_1463))
| ~ hBOOL(hAPP(hAPP(U_1459,U_1460),U_1461)) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [V_ba_2,V_aa_2,V_R_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_R_2),V_aa_2),V_ba_2))
& V_aa_2 != V_ba_2 )
| V_aa_2 = V_ba_2
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_R_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtranclpD]) ).
fof(f_241_2,plain,
! [U_1467,U_1466,U_1465,U_1464] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1464,U_1465),U_1466),U_1467))
& U_1466 != U_1467 )
| U_1466 = U_1467
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1464,U_1465),U_1466),U_1467)) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
( ! [U_1464,U_1465,U_1466,U_1467] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1464,U_1465),U_1466),U_1467))
| ~ sP100(U_1464,U_1465,U_1466,U_1467) )
& ! [U_1464,U_1465,U_1466,U_1467] :
( U_1466 != U_1467
| ~ sP100(U_1464,U_1465,U_1466,U_1467) )
& ! [U_1464,U_1465,U_1466,U_1467] :
( sP100(U_1464,U_1465,U_1466,U_1467)
| U_1466 = U_1467
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1464,U_1465),U_1466),U_1467)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_241_2]) ).
cnf(f_241_4,plain,
( sP100(U_1464,U_1465,U_1466,U_1467)
| U_1466 = U_1467
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1464,U_1465),U_1466),U_1467)) ),
inference(clausify,[status(thm)],[f_241_3]) ).
cnf(f_241_5,plain,
( U_1466 != U_1467
| ~ sP100(U_1464,U_1465,U_1466,U_1467) ),
inference(clausify,[status(thm)],[f_241_3]) ).
cnf(f_241_6,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1464,U_1465),U_1466),U_1467))
| ~ sP100(U_1464,U_1465,U_1466,U_1467) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
! [V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ba_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_tranclp__into__rtranclp]) ).
fof(f_242_2,plain,
! [U_1471,U_1470,U_1469,U_1468] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1468,U_1469),U_1470),U_1471))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1468,U_1469),U_1470),U_1471)) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_1469,U_1468,U_1470,U_1471] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1468,U_1469),U_1470),U_1471))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1468,U_1469),U_1470),U_1471)) ),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1468,U_1469),U_1470),U_1471))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1468,U_1469),U_1470),U_1471)) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_1,plain,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp__into__tranclp1]) ).
fof(f_243_2,plain,
! [U_1476,U_1475,U_1474,U_1473,U_1472] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1472,U_1473),U_1474),U_1476))
| ~ hBOOL(hAPP(hAPP(U_1473,U_1475),U_1476))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1472,U_1473),U_1474),U_1475)) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_1472,U_1473,U_1474,U_1475,U_1476] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1472,U_1473),U_1474),U_1476))
| ~ hBOOL(hAPP(hAPP(U_1473,U_1475),U_1476))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1472,U_1473),U_1474),U_1475)) ),
inference(definitional_conversion,[status(esa)],[f_243_2]) ).
cnf(f_243_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1472,U_1473),U_1474),U_1476))
| ~ hBOOL(hAPP(hAPP(U_1473,U_1475),U_1476))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1472,U_1473),U_1474),U_1475)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [V_ca_2,V_ba_2,V_aa_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_aa_2),V_ba_2)) ),
inference(fof_nnf,[status(thm)],[fact_tranclp__rtranclp__tranclp]) ).
fof(f_244_2,plain,
! [U_1481,U_1480,U_1479,U_1478,U_1477] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1477,U_1478),U_1479),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1477,U_1478),U_1480),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1477,U_1478),U_1479),U_1480)) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_1477,U_1478,U_1479,U_1480,U_1481] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1477,U_1478),U_1479),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1477,U_1478),U_1480),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1477,U_1478),U_1479),U_1480)) ),
inference(definitional_conversion,[status(esa)],[f_244_2]) ).
cnf(f_244_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1477,U_1478),U_1479),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1477,U_1478),U_1480),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1477,U_1478),U_1479),U_1480)) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(T_a,V_r_2),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp__tranclp__tranclp]) ).
fof(f_245_2,plain,
! [U_1486,U_1485,U_1484,U_1483,U_1482] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1482,U_1483),U_1484),U_1486))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1482,U_1483),U_1485),U_1486))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1482,U_1483),U_1484),U_1485)) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_1482,U_1483,U_1484,U_1485,U_1486] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1482,U_1483),U_1484),U_1486))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1482,U_1483),U_1485),U_1486))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1482,U_1483),U_1484),U_1485)) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1482,U_1483),U_1484),U_1486))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1482,U_1483),U_1485),U_1486))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1482,U_1483),U_1484),U_1485)) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
! [V_B_2,V_C_2,V_aa_2,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1]) ).
fof(f_246_2,plain,
! [U_1490,U_1489,U_1488,U_1487] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1487,tc_HOL_Obool),c_Set_Oinsert(U_1487,U_1488,U_1490),U_1489) = c_Set_Oinsert(U_1487,U_1488,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1487,tc_HOL_Obool),U_1490,U_1489))
| ~ hBOOL(hAPP(hAPP(c_member(U_1487),U_1488),U_1489)) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_1488,U_1487,U_1489,U_1490] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1487,tc_HOL_Obool),c_Set_Oinsert(U_1487,U_1488,U_1490),U_1489) = c_Set_Oinsert(U_1487,U_1488,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1487,tc_HOL_Obool),U_1490,U_1489))
| ~ hBOOL(hAPP(hAPP(c_member(U_1487),U_1488),U_1489)) ),
inference(definitional_conversion,[status(esa)],[f_246_2]) ).
cnf(f_246_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1487,tc_HOL_Obool),c_Set_Oinsert(U_1487,U_1488,U_1490),U_1489) = c_Set_Oinsert(U_1487,U_1488,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1487,tc_HOL_Obool),U_1490,U_1489))
| ~ hBOOL(hAPP(hAPP(c_member(U_1487),U_1488),U_1489)) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
! [V_B_2,V_A_2,V_aa_2,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1]) ).
fof(f_247_2,plain,
! [U_1494,U_1493,U_1492,U_1491] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1491,tc_HOL_Obool),U_1493,c_Set_Oinsert(U_1491,U_1492,U_1494)) = c_Set_Oinsert(U_1491,U_1492,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1491,tc_HOL_Obool),U_1493,U_1494))
| ~ hBOOL(hAPP(hAPP(c_member(U_1491),U_1492),U_1493)) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_1491,U_1492,U_1493,U_1494] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1491,tc_HOL_Obool),U_1493,c_Set_Oinsert(U_1491,U_1492,U_1494)) = c_Set_Oinsert(U_1491,U_1492,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1491,tc_HOL_Obool),U_1493,U_1494))
| ~ hBOOL(hAPP(hAPP(c_member(U_1491),U_1492),U_1493)) ),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1491,tc_HOL_Obool),U_1493,c_Set_Oinsert(U_1491,U_1492,U_1494)) = c_Set_Oinsert(U_1491,U_1492,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1491,tc_HOL_Obool),U_1493,U_1494))
| ~ hBOOL(hAPP(hAPP(c_member(U_1491),U_1492),U_1493)) ),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [V_B_2,V_C_2,V_aa_2,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
| hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(f_248_2,plain,
! [U_1498,U_1497,U_1496,U_1495] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1495,tc_HOL_Obool),c_Set_Oinsert(U_1495,U_1496,U_1498),U_1497) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1495,tc_HOL_Obool),U_1498,U_1497)
| hBOOL(hAPP(hAPP(c_member(U_1495),U_1496),U_1497)) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_1495,U_1496,U_1497,U_1498] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1495,tc_HOL_Obool),c_Set_Oinsert(U_1495,U_1496,U_1498),U_1497) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1495,tc_HOL_Obool),U_1498,U_1497)
| hBOOL(hAPP(hAPP(c_member(U_1495),U_1496),U_1497)) ),
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1495,tc_HOL_Obool),c_Set_Oinsert(U_1495,U_1496,U_1498),U_1497) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1495,tc_HOL_Obool),U_1498,U_1497)
| hBOOL(hAPP(hAPP(c_member(U_1495),U_1496),U_1497)) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [V_B_2,V_A_2,V_aa_2,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(f_249_2,plain,
! [U_1502,U_1501,U_1500,U_1499] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool),U_1501,c_Set_Oinsert(U_1499,U_1500,U_1502)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool),U_1501,U_1502)
| hBOOL(hAPP(hAPP(c_member(U_1499),U_1500),U_1501)) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_1502,U_1499,U_1500,U_1501] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool),U_1501,c_Set_Oinsert(U_1499,U_1500,U_1502)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool),U_1501,U_1502)
| hBOOL(hAPP(hAPP(c_member(U_1499),U_1500),U_1501)) ),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool),U_1501,c_Set_Oinsert(U_1499,U_1500,U_1502)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool),U_1501,U_1502)
| hBOOL(hAPP(hAPP(c_member(U_1499),U_1500),U_1501)) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_1,plain,
! [V_B_2,V_C_2,V_aa_2,T_a] :
( ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
| hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left]) ).
fof(f_250_2,plain,
! [U_1506,U_1505,U_1504,U_1503] :
( ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1503,tc_HOL_Obool),c_Set_Oinsert(U_1503,U_1504,U_1506),U_1505) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1503,tc_HOL_Obool),U_1506,U_1505)
| hBOOL(hAPP(hAPP(c_member(U_1503),U_1504),U_1505)) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1503,tc_HOL_Obool),c_Set_Oinsert(U_1503,U_1504,U_1506),U_1505) = c_Set_Oinsert(U_1503,U_1504,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1503,tc_HOL_Obool),U_1506,U_1505))
| ~ hBOOL(hAPP(hAPP(c_member(U_1503),U_1504),U_1505)) ) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
( ! [U_1514,U_1512,U_1510,U_1508] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1508,tc_HOL_Obool),c_Set_Oinsert(U_1508,U_1510,U_1514),U_1512) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1508,tc_HOL_Obool),U_1514,U_1512)
| hBOOL(hAPP(hAPP(c_member(U_1508),U_1510),U_1512)) )
& ! [U_1513,U_1511,U_1509,U_1507] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1507,tc_HOL_Obool),c_Set_Oinsert(U_1507,U_1509,U_1513),U_1511) = c_Set_Oinsert(U_1507,U_1509,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1507,tc_HOL_Obool),U_1513,U_1511))
| ~ hBOOL(hAPP(hAPP(c_member(U_1507),U_1509),U_1511)) ) ),
inference(miniscope,[status(thm)],[f_250_2]) ).
fof(f_250_4,plain,
( ! [U_1514,U_1508,U_1512,U_1510] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1508,tc_HOL_Obool),c_Set_Oinsert(U_1508,U_1510,U_1514),U_1512) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1508,tc_HOL_Obool),U_1514,U_1512)
| hBOOL(hAPP(hAPP(c_member(U_1508),U_1510),U_1512)) )
& ! [U_1507,U_1509,U_1511,U_1513] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1507,tc_HOL_Obool),c_Set_Oinsert(U_1507,U_1509,U_1513),U_1511) = c_Set_Oinsert(U_1507,U_1509,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1507,tc_HOL_Obool),U_1513,U_1511))
| ~ hBOOL(hAPP(hAPP(c_member(U_1507),U_1509),U_1511)) ) ),
inference(definitional_conversion,[status(esa)],[f_250_3]) ).
cnf(f_250_5,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1507,tc_HOL_Obool),c_Set_Oinsert(U_1507,U_1509,U_1513),U_1511) = c_Set_Oinsert(U_1507,U_1509,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1507,tc_HOL_Obool),U_1513,U_1511))
| ~ hBOOL(hAPP(hAPP(c_member(U_1507),U_1509),U_1511)) ),
inference(clausify,[status(thm)],[f_250_4]) ).
cnf(f_250_6,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1508,tc_HOL_Obool),c_Set_Oinsert(U_1508,U_1510,U_1514),U_1512) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1508,tc_HOL_Obool),U_1514,U_1512)
| hBOOL(hAPP(hAPP(c_member(U_1508),U_1510),U_1512)) ),
inference(clausify,[status(thm)],[f_250_4]) ).
fof(f_251_1,plain,
! [V_B_2,V_A_2,V_aa_2,T_a] :
( ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right]) ).
fof(f_251_2,plain,
! [U_1518,U_1517,U_1516,U_1515] :
( ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1515,tc_HOL_Obool),U_1517,c_Set_Oinsert(U_1515,U_1516,U_1518)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1515,tc_HOL_Obool),U_1517,U_1518)
| hBOOL(hAPP(hAPP(c_member(U_1515),U_1516),U_1517)) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1515,tc_HOL_Obool),U_1517,c_Set_Oinsert(U_1515,U_1516,U_1518)) = c_Set_Oinsert(U_1515,U_1516,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1515,tc_HOL_Obool),U_1517,U_1518))
| ~ hBOOL(hAPP(hAPP(c_member(U_1515),U_1516),U_1517)) ) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_1526,U_1524,U_1522,U_1520] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1520,tc_HOL_Obool),U_1524,c_Set_Oinsert(U_1520,U_1522,U_1526)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1520,tc_HOL_Obool),U_1524,U_1526)
| hBOOL(hAPP(hAPP(c_member(U_1520),U_1522),U_1524)) )
& ! [U_1525,U_1523,U_1521,U_1519] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1519,tc_HOL_Obool),U_1523,c_Set_Oinsert(U_1519,U_1521,U_1525)) = c_Set_Oinsert(U_1519,U_1521,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1519,tc_HOL_Obool),U_1523,U_1525))
| ~ hBOOL(hAPP(hAPP(c_member(U_1519),U_1521),U_1523)) ) ),
inference(miniscope,[status(thm)],[f_251_2]) ).
fof(f_251_4,plain,
( ! [U_1526,U_1520,U_1524,U_1522] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1520,tc_HOL_Obool),U_1524,c_Set_Oinsert(U_1520,U_1522,U_1526)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1520,tc_HOL_Obool),U_1524,U_1526)
| hBOOL(hAPP(hAPP(c_member(U_1520),U_1522),U_1524)) )
& ! [U_1519,U_1521,U_1523,U_1525] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1519,tc_HOL_Obool),U_1523,c_Set_Oinsert(U_1519,U_1521,U_1525)) = c_Set_Oinsert(U_1519,U_1521,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1519,tc_HOL_Obool),U_1523,U_1525))
| ~ hBOOL(hAPP(hAPP(c_member(U_1519),U_1521),U_1523)) ) ),
inference(definitional_conversion,[status(esa)],[f_251_3]) ).
cnf(f_251_5,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1519,tc_HOL_Obool),U_1523,c_Set_Oinsert(U_1519,U_1521,U_1525)) = c_Set_Oinsert(U_1519,U_1521,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1519,tc_HOL_Obool),U_1523,U_1525))
| ~ hBOOL(hAPP(hAPP(c_member(U_1519),U_1521),U_1523)) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_6,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1520,tc_HOL_Obool),U_1524,c_Set_Oinsert(U_1520,U_1522,U_1526)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1520,tc_HOL_Obool),U_1524,U_1526)
| hBOOL(hAPP(hAPP(c_member(U_1520),U_1522),U_1524)) ),
inference(clausify,[status(thm)],[f_251_4]) ).
fof(f_252_1,plain,
! [V_T_2,V_f_2,T_b,V_S_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,c_HOL_Oundefined(T_b))),c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional__funcset(T_a,T_b,c_Set_Oinsert(T_a,V_x_2,V_S_2),V_T_2)))
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_extensional__funcset__restrict__domain]) ).
fof(f_252_2,plain,
! [U_1532,U_1531,U_1530,U_1529,U_1528,U_1527] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1527,U_1530)),c_Fun_Ofun__upd(U_1527,U_1530,U_1531,U_1528,c_HOL_Oundefined(U_1530))),c_FuncSet_Oextensional__funcset(U_1527,U_1530,U_1529,U_1532)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1527,U_1530)),U_1531),c_FuncSet_Oextensional__funcset(U_1527,U_1530,c_Set_Oinsert(U_1527,U_1528,U_1529),U_1532)))
| hBOOL(hAPP(hAPP(c_member(U_1527),U_1528),U_1529)) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_1527,U_1528,U_1529,U_1530,U_1531,U_1532] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1527,U_1530)),c_Fun_Ofun__upd(U_1527,U_1530,U_1531,U_1528,c_HOL_Oundefined(U_1530))),c_FuncSet_Oextensional__funcset(U_1527,U_1530,U_1529,U_1532)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1527,U_1530)),U_1531),c_FuncSet_Oextensional__funcset(U_1527,U_1530,c_Set_Oinsert(U_1527,U_1528,U_1529),U_1532)))
| hBOOL(hAPP(hAPP(c_member(U_1527),U_1528),U_1529)) ),
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1527,U_1530)),c_Fun_Ofun__upd(U_1527,U_1530,U_1531,U_1528,c_HOL_Oundefined(U_1530))),c_FuncSet_Oextensional__funcset(U_1527,U_1530,U_1529,U_1532)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1527,U_1530)),U_1531),c_FuncSet_Oextensional__funcset(U_1527,U_1530,c_Set_Oinsert(U_1527,U_1528,U_1529),U_1532)))
| hBOOL(hAPP(hAPP(c_member(U_1527),U_1528),U_1529)) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_1,plain,
! [V_x_2,V_S_2,V_f_2,T_b,V_T_2,V_y_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2)),c_FuncSet_Oextensional__funcset(T_b,T_a,c_Set_Oinsert(T_b,V_x_2,V_S_2),V_T_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_f_2),c_FuncSet_Oextensional__funcset(T_b,T_a,V_S_2,V_T_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_T_2)) ),
inference(fof_nnf,[status(thm)],[fact_extensional__funcset__extend__domainI]) ).
fof(f_253_2,plain,
! [U_1539,U_1538,U_1537,U_1536,U_1535,U_1534,U_1533] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1536,U_1533)),c_Fun_Ofun__upd(U_1536,U_1533,U_1537,U_1539,U_1534)),c_FuncSet_Oextensional__funcset(U_1536,U_1533,c_Set_Oinsert(U_1536,U_1539,U_1538),U_1535)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1536,U_1533)),U_1537),c_FuncSet_Oextensional__funcset(U_1536,U_1533,U_1538,U_1535)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1533),U_1534),U_1535)) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
! [U_1533,U_1534,U_1535,U_1536,U_1537,U_1538,U_1539] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1536,U_1533)),c_Fun_Ofun__upd(U_1536,U_1533,U_1537,U_1539,U_1534)),c_FuncSet_Oextensional__funcset(U_1536,U_1533,c_Set_Oinsert(U_1536,U_1539,U_1538),U_1535)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1536,U_1533)),U_1537),c_FuncSet_Oextensional__funcset(U_1536,U_1533,U_1538,U_1535)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1533),U_1534),U_1535)) ),
inference(definitional_conversion,[status(esa)],[f_253_2]) ).
cnf(f_253_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1536,U_1533)),c_Fun_Ofun__upd(U_1536,U_1533,U_1537,U_1539,U_1534)),c_FuncSet_Oextensional__funcset(U_1536,U_1533,c_Set_Oinsert(U_1536,U_1539,U_1538),U_1535)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1536,U_1533)),U_1537),c_FuncSet_Oextensional__funcset(U_1536,U_1533,U_1538,U_1535)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1533),U_1534),U_1535)) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [V_r_2,V_x_2,V_y_2,T_a] :
( ( c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
| ~ c_Wellfounded_Owf(T_a,V_r_2) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
& c_Wellfounded_Owf(T_a,V_r_2) )
| ~ c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__insert]) ).
fof(f_254_2,plain,
! [U_1543,U_1542,U_1541,U_1540] :
( ( c_Wellfounded_Owf(U_1540,c_Set_Oinsert(tc_prod(U_1540,U_1540),hAPP(hAPP(c_Product__Type_OPair(U_1540,U_1540),U_1541),U_1542),U_1543))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1540,U_1540)),hAPP(hAPP(c_Product__Type_OPair(U_1540,U_1540),U_1542),U_1541)),c_Transitive__Closure_Ortrancl(U_1540,U_1543)))
| ~ c_Wellfounded_Owf(U_1540,U_1543) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1540,U_1540)),hAPP(hAPP(c_Product__Type_OPair(U_1540,U_1540),U_1542),U_1541)),c_Transitive__Closure_Ortrancl(U_1540,U_1543)))
& c_Wellfounded_Owf(U_1540,U_1543) )
| ~ c_Wellfounded_Owf(U_1540,c_Set_Oinsert(tc_prod(U_1540,U_1540),hAPP(hAPP(c_Product__Type_OPair(U_1540,U_1540),U_1541),U_1542),U_1543)) ) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
( ! [U_1551,U_1549,U_1547,U_1545] :
( c_Wellfounded_Owf(U_1545,c_Set_Oinsert(tc_prod(U_1545,U_1545),hAPP(hAPP(c_Product__Type_OPair(U_1545,U_1545),U_1547),U_1549),U_1551))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1545,U_1545)),hAPP(hAPP(c_Product__Type_OPair(U_1545,U_1545),U_1549),U_1547)),c_Transitive__Closure_Ortrancl(U_1545,U_1551)))
| ~ c_Wellfounded_Owf(U_1545,U_1551) )
& ! [U_1550,U_1548,U_1546,U_1544] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1544,U_1544)),hAPP(hAPP(c_Product__Type_OPair(U_1544,U_1544),U_1548),U_1546)),c_Transitive__Closure_Ortrancl(U_1544,U_1550)))
& c_Wellfounded_Owf(U_1544,U_1550) )
| ~ c_Wellfounded_Owf(U_1544,c_Set_Oinsert(tc_prod(U_1544,U_1544),hAPP(hAPP(c_Product__Type_OPair(U_1544,U_1544),U_1546),U_1548),U_1550)) ) ),
inference(miniscope,[status(thm)],[f_254_2]) ).
fof(f_254_4,plain,
( ! [U_1544,U_1546,U_1548,U_1550] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1544,U_1544)),hAPP(hAPP(c_Product__Type_OPair(U_1544,U_1544),U_1548),U_1546)),c_Transitive__Closure_Ortrancl(U_1544,U_1550)))
| ~ sP101(U_1544,U_1546,U_1548,U_1550) )
& ! [U_1544,U_1546,U_1548,U_1550] :
( c_Wellfounded_Owf(U_1544,U_1550)
| ~ sP101(U_1544,U_1546,U_1548,U_1550) )
& ! [U_1549,U_1545,U_1547,U_1551] :
( c_Wellfounded_Owf(U_1545,c_Set_Oinsert(tc_prod(U_1545,U_1545),hAPP(hAPP(c_Product__Type_OPair(U_1545,U_1545),U_1547),U_1549),U_1551))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1545,U_1545)),hAPP(hAPP(c_Product__Type_OPair(U_1545,U_1545),U_1549),U_1547)),c_Transitive__Closure_Ortrancl(U_1545,U_1551)))
| ~ c_Wellfounded_Owf(U_1545,U_1551) )
& ! [U_1544,U_1546,U_1548,U_1550] :
( sP101(U_1544,U_1546,U_1548,U_1550)
| ~ c_Wellfounded_Owf(U_1544,c_Set_Oinsert(tc_prod(U_1544,U_1544),hAPP(hAPP(c_Product__Type_OPair(U_1544,U_1544),U_1546),U_1548),U_1550)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_254_3]) ).
cnf(f_254_5,plain,
( sP101(U_1544,U_1546,U_1548,U_1550)
| ~ c_Wellfounded_Owf(U_1544,c_Set_Oinsert(tc_prod(U_1544,U_1544),hAPP(hAPP(c_Product__Type_OPair(U_1544,U_1544),U_1546),U_1548),U_1550)) ),
inference(clausify,[status(thm)],[f_254_4]) ).
cnf(f_254_6,plain,
( c_Wellfounded_Owf(U_1545,c_Set_Oinsert(tc_prod(U_1545,U_1545),hAPP(hAPP(c_Product__Type_OPair(U_1545,U_1545),U_1547),U_1549),U_1551))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1545,U_1545)),hAPP(hAPP(c_Product__Type_OPair(U_1545,U_1545),U_1549),U_1547)),c_Transitive__Closure_Ortrancl(U_1545,U_1551)))
| ~ c_Wellfounded_Owf(U_1545,U_1551) ),
inference(clausify,[status(thm)],[f_254_4]) ).
cnf(f_254_7,plain,
( c_Wellfounded_Owf(U_1544,U_1550)
| ~ sP101(U_1544,U_1546,U_1548,U_1550) ),
inference(clausify,[status(thm)],[f_254_4]) ).
cnf(f_254_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1544,U_1544)),hAPP(hAPP(c_Product__Type_OPair(U_1544,U_1544),U_1548),U_1546)),c_Transitive__Closure_Ortrancl(U_1544,U_1550)))
| ~ sP101(U_1544,U_1546,U_1548,U_1550) ),
inference(clausify,[status(thm)],[f_254_4]) ).
fof(f_255_1,plain,
! [V_r_2,T_a] :
( c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))
| ~ c_Wellfounded_Oacyclic(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__impl__antisym__rtrancl]) ).
fof(f_255_2,plain,
! [U_1553,U_1552] :
( c_Relation_Oantisym(U_1552,c_Transitive__Closure_Ortrancl(U_1552,U_1553))
| ~ c_Wellfounded_Oacyclic(U_1552,U_1553) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_1552,U_1553] :
( c_Relation_Oantisym(U_1552,c_Transitive__Closure_Ortrancl(U_1552,U_1553))
| ~ c_Wellfounded_Oacyclic(U_1552,U_1553) ),
inference(definitional_conversion,[status(esa)],[f_255_2]) ).
cnf(f_255_4,plain,
( c_Relation_Oantisym(U_1552,c_Transitive__Closure_Ortrancl(U_1552,U_1553))
| ~ c_Wellfounded_Oacyclic(U_1552,U_1553) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [V_f_2,T_b,V_r_2,T_a] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__inv__image]) ).
fof(f_256_2,plain,
! [U_1557,U_1556,U_1555,U_1554] :
( c_Wellfounded_Owf(U_1556,hAPP(hAPP(c_Relation_Oinv__image(U_1554,U_1556),U_1555),U_1557))
| ~ c_Wellfounded_Owf(U_1554,U_1555) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_1554,U_1557,U_1556,U_1555] :
( c_Wellfounded_Owf(U_1556,hAPP(hAPP(c_Relation_Oinv__image(U_1554,U_1556),U_1555),U_1557))
| ~ c_Wellfounded_Owf(U_1554,U_1555) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( c_Wellfounded_Owf(U_1556,hAPP(hAPP(c_Relation_Oinv__image(U_1554,U_1556),U_1555),U_1557))
| ~ c_Wellfounded_Owf(U_1554,U_1555) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_1,plain,
! [V_rb_2,T_b,V_ra_2,T_a] :
( c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2))
| ~ c_Wellfounded_Owf(T_b,V_rb_2)
| ~ c_Wellfounded_Owf(T_a,V_ra_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__lex__prod]) ).
fof(f_257_2,plain,
! [U_1561,U_1560,U_1559,U_1558] :
( c_Wellfounded_Owf(tc_prod(U_1558,U_1560),c_Wellfounded_Olex__prod(U_1558,U_1560,U_1559,U_1561))
| ~ c_Wellfounded_Owf(U_1560,U_1561)
| ~ c_Wellfounded_Owf(U_1558,U_1559) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_1560,U_1559,U_1558,U_1561] :
( c_Wellfounded_Owf(tc_prod(U_1558,U_1560),c_Wellfounded_Olex__prod(U_1558,U_1560,U_1559,U_1561))
| ~ c_Wellfounded_Owf(U_1560,U_1561)
| ~ c_Wellfounded_Owf(U_1558,U_1559) ),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
( c_Wellfounded_Owf(tc_prod(U_1558,U_1560),c_Wellfounded_Olex__prod(U_1558,U_1560,U_1559,U_1561))
| ~ c_Wellfounded_Owf(U_1560,U_1561)
| ~ c_Wellfounded_Owf(U_1558,U_1559) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__trancl]) ).
fof(f_258_2,plain,
! [U_1563,U_1562] :
( c_Wellfounded_Owf(U_1562,c_Transitive__Closure_Otrancl(U_1562,U_1563))
| ~ c_Wellfounded_Owf(U_1562,U_1563) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_1563,U_1562] :
( c_Wellfounded_Owf(U_1562,c_Transitive__Closure_Otrancl(U_1562,U_1563))
| ~ c_Wellfounded_Owf(U_1562,U_1563) ),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
( c_Wellfounded_Owf(U_1562,c_Transitive__Closure_Otrancl(U_1562,U_1563))
| ~ c_Wellfounded_Owf(U_1562,U_1563) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [V_r_H_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_H_2,V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__Int2]) ).
fof(f_259_2,plain,
! [U_1566,U_1565,U_1564] :
( c_Wellfounded_Owf(U_1564,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1564,U_1564),tc_HOL_Obool),U_1566,U_1565))
| ~ c_Wellfounded_Owf(U_1564,U_1565) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_1564,U_1565,U_1566] :
( c_Wellfounded_Owf(U_1564,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1564,U_1564),tc_HOL_Obool),U_1566,U_1565))
| ~ c_Wellfounded_Owf(U_1564,U_1565) ),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
( c_Wellfounded_Owf(U_1564,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1564,U_1564),tc_HOL_Obool),U_1566,U_1565))
| ~ c_Wellfounded_Owf(U_1564,U_1565) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_r_H_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_r_H_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__Int1]) ).
fof(f_260_2,plain,
! [U_1569,U_1568,U_1567] :
( c_Wellfounded_Owf(U_1567,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1567,U_1567),tc_HOL_Obool),U_1568,U_1569))
| ~ c_Wellfounded_Owf(U_1567,U_1568) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_1567,U_1568,U_1569] :
( c_Wellfounded_Owf(U_1567,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1567,U_1567),tc_HOL_Obool),U_1568,U_1569))
| ~ c_Wellfounded_Owf(U_1567,U_1568) ),
inference(definitional_conversion,[status(esa)],[f_260_2]) ).
cnf(f_260_4,plain,
( c_Wellfounded_Owf(U_1567,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1567,U_1567),tc_HOL_Obool),U_1568,U_1569))
| ~ c_Wellfounded_Owf(U_1567,U_1568) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [V_r_2,T_a] :
( c_Wellfounded_Oacyclic(T_a,V_r_2)
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__acyclic]) ).
fof(f_261_2,plain,
! [U_1571,U_1570] :
( c_Wellfounded_Oacyclic(U_1570,U_1571)
| ~ c_Wellfounded_Owf(U_1570,U_1571) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
! [U_1571,U_1570] :
( c_Wellfounded_Oacyclic(U_1570,U_1571)
| ~ c_Wellfounded_Owf(U_1570,U_1571) ),
inference(definitional_conversion,[status(esa)],[f_261_2]) ).
cnf(f_261_4,plain,
( c_Wellfounded_Oacyclic(U_1570,U_1571)
| ~ c_Wellfounded_Owf(U_1570,U_1571) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_1,plain,
! [V_aa_2,V_r_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__irrefl]) ).
fof(f_262_2,plain,
! [U_1574,U_1573,U_1572] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1572,U_1572)),hAPP(hAPP(c_Product__Type_OPair(U_1572,U_1572),U_1574),U_1574)),U_1573))
| ~ c_Wellfounded_Owf(U_1572,U_1573) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_1572,U_1573,U_1574] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1572,U_1572)),hAPP(hAPP(c_Product__Type_OPair(U_1572,U_1572),U_1574),U_1574)),U_1573))
| ~ c_Wellfounded_Owf(U_1572,U_1573) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1572,U_1572)),hAPP(hAPP(c_Product__Type_OPair(U_1572,U_1572),U_1574),U_1574)),U_1573))
| ~ c_Wellfounded_Owf(U_1572,U_1573) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [V_x_2,V_aa_2,V_r_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_x_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__asym]) ).
fof(f_263_2,plain,
! [U_1578,U_1577,U_1576,U_1575] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1575,U_1575)),hAPP(hAPP(c_Product__Type_OPair(U_1575,U_1575),U_1578),U_1577)),U_1576))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1575,U_1575)),hAPP(hAPP(c_Product__Type_OPair(U_1575,U_1575),U_1577),U_1578)),U_1576))
| ~ c_Wellfounded_Owf(U_1575,U_1576) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_1575,U_1576,U_1577,U_1578] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1575,U_1575)),hAPP(hAPP(c_Product__Type_OPair(U_1575,U_1575),U_1578),U_1577)),U_1576))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1575,U_1575)),hAPP(hAPP(c_Product__Type_OPair(U_1575,U_1575),U_1577),U_1578)),U_1576))
| ~ c_Wellfounded_Owf(U_1575,U_1576) ),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1575,U_1575)),hAPP(hAPP(c_Product__Type_OPair(U_1575,U_1575),U_1578),U_1577)),U_1576))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1575,U_1575)),hAPP(hAPP(c_Product__Type_OPair(U_1575,U_1575),U_1577),U_1578)),U_1576))
| ~ c_Wellfounded_Owf(U_1575,U_1576) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [V_x_2,V_aa_2,V_r_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_aa_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_x_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__not__sym]) ).
fof(f_264_2,plain,
! [U_1582,U_1581,U_1580,U_1579] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1579,U_1579)),hAPP(hAPP(c_Product__Type_OPair(U_1579,U_1579),U_1582),U_1581)),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1579,U_1579)),hAPP(hAPP(c_Product__Type_OPair(U_1579,U_1579),U_1581),U_1582)),U_1580))
| ~ c_Wellfounded_Owf(U_1579,U_1580) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_1580,U_1581,U_1579,U_1582] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1579,U_1579)),hAPP(hAPP(c_Product__Type_OPair(U_1579,U_1579),U_1582),U_1581)),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1579,U_1579)),hAPP(hAPP(c_Product__Type_OPair(U_1579,U_1579),U_1581),U_1582)),U_1580))
| ~ c_Wellfounded_Owf(U_1579,U_1580) ),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1579,U_1579)),hAPP(hAPP(c_Product__Type_OPair(U_1579,U_1579),U_1582),U_1581)),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1579,U_1579)),hAPP(hAPP(c_Product__Type_OPair(U_1579,U_1579),U_1581),U_1582)),U_1580))
| ~ c_Wellfounded_Owf(U_1579,U_1580) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [V_aa_2,V_r_2,T_a] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__not__refl]) ).
fof(f_265_2,plain,
! [U_1585,U_1584,U_1583] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1583,U_1583)),hAPP(hAPP(c_Product__Type_OPair(U_1583,U_1583),U_1585),U_1585)),U_1584))
| ~ c_Wellfounded_Owf(U_1583,U_1584) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_1583,U_1584,U_1585] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1583,U_1583)),hAPP(hAPP(c_Product__Type_OPair(U_1583,U_1583),U_1585),U_1585)),U_1584))
| ~ c_Wellfounded_Owf(U_1583,U_1584) ),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1583,U_1583)),hAPP(hAPP(c_Product__Type_OPair(U_1583,U_1583),U_1585),U_1585)),U_1584))
| ~ c_Wellfounded_Owf(U_1583,U_1584) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [V_r_2,T_a] :
( ( c_Wellfounded_Owf(T_a,V_r_2)
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) )
& ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__acc__iff]) ).
fof(f_266_2,plain,
! [U_1589,U_1588] :
( ( c_Wellfounded_Owf(U_1588,U_1589)
| ? [U_1587] : ~ hBOOL(hAPP(hAPP(c_member(U_1588),U_1587),c_Wellfounded_Oacc(U_1588,U_1589))) )
& ( ! [U_1586] : hBOOL(hAPP(hAPP(c_member(U_1588),U_1586),c_Wellfounded_Oacc(U_1588,U_1589)))
| ~ c_Wellfounded_Owf(U_1588,U_1589) ) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
( ! [U_1593,U_1591] :
( c_Wellfounded_Owf(U_1591,U_1593)
| ? [U_1587] : ~ hBOOL(hAPP(hAPP(c_member(U_1591),U_1587),c_Wellfounded_Oacc(U_1591,U_1593))) )
& ! [U_1592,U_1590] :
( ! [U_1586] : hBOOL(hAPP(hAPP(c_member(U_1590),U_1586),c_Wellfounded_Oacc(U_1590,U_1592)))
| ~ c_Wellfounded_Owf(U_1590,U_1592) ) ),
inference(miniscope,[status(thm)],[f_266_2]) ).
fof(f_266_4,plain,
( ! [U_1593,U_1591] :
( c_Wellfounded_Owf(U_1591,U_1593)
| ~ hBOOL(hAPP(hAPP(c_member(U_1591),sK88(U_1593,U_1591)),c_Wellfounded_Oacc(U_1591,U_1593))) )
& ! [U_1592,U_1590] :
( ! [U_1586] : hBOOL(hAPP(hAPP(c_member(U_1590),U_1586),c_Wellfounded_Oacc(U_1590,U_1592)))
| ~ c_Wellfounded_Owf(U_1590,U_1592) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_1587,sK88(U_1593,U_1591))],[f_266_3]) ).
fof(f_266_5,plain,
( ! [U_1591,U_1593] :
( c_Wellfounded_Owf(U_1591,U_1593)
| ~ hBOOL(hAPP(hAPP(c_member(U_1591),sK88(U_1593,U_1591)),c_Wellfounded_Oacc(U_1591,U_1593))) )
& ! [U_1592,U_1586,U_1590] :
( hBOOL(hAPP(hAPP(c_member(U_1590),U_1586),c_Wellfounded_Oacc(U_1590,U_1592)))
| ~ c_Wellfounded_Owf(U_1590,U_1592) ) ),
inference(definitional_conversion,[status(esa)],[f_266_4]) ).
cnf(f_266_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1590),U_1586),c_Wellfounded_Oacc(U_1590,U_1592)))
| ~ c_Wellfounded_Owf(U_1590,U_1592) ),
inference(clausify,[status(thm)],[f_266_5]) ).
cnf(f_266_7,plain,
( c_Wellfounded_Owf(U_1591,U_1593)
| ~ hBOOL(hAPP(hAPP(c_member(U_1591),sK88(U_1593,U_1591)),c_Wellfounded_Oacc(U_1591,U_1593))) ),
inference(clausify,[status(thm)],[f_266_5]) ).
fof(f_267_1,plain,
! [V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_acc__wfD]) ).
fof(f_267_2,plain,
! [U_1596,U_1595,U_1594] :
( hBOOL(hAPP(hAPP(c_member(U_1594),U_1596),c_Wellfounded_Oacc(U_1594,U_1595)))
| ~ c_Wellfounded_Owf(U_1594,U_1595) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_1594,U_1595,U_1596] :
( hBOOL(hAPP(hAPP(c_member(U_1594),U_1596),c_Wellfounded_Oacc(U_1594,U_1595)))
| ~ c_Wellfounded_Owf(U_1594,U_1595) ),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1594),U_1596),c_Wellfounded_Oacc(U_1594,U_1595)))
| ~ c_Wellfounded_Owf(U_1594,U_1595) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [V_A_2,T_a] : c_Relation_Oantisym(T_a,c_Relation_OId__on(T_a,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_antisym__Id__on]) ).
fof(f_268_2,plain,
! [U_1598,U_1597] : c_Relation_Oantisym(U_1597,c_Relation_OId__on(U_1597,U_1598)),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_1597,U_1598] : c_Relation_Oantisym(U_1597,c_Relation_OId__on(U_1597,U_1598)),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
c_Relation_Oantisym(U_1597,c_Relation_OId__on(U_1597,U_1598)),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
! [V_ba_2,V_aa_2,V_r_2,T_a] :
( V_aa_2 = V_ba_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2))
| ~ c_Relation_Oantisym(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_antisymD]) ).
fof(f_269_2,plain,
! [U_1602,U_1601,U_1600,U_1599] :
( U_1601 = U_1602
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1599,U_1599)),hAPP(hAPP(c_Product__Type_OPair(U_1599,U_1599),U_1602),U_1601)),U_1600))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1599,U_1599)),hAPP(hAPP(c_Product__Type_OPair(U_1599,U_1599),U_1601),U_1602)),U_1600))
| ~ c_Relation_Oantisym(U_1599,U_1600) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
! [U_1599,U_1600,U_1601,U_1602] :
( U_1601 = U_1602
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1599,U_1599)),hAPP(hAPP(c_Product__Type_OPair(U_1599,U_1599),U_1602),U_1601)),U_1600))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1599,U_1599)),hAPP(hAPP(c_Product__Type_OPair(U_1599,U_1599),U_1601),U_1602)),U_1600))
| ~ c_Relation_Oantisym(U_1599,U_1600) ),
inference(definitional_conversion,[status(esa)],[f_269_2]) ).
cnf(f_269_4,plain,
( U_1601 = U_1602
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1599,U_1599)),hAPP(hAPP(c_Product__Type_OPair(U_1599,U_1599),U_1602),U_1601)),U_1600))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1599,U_1599)),hAPP(hAPP(c_Product__Type_OPair(U_1599,U_1599),U_1601),U_1602)),U_1600))
| ~ c_Relation_Oantisym(U_1599,U_1600) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [V_r_2,T_a] :
( ( c_Relation_Oantisym(T_a,V_r_2)
| ? [B_x,B_y] :
( B_x != B_y
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) )
& ( ! [B_x,B_y] :
( B_x = B_y
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) )
| ~ c_Relation_Oantisym(T_a,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_antisym__def]) ).
fof(f_270_2,plain,
! [U_1608,U_1607] :
( ( c_Relation_Oantisym(U_1607,U_1608)
| ? [U_1606,U_1605] :
( U_1606 != U_1605
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1607,U_1607)),hAPP(hAPP(c_Product__Type_OPair(U_1607,U_1607),U_1605),U_1606)),U_1608))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1607,U_1607)),hAPP(hAPP(c_Product__Type_OPair(U_1607,U_1607),U_1606),U_1605)),U_1608)) ) )
& ( ! [U_1604,U_1603] :
( U_1604 = U_1603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1607,U_1607)),hAPP(hAPP(c_Product__Type_OPair(U_1607,U_1607),U_1603),U_1604)),U_1608))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1607,U_1607)),hAPP(hAPP(c_Product__Type_OPair(U_1607,U_1607),U_1604),U_1603)),U_1608)) )
| ~ c_Relation_Oantisym(U_1607,U_1608) ) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
( ! [U_1612,U_1610] :
( c_Relation_Oantisym(U_1610,U_1612)
| ? [U_1606,U_1605] :
( U_1606 != U_1605
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),U_1605),U_1606)),U_1612))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),U_1606),U_1605)),U_1612)) ) )
& ! [U_1611,U_1609] :
( ! [U_1604,U_1603] :
( U_1604 = U_1603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1603),U_1604)),U_1611))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1604),U_1603)),U_1611)) )
| ~ c_Relation_Oantisym(U_1609,U_1611) ) ),
inference(miniscope,[status(thm)],[f_270_2]) ).
fof(f_270_4,plain,
( ! [U_1612,U_1610] :
( c_Relation_Oantisym(U_1610,U_1612)
| ? [U_1605] :
( sK89(U_1612,U_1610) != U_1605
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),U_1605),sK89(U_1612,U_1610))),U_1612))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),sK89(U_1612,U_1610)),U_1605)),U_1612)) ) )
& ! [U_1611,U_1609] :
( ! [U_1604,U_1603] :
( U_1604 = U_1603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1603),U_1604)),U_1611))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1604),U_1603)),U_1611)) )
| ~ c_Relation_Oantisym(U_1609,U_1611) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_1606,sK89(U_1612,U_1610))],[f_270_3]) ).
fof(f_270_5,plain,
( ! [U_1612,U_1610] :
( c_Relation_Oantisym(U_1610,U_1612)
| ( sK89(U_1612,U_1610) != sK90(U_1612,U_1610)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),sK90(U_1612,U_1610)),sK89(U_1612,U_1610))),U_1612))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),sK89(U_1612,U_1610)),sK90(U_1612,U_1610))),U_1612)) ) )
& ! [U_1611,U_1609] :
( ! [U_1604,U_1603] :
( U_1604 = U_1603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1603),U_1604)),U_1611))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1604),U_1603)),U_1611)) )
| ~ c_Relation_Oantisym(U_1609,U_1611) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_1605,sK90(U_1612,U_1610))],[f_270_4]) ).
fof(f_270_6,plain,
( ! [U_1612,U_1610] :
( sK89(U_1612,U_1610) != sK90(U_1612,U_1610)
| ~ sP102(U_1612,U_1610) )
& ! [U_1612,U_1610] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),sK90(U_1612,U_1610)),sK89(U_1612,U_1610))),U_1612))
| ~ sP102(U_1612,U_1610) )
& ! [U_1612,U_1610] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),sK89(U_1612,U_1610)),sK90(U_1612,U_1610))),U_1612))
| ~ sP102(U_1612,U_1610) )
& ! [U_1612,U_1610] :
( c_Relation_Oantisym(U_1610,U_1612)
| sP102(U_1612,U_1610) )
& ! [U_1603,U_1604,U_1609,U_1611] :
( U_1604 = U_1603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1603),U_1604)),U_1611))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1604),U_1603)),U_1611))
| ~ c_Relation_Oantisym(U_1609,U_1611) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_270_5]) ).
cnf(f_270_7,plain,
( U_1604 = U_1603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1603),U_1604)),U_1611))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1604),U_1603)),U_1611))
| ~ c_Relation_Oantisym(U_1609,U_1611) ),
inference(clausify,[status(thm)],[f_270_6]) ).
cnf(f_270_8,plain,
( c_Relation_Oantisym(U_1610,U_1612)
| sP102(U_1612,U_1610) ),
inference(clausify,[status(thm)],[f_270_6]) ).
cnf(f_270_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),sK89(U_1612,U_1610)),sK90(U_1612,U_1610))),U_1612))
| ~ sP102(U_1612,U_1610) ),
inference(clausify,[status(thm)],[f_270_6]) ).
cnf(f_270_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1610,U_1610)),hAPP(hAPP(c_Product__Type_OPair(U_1610,U_1610),sK90(U_1612,U_1610)),sK89(U_1612,U_1610))),U_1612))
| ~ sP102(U_1612,U_1610) ),
inference(clausify,[status(thm)],[f_270_6]) ).
cnf(f_270_11,plain,
( sK89(U_1612,U_1610) != sK90(U_1612,U_1610)
| ~ sP102(U_1612,U_1610) ),
inference(clausify,[status(thm)],[f_270_6]) ).
fof(f_271_1,plain,
! [V_x_2,V_f_2,T_b,T_a] : c_Fun_Ofun__upd(T_a,T_b,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_271_2,plain,
! [U_1616,U_1615,U_1614,U_1613] : c_Fun_Ofun__upd(U_1613,U_1614,U_1615,U_1616,hAPP(U_1615,U_1616)) = U_1615,
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_1614,U_1615,U_1613,U_1616] : c_Fun_Ofun__upd(U_1613,U_1614,U_1615,U_1616,hAPP(U_1615,U_1616)) = U_1615,
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
c_Fun_Ofun__upd(U_1613,U_1614,U_1615,U_1616,hAPP(U_1615,U_1616)) = U_1615,
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_wf__measure]) ).
fof(f_272_2,plain,
! [U_1618,U_1617] : c_Wellfounded_Owf(U_1617,hAPP(c_Wellfounded_Omeasure(U_1617),U_1618)),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_1618,U_1617] : c_Wellfounded_Owf(U_1617,hAPP(c_Wellfounded_Omeasure(U_1617),U_1618)),
inference(definitional_conversion,[status(esa)],[f_272_2]) ).
cnf(f_272_4,plain,
c_Wellfounded_Owf(U_1617,hAPP(c_Wellfounded_Omeasure(U_1617),U_1618)),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [T_b,T_a,B_M,B_R] :
( ! [B_x] : hAPP(c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_x) = hAPP(hAPP(B_M,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),c_Recdef_Owfrec(T_a,T_b,B_R,B_M)),B_R),B_x)),B_x)
| ~ c_Wellfounded_Owf(T_a,B_R) ),
inference(fof_nnf,[status(thm)],[fact_tfl__wfrec]) ).
fof(f_273_2,plain,
! [U_1623,U_1622,U_1621,U_1620] :
( ! [U_1619] : hAPP(c_Recdef_Owfrec(U_1622,U_1623,U_1620,U_1621),U_1619) = hAPP(hAPP(U_1621,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1622,U_1623),c_Recdef_Owfrec(U_1622,U_1623,U_1620,U_1621)),U_1620),U_1619)),U_1619)
| ~ c_Wellfounded_Owf(U_1622,U_1620) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_1621,U_1622,U_1623,U_1619,U_1620] :
( hAPP(c_Recdef_Owfrec(U_1622,U_1623,U_1620,U_1621),U_1619) = hAPP(hAPP(U_1621,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1622,U_1623),c_Recdef_Owfrec(U_1622,U_1623,U_1620,U_1621)),U_1620),U_1619)),U_1619)
| ~ c_Wellfounded_Owf(U_1622,U_1620) ),
inference(definitional_conversion,[status(esa)],[f_273_2]) ).
cnf(f_273_4,plain,
( hAPP(c_Recdef_Owfrec(U_1622,U_1623,U_1620,U_1621),U_1619) = hAPP(hAPP(U_1621,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1622,U_1623),c_Recdef_Owfrec(U_1622,U_1623,U_1620,U_1621)),U_1620),U_1619)),U_1619)
| ~ c_Wellfounded_Owf(U_1622,U_1620) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
! [V_aa_2,V_H_2,T_b,V_r_2,T_a] :
( hAPP(c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_aa_2) = hAPP(hAPP(V_H_2,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2)),V_r_2),V_aa_2)),V_aa_2)
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wfrec]) ).
fof(f_274_2,plain,
! [U_1628,U_1627,U_1626,U_1625,U_1624] :
( hAPP(c_Recdef_Owfrec(U_1624,U_1626,U_1625,U_1627),U_1628) = hAPP(hAPP(U_1627,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1624,U_1626),c_Recdef_Owfrec(U_1624,U_1626,U_1625,U_1627)),U_1625),U_1628)),U_1628)
| ~ c_Wellfounded_Owf(U_1624,U_1625) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_1624,U_1625,U_1626,U_1627,U_1628] :
( hAPP(c_Recdef_Owfrec(U_1624,U_1626,U_1625,U_1627),U_1628) = hAPP(hAPP(U_1627,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1624,U_1626),c_Recdef_Owfrec(U_1624,U_1626,U_1625,U_1627)),U_1625),U_1628)),U_1628)
| ~ c_Wellfounded_Owf(U_1624,U_1625) ),
inference(definitional_conversion,[status(esa)],[f_274_2]) ).
cnf(f_274_4,plain,
( hAPP(c_Recdef_Owfrec(U_1624,U_1626,U_1625,U_1627),U_1628) = hAPP(hAPP(U_1627,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1624,U_1626),c_Recdef_Owfrec(U_1624,U_1626,U_1625,U_1627)),U_1625),U_1628)),U_1628)
| ~ c_Wellfounded_Owf(U_1624,U_1625) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
( c_Fun_Ofun__upd(T_b,T_a,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_275_2,plain,
! [U_1633,U_1632,U_1631,U_1630,U_1629] :
( c_Fun_Ofun__upd(U_1632,U_1633,U_1629,U_1630,U_1631) = U_1629
| hAPP(U_1629,U_1630) != U_1631 ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_1631,U_1630,U_1629,U_1632,U_1633] :
( c_Fun_Ofun__upd(U_1632,U_1633,U_1629,U_1630,U_1631) = U_1629
| hAPP(U_1629,U_1630) != U_1631 ),
inference(definitional_conversion,[status(esa)],[f_275_2]) ).
cnf(f_275_4,plain,
( c_Fun_Ofun__upd(U_1632,U_1633,U_1629,U_1630,U_1631) = U_1629
| hAPP(U_1629,U_1630) != U_1631 ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
( hAPP(c_Fun_Ofun__upd(T_a,T_b,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_276_2,plain,
! [U_1639,U_1638,U_1637,U_1636,U_1635,U_1634] :
( hAPP(c_Fun_Ofun__upd(U_1636,U_1637,U_1638,U_1635,U_1639),U_1634) = hAPP(U_1638,U_1634)
| U_1634 = U_1635 ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_1635,U_1634,U_1636,U_1637,U_1638,U_1639] :
( hAPP(c_Fun_Ofun__upd(U_1636,U_1637,U_1638,U_1635,U_1639),U_1634) = hAPP(U_1638,U_1634)
| U_1634 = U_1635 ),
inference(definitional_conversion,[status(esa)],[f_276_2]) ).
cnf(f_276_4,plain,
( hAPP(c_Fun_Ofun__upd(U_1636,U_1637,U_1638,U_1635,U_1639),U_1634) = hAPP(U_1638,U_1634)
| U_1634 = U_1635 ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [V_d_2,V_ba_2,V_m_2,T_b,T_a,V_ca_2,V_aa_2] :
( c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_aa_2,V_ba_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_ca_2,V_d_2),V_aa_2,V_ba_2)
| V_aa_2 = V_ca_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__twist]) ).
fof(f_277_2,plain,
! [U_1646,U_1645,U_1644,U_1643,U_1642,U_1641,U_1640] :
( c_Fun_Ofun__upd(U_1642,U_1643,c_Fun_Ofun__upd(U_1642,U_1643,U_1644,U_1640,U_1645),U_1641,U_1646) = c_Fun_Ofun__upd(U_1642,U_1643,c_Fun_Ofun__upd(U_1642,U_1643,U_1644,U_1641,U_1646),U_1640,U_1645)
| U_1640 = U_1641 ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_1641,U_1640,U_1642,U_1643,U_1644,U_1645,U_1646] :
( c_Fun_Ofun__upd(U_1642,U_1643,c_Fun_Ofun__upd(U_1642,U_1643,U_1644,U_1640,U_1645),U_1641,U_1646) = c_Fun_Ofun__upd(U_1642,U_1643,c_Fun_Ofun__upd(U_1642,U_1643,U_1644,U_1641,U_1646),U_1640,U_1645)
| U_1640 = U_1641 ),
inference(definitional_conversion,[status(esa)],[f_277_2]) ).
cnf(f_277_4,plain,
( c_Fun_Ofun__upd(U_1642,U_1643,c_Fun_Ofun__upd(U_1642,U_1643,U_1644,U_1640,U_1645),U_1641,U_1646) = c_Fun_Ofun__upd(U_1642,U_1643,c_Fun_Ofun__upd(U_1642,U_1643,U_1644,U_1641,U_1646),U_1640,U_1645)
| U_1640 = U_1641 ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
( ( hAPP(c_Fun_Ofun__upd(T_a,T_b,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_a,T_b,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_278_2,plain,
! [U_1652,U_1651,U_1650,U_1649,U_1648,U_1647] :
( ( hAPP(c_Fun_Ofun__upd(U_1649,U_1650,U_1651,U_1648,U_1652),U_1647) = hAPP(U_1651,U_1647)
| U_1647 = U_1648 )
& ( hAPP(c_Fun_Ofun__upd(U_1649,U_1650,U_1651,U_1648,U_1652),U_1647) = U_1652
| U_1647 != U_1648 ) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
( ! [U_1664,U_1662,U_1660,U_1658,U_1656,U_1654] :
( hAPP(c_Fun_Ofun__upd(U_1658,U_1660,U_1662,U_1656,U_1664),U_1654) = hAPP(U_1662,U_1654)
| U_1654 = U_1656 )
& ! [U_1663,U_1661,U_1659,U_1657,U_1655,U_1653] :
( hAPP(c_Fun_Ofun__upd(U_1657,U_1659,U_1661,U_1655,U_1663),U_1653) = U_1663
| U_1653 != U_1655 ) ),
inference(miniscope,[status(thm)],[f_278_2]) ).
fof(f_278_4,plain,
( ! [U_1654,U_1656,U_1658,U_1660,U_1662,U_1664] :
( hAPP(c_Fun_Ofun__upd(U_1658,U_1660,U_1662,U_1656,U_1664),U_1654) = hAPP(U_1662,U_1654)
| U_1654 = U_1656 )
& ! [U_1653,U_1657,U_1661,U_1663,U_1659,U_1655] :
( hAPP(c_Fun_Ofun__upd(U_1657,U_1659,U_1661,U_1655,U_1663),U_1653) = U_1663
| U_1653 != U_1655 ) ),
inference(definitional_conversion,[status(esa)],[f_278_3]) ).
cnf(f_278_5,plain,
( hAPP(c_Fun_Ofun__upd(U_1657,U_1659,U_1661,U_1655,U_1663),U_1653) = U_1663
| U_1653 != U_1655 ),
inference(clausify,[status(thm)],[f_278_4]) ).
cnf(f_278_6,plain,
( hAPP(c_Fun_Ofun__upd(U_1658,U_1660,U_1662,U_1656,U_1664),U_1654) = hAPP(U_1662,U_1654)
| U_1654 = U_1656 ),
inference(clausify,[status(thm)],[f_278_4]) ).
fof(f_279_1,plain,
! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(c_Fun_Ofun__upd(T_b,T_a,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_279_2,plain,
! [U_1669,U_1668,U_1667,U_1666,U_1665] : hAPP(c_Fun_Ofun__upd(U_1665,U_1666,U_1667,U_1668,U_1669),U_1668) = U_1669,
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1665,U_1666,U_1667,U_1668,U_1669] : hAPP(c_Fun_Ofun__upd(U_1665,U_1666,U_1667,U_1668,U_1669),U_1668) = U_1669,
inference(definitional_conversion,[status(esa)],[f_279_2]) ).
cnf(f_279_4,plain,
hAPP(c_Fun_Ofun__upd(U_1665,U_1666,U_1667,U_1668,U_1669),U_1668) = U_1669,
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_1,plain,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_z_2),
inference(fof_nnf,[status(thm)],[fact_fun__upd__upd]) ).
fof(f_280_2,plain,
! [U_1675,U_1674,U_1673,U_1672,U_1671,U_1670] : c_Fun_Ofun__upd(U_1670,U_1671,c_Fun_Ofun__upd(U_1670,U_1671,U_1672,U_1673,U_1674),U_1673,U_1675) = c_Fun_Ofun__upd(U_1670,U_1671,U_1672,U_1673,U_1675),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_1671,U_1670,U_1672,U_1673,U_1674,U_1675] : c_Fun_Ofun__upd(U_1670,U_1671,c_Fun_Ofun__upd(U_1670,U_1671,U_1672,U_1673,U_1674),U_1673,U_1675) = c_Fun_Ofun__upd(U_1670,U_1671,U_1672,U_1673,U_1675),
inference(definitional_conversion,[status(esa)],[f_280_2]) ).
cnf(f_280_4,plain,
c_Fun_Ofun__upd(U_1670,U_1671,c_Fun_Ofun__upd(U_1670,U_1671,U_1672,U_1673,U_1674),U_1673,U_1675) = c_Fun_Ofun__upd(U_1670,U_1671,U_1672,U_1673,U_1675),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
( ( c_Fun_Ofun__upd(T_a,T_b,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_a,T_b,V_f_2,V_x_2,V_y_2) != V_f_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff]) ).
fof(f_281_2,plain,
! [U_1680,U_1679,U_1678,U_1677,U_1676] :
( ( c_Fun_Ofun__upd(U_1676,U_1677,U_1678,U_1679,U_1680) = U_1678
| hAPP(U_1678,U_1679) != U_1680 )
& ( hAPP(U_1678,U_1679) = U_1680
| c_Fun_Ofun__upd(U_1676,U_1677,U_1678,U_1679,U_1680) != U_1678 ) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
( ! [U_1690,U_1688,U_1686] :
( ! [U_1684,U_1682] : c_Fun_Ofun__upd(U_1682,U_1684,U_1686,U_1688,U_1690) = U_1686
| hAPP(U_1686,U_1688) != U_1690 )
& ! [U_1689,U_1687,U_1685] :
( ! [U_1683,U_1681] : c_Fun_Ofun__upd(U_1681,U_1683,U_1685,U_1687,U_1689) != U_1685
| hAPP(U_1685,U_1687) = U_1689 ) ),
inference(miniscope,[status(thm)],[f_281_2]) ).
fof(f_281_4,plain,
( ! [U_1690,U_1684,U_1682,U_1688,U_1686] :
( c_Fun_Ofun__upd(U_1682,U_1684,U_1686,U_1688,U_1690) = U_1686
| hAPP(U_1686,U_1688) != U_1690 )
& ! [U_1681,U_1683,U_1685,U_1687,U_1689] :
( c_Fun_Ofun__upd(U_1681,U_1683,U_1685,U_1687,U_1689) != U_1685
| hAPP(U_1685,U_1687) = U_1689 ) ),
inference(definitional_conversion,[status(esa)],[f_281_3]) ).
cnf(f_281_5,plain,
( c_Fun_Ofun__upd(U_1681,U_1683,U_1685,U_1687,U_1689) != U_1685
| hAPP(U_1685,U_1687) = U_1689 ),
inference(clausify,[status(thm)],[f_281_4]) ).
cnf(f_281_6,plain,
( c_Fun_Ofun__upd(U_1682,U_1684,U_1686,U_1688,U_1690) = U_1686
| hAPP(U_1686,U_1688) != U_1690 ),
inference(clausify,[status(thm)],[f_281_4]) ).
fof(f_282_1,plain,
! [V_ba_2,V_f_2,T_b,T_a,V_aa_2,V_x_2] :
( ( hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_aa_2,V_ba_2),V_x_2) = hAPP(V_f_2,V_x_2)
| V_x_2 = V_aa_2 )
& ( hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_aa_2,V_ba_2),V_x_2) = V_ba_2
| V_x_2 != V_aa_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__def]) ).
fof(f_282_2,plain,
! [U_1696,U_1695,U_1694,U_1693,U_1692,U_1691] :
( ( hAPP(c_Fun_Ofun__upd(U_1693,U_1694,U_1695,U_1692,U_1696),U_1691) = hAPP(U_1695,U_1691)
| U_1691 = U_1692 )
& ( hAPP(c_Fun_Ofun__upd(U_1693,U_1694,U_1695,U_1692,U_1696),U_1691) = U_1696
| U_1691 != U_1692 ) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
( ! [U_1708,U_1706,U_1704,U_1702,U_1700,U_1698] :
( hAPP(c_Fun_Ofun__upd(U_1702,U_1704,U_1706,U_1700,U_1708),U_1698) = hAPP(U_1706,U_1698)
| U_1698 = U_1700 )
& ! [U_1707,U_1705,U_1703,U_1701,U_1699,U_1697] :
( hAPP(c_Fun_Ofun__upd(U_1701,U_1703,U_1705,U_1699,U_1707),U_1697) = U_1707
| U_1697 != U_1699 ) ),
inference(miniscope,[status(thm)],[f_282_2]) ).
fof(f_282_4,plain,
( ! [U_1698,U_1700,U_1702,U_1704,U_1706,U_1708] :
( hAPP(c_Fun_Ofun__upd(U_1702,U_1704,U_1706,U_1700,U_1708),U_1698) = hAPP(U_1706,U_1698)
| U_1698 = U_1700 )
& ! [U_1703,U_1701,U_1699,U_1697,U_1705,U_1707] :
( hAPP(c_Fun_Ofun__upd(U_1701,U_1703,U_1705,U_1699,U_1707),U_1697) = U_1707
| U_1697 != U_1699 ) ),
inference(definitional_conversion,[status(esa)],[f_282_3]) ).
cnf(f_282_5,plain,
( hAPP(c_Fun_Ofun__upd(U_1701,U_1703,U_1705,U_1699,U_1707),U_1697) = U_1707
| U_1697 != U_1699 ),
inference(clausify,[status(thm)],[f_282_4]) ).
cnf(f_282_6,plain,
( hAPP(c_Fun_Ofun__upd(U_1702,U_1704,U_1706,U_1700,U_1708),U_1698) = hAPP(U_1706,U_1698)
| U_1698 = U_1700 ),
inference(clausify,[status(thm)],[f_282_4]) ).
fof(f_283_1,plain,
! [V_aa_2,V_H_2,V_r_2,T_b,T_a,V_f_2] :
( hAPP(V_f_2,V_aa_2) = hAPP(hAPP(V_H_2,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_aa_2)),V_aa_2)
| ~ c_Wellfounded_Owf(T_a,V_r_2)
| V_f_2 != c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2) ),
inference(fof_nnf,[status(thm)],[fact_def__wfrec]) ).
fof(f_283_2,plain,
! [U_1714,U_1713,U_1712,U_1711,U_1710,U_1709] :
( hAPP(U_1709,U_1714) = hAPP(hAPP(U_1713,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1710,U_1711),U_1709),U_1712),U_1714)),U_1714)
| ~ c_Wellfounded_Owf(U_1710,U_1712)
| U_1709 != c_Recdef_Owfrec(U_1710,U_1711,U_1712,U_1713) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1709,U_1710,U_1711,U_1712,U_1713,U_1714] :
( hAPP(U_1709,U_1714) = hAPP(hAPP(U_1713,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1710,U_1711),U_1709),U_1712),U_1714)),U_1714)
| ~ c_Wellfounded_Owf(U_1710,U_1712)
| U_1709 != c_Recdef_Owfrec(U_1710,U_1711,U_1712,U_1713) ),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
( hAPP(U_1709,U_1714) = hAPP(hAPP(U_1713,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1710,U_1711),U_1709),U_1712),U_1714)),U_1714)
| ~ c_Wellfounded_Owf(U_1710,U_1712)
| U_1709 != c_Recdef_Owfrec(U_1710,U_1711,U_1712,U_1713) ),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_1,plain,
! [V_x_2,V_Fa_2,V_R_2,T_a,T_b] : hAPP(c_Recdef_Owfrec(T_b,T_a,V_R_2,V_Fa_2),V_x_2) = c_HOL_OThe(T_a,c_Recdef_Owfrec__rel(T_b,T_a,V_R_2,hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(T_b,T_b),tc_fun(T_b,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_a)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_a)),tc_fun(T_b,T_a)),c_COMBS(T_b,T_b,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_a)),tc_fun(T_b,tc_fun(T_b,T_a)),tc_fun(T_b,T_a)),hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(T_b,T_a),T_b),V_Fa_2)),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,T_a))),c_Recdef_Ocut(T_b,T_a)),V_R_2)))),c_COMBI(T_b)),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_wfrec__def]) ).
fof(f_284_2,plain,
! [U_1719,U_1718,U_1717,U_1716,U_1715] : hAPP(c_Recdef_Owfrec(U_1715,U_1716,U_1717,U_1718),U_1719) = c_HOL_OThe(U_1716,c_Recdef_Owfrec__rel(U_1715,U_1716,U_1717,hAPP(hAPP(c_COMBC(tc_fun(U_1715,U_1716),tc_fun(U_1715,U_1715),tc_fun(U_1715,U_1716)),hAPP(hAPP(c_COMBB(tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(tc_fun(U_1715,U_1715),tc_fun(U_1715,U_1716)),tc_fun(U_1715,U_1716)),c_COMBS(U_1715,U_1715,U_1716)),hAPP(hAPP(c_COMBB(tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(U_1715,U_1716)),hAPP(c_COMBB(tc_fun(U_1715,U_1716),tc_fun(U_1715,U_1716),U_1715),U_1718)),hAPP(hAPP(c_COMBC(tc_fun(U_1715,U_1716),tc_fun(tc_prod(U_1715,U_1715),tc_HOL_Obool),tc_fun(U_1715,tc_fun(U_1715,U_1716))),c_Recdef_Ocut(U_1715,U_1716)),U_1717)))),c_COMBI(U_1715)),U_1719)),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_1715,U_1716,U_1717,U_1718,U_1719] : hAPP(c_Recdef_Owfrec(U_1715,U_1716,U_1717,U_1718),U_1719) = c_HOL_OThe(U_1716,c_Recdef_Owfrec__rel(U_1715,U_1716,U_1717,hAPP(hAPP(c_COMBC(tc_fun(U_1715,U_1716),tc_fun(U_1715,U_1715),tc_fun(U_1715,U_1716)),hAPP(hAPP(c_COMBB(tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(tc_fun(U_1715,U_1715),tc_fun(U_1715,U_1716)),tc_fun(U_1715,U_1716)),c_COMBS(U_1715,U_1715,U_1716)),hAPP(hAPP(c_COMBB(tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(U_1715,U_1716)),hAPP(c_COMBB(tc_fun(U_1715,U_1716),tc_fun(U_1715,U_1716),U_1715),U_1718)),hAPP(hAPP(c_COMBC(tc_fun(U_1715,U_1716),tc_fun(tc_prod(U_1715,U_1715),tc_HOL_Obool),tc_fun(U_1715,tc_fun(U_1715,U_1716))),c_Recdef_Ocut(U_1715,U_1716)),U_1717)))),c_COMBI(U_1715)),U_1719)),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
hAPP(c_Recdef_Owfrec(U_1715,U_1716,U_1717,U_1718),U_1719) = c_HOL_OThe(U_1716,c_Recdef_Owfrec__rel(U_1715,U_1716,U_1717,hAPP(hAPP(c_COMBC(tc_fun(U_1715,U_1716),tc_fun(U_1715,U_1715),tc_fun(U_1715,U_1716)),hAPP(hAPP(c_COMBB(tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(tc_fun(U_1715,U_1715),tc_fun(U_1715,U_1716)),tc_fun(U_1715,U_1716)),c_COMBS(U_1715,U_1715,U_1716)),hAPP(hAPP(c_COMBB(tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(U_1715,tc_fun(U_1715,U_1716)),tc_fun(U_1715,U_1716)),hAPP(c_COMBB(tc_fun(U_1715,U_1716),tc_fun(U_1715,U_1716),U_1715),U_1718)),hAPP(hAPP(c_COMBC(tc_fun(U_1715,U_1716),tc_fun(tc_prod(U_1715,U_1715),tc_HOL_Obool),tc_fun(U_1715,tc_fun(U_1715,U_1716))),c_Recdef_Ocut(U_1715,U_1716)),U_1717)))),c_COMBI(U_1715)),U_1719)),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_1,plain,
! [T_a,V_R_2,T_b,V_Pa_2] :
( c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2))
| ? [B_x] :
( ~ c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x))
& hBOOL(hAPP(V_Pa_2,B_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).
fof(f_285_2,plain,
! [U_1724,U_1723,U_1722,U_1721] :
( c_Wellfounded_Owf(tc_prod(U_1724,U_1722),c_Recdef_Osame__fst(U_1724,U_1722,U_1721,U_1723))
| ? [U_1720] :
( ~ c_Wellfounded_Owf(U_1722,hAPP(U_1723,U_1720))
& hBOOL(hAPP(U_1721,U_1720)) ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1724,U_1723,U_1722,U_1721] :
( c_Wellfounded_Owf(tc_prod(U_1724,U_1722),c_Recdef_Osame__fst(U_1724,U_1722,U_1721,U_1723))
| ( ~ c_Wellfounded_Owf(U_1722,hAPP(U_1723,sK91(U_1724,U_1723,U_1722,U_1721)))
& hBOOL(hAPP(U_1721,sK91(U_1724,U_1723,U_1722,U_1721))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_1720,sK91(U_1724,U_1723,U_1722,U_1721))],[f_285_2]) ).
fof(f_285_4,plain,
( ! [U_1724,U_1721,U_1723,U_1722] :
( ~ c_Wellfounded_Owf(U_1722,hAPP(U_1723,sK91(U_1724,U_1723,U_1722,U_1721)))
| ~ sP103(U_1724,U_1721,U_1723,U_1722) )
& ! [U_1724,U_1721,U_1723,U_1722] :
( hBOOL(hAPP(U_1721,sK91(U_1724,U_1723,U_1722,U_1721)))
| ~ sP103(U_1724,U_1721,U_1723,U_1722) )
& ! [U_1724,U_1721,U_1723,U_1722] :
( c_Wellfounded_Owf(tc_prod(U_1724,U_1722),c_Recdef_Osame__fst(U_1724,U_1722,U_1721,U_1723))
| sP103(U_1724,U_1721,U_1723,U_1722) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_285_3]) ).
cnf(f_285_5,plain,
( c_Wellfounded_Owf(tc_prod(U_1724,U_1722),c_Recdef_Osame__fst(U_1724,U_1722,U_1721,U_1723))
| sP103(U_1724,U_1721,U_1723,U_1722) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_6,plain,
( hBOOL(hAPP(U_1721,sK91(U_1724,U_1723,U_1722,U_1721)))
| ~ sP103(U_1724,U_1721,U_1723,U_1722) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_7,plain,
( ~ c_Wellfounded_Owf(U_1722,hAPP(U_1723,sK91(U_1724,U_1723,U_1722,U_1721)))
| ~ sP103(U_1724,U_1721,U_1723,U_1722) ),
inference(clausify,[status(thm)],[f_285_4]) ).
fof(f_286_1,plain,
! [V_x_2,V_Fa_2,V_R_2,T_b,T_a] :
( ? [B_x] :
( ! [B_y] :
( B_y = B_x
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2),B_y)) )
& hBOOL(hAPP(c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2),B_x)) )
| ~ c_Wellfounded_Owf(T_a,V_R_2)
| ~ c_Recdef_Oadm__wf(T_a,T_b,V_R_2,V_Fa_2) ),
inference(fof_nnf,[status(thm)],[fact_wfrec__unique]) ).
fof(f_286_2,plain,
! [U_1731,U_1730,U_1729,U_1728,U_1727] :
( ? [U_1726] :
( ! [U_1725] :
( U_1725 = U_1726
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),U_1725)) )
& hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),U_1726)) )
| ~ c_Wellfounded_Owf(U_1727,U_1729)
| ~ c_Recdef_Oadm__wf(U_1727,U_1728,U_1729,U_1730) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1731,U_1730,U_1729,U_1728,U_1727] :
( ( ! [U_1725] :
( U_1725 = sK92(U_1731,U_1730,U_1729,U_1728,U_1727)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),U_1725)) )
& hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),sK92(U_1731,U_1730,U_1729,U_1728,U_1727))) )
| ~ c_Wellfounded_Owf(U_1727,U_1729)
| ~ c_Recdef_Oadm__wf(U_1727,U_1728,U_1729,U_1730) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_1726,sK92(U_1731,U_1730,U_1729,U_1728,U_1727))],[f_286_2]) ).
fof(f_286_4,plain,
( ! [U_1725,U_1727,U_1728,U_1729,U_1730,U_1731] :
( U_1725 = sK92(U_1731,U_1730,U_1729,U_1728,U_1727)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),U_1725))
| ~ sP104(U_1725,U_1727,U_1728,U_1729,U_1730,U_1731) )
& ! [U_1725,U_1727,U_1728,U_1729,U_1730,U_1731] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),sK92(U_1731,U_1730,U_1729,U_1728,U_1727)))
| ~ sP104(U_1725,U_1727,U_1728,U_1729,U_1730,U_1731) )
& ! [U_1725,U_1727,U_1728,U_1729,U_1730,U_1731] :
( sP104(U_1725,U_1727,U_1728,U_1729,U_1730,U_1731)
| ~ c_Wellfounded_Owf(U_1727,U_1729)
| ~ c_Recdef_Oadm__wf(U_1727,U_1728,U_1729,U_1730) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_286_3]) ).
cnf(f_286_5,plain,
( sP104(U_1725,U_1727,U_1728,U_1729,U_1730,U_1731)
| ~ c_Wellfounded_Owf(U_1727,U_1729)
| ~ c_Recdef_Oadm__wf(U_1727,U_1728,U_1729,U_1730) ),
inference(clausify,[status(thm)],[f_286_4]) ).
cnf(f_286_6,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),sK92(U_1731,U_1730,U_1729,U_1728,U_1727)))
| ~ sP104(U_1725,U_1727,U_1728,U_1729,U_1730,U_1731) ),
inference(clausify,[status(thm)],[f_286_4]) ).
cnf(f_286_7,plain,
( U_1725 = sK92(U_1731,U_1730,U_1729,U_1728,U_1727)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1727,U_1728,U_1729,U_1730,U_1731),U_1725))
| ~ sP104(U_1725,U_1727,U_1728,U_1729,U_1730,U_1731) ),
inference(clausify,[status(thm)],[f_286_4]) ).
fof(f_287_1,plain,
! [V_x_2,V_Fa_2,T_b,V_R_2,T_a] :
( ( c_Nitpick_Owfrec_H(T_a,T_b,V_R_2,V_Fa_2,V_x_2) = c_HOL_OThe(T_b,c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(T_a,T_a),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),c_COMBS(T_a,T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,T_b)),hAPP(c_COMBB(tc_fun(T_a,T_b),tc_fun(T_a,T_b),T_a),V_Fa_2)),hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_fun(T_a,T_b))),c_Recdef_Ocut(T_a,T_b)),V_R_2)))),c_COMBI(T_a)),V_x_2))
| c_Wellfounded_Owf(T_a,V_R_2) )
& ( c_Nitpick_Owfrec_H(T_a,T_b,V_R_2,V_Fa_2,V_x_2) = c_Nitpick_Owf__wfrec_H(T_a,T_b,V_R_2,V_Fa_2,V_x_2)
| ~ c_Wellfounded_Owf(T_a,V_R_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Owfrec_H__def]) ).
fof(f_287_2,plain,
! [U_1736,U_1735,U_1734,U_1733,U_1732] :
( ( c_Nitpick_Owfrec_H(U_1732,U_1734,U_1733,U_1735,U_1736) = c_HOL_OThe(U_1734,c_Recdef_Owfrec__rel(U_1732,U_1734,U_1733,hAPP(hAPP(c_COMBC(tc_fun(U_1732,U_1734),tc_fun(U_1732,U_1732),tc_fun(U_1732,U_1734)),hAPP(hAPP(c_COMBB(tc_fun(U_1732,tc_fun(U_1732,U_1734)),tc_fun(tc_fun(U_1732,U_1732),tc_fun(U_1732,U_1734)),tc_fun(U_1732,U_1734)),c_COMBS(U_1732,U_1732,U_1734)),hAPP(hAPP(c_COMBB(tc_fun(U_1732,tc_fun(U_1732,U_1734)),tc_fun(U_1732,tc_fun(U_1732,U_1734)),tc_fun(U_1732,U_1734)),hAPP(c_COMBB(tc_fun(U_1732,U_1734),tc_fun(U_1732,U_1734),U_1732),U_1735)),hAPP(hAPP(c_COMBC(tc_fun(U_1732,U_1734),tc_fun(tc_prod(U_1732,U_1732),tc_HOL_Obool),tc_fun(U_1732,tc_fun(U_1732,U_1734))),c_Recdef_Ocut(U_1732,U_1734)),U_1733)))),c_COMBI(U_1732)),U_1736))
| c_Wellfounded_Owf(U_1732,U_1733) )
& ( c_Nitpick_Owfrec_H(U_1732,U_1734,U_1733,U_1735,U_1736) = c_Nitpick_Owf__wfrec_H(U_1732,U_1734,U_1733,U_1735,U_1736)
| ~ c_Wellfounded_Owf(U_1732,U_1733) ) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
( ! [U_1746,U_1744,U_1742,U_1740,U_1738] :
( c_Nitpick_Owfrec_H(U_1738,U_1742,U_1740,U_1744,U_1746) = c_HOL_OThe(U_1742,c_Recdef_Owfrec__rel(U_1738,U_1742,U_1740,hAPP(hAPP(c_COMBC(tc_fun(U_1738,U_1742),tc_fun(U_1738,U_1738),tc_fun(U_1738,U_1742)),hAPP(hAPP(c_COMBB(tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(tc_fun(U_1738,U_1738),tc_fun(U_1738,U_1742)),tc_fun(U_1738,U_1742)),c_COMBS(U_1738,U_1738,U_1742)),hAPP(hAPP(c_COMBB(tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(U_1738,U_1742)),hAPP(c_COMBB(tc_fun(U_1738,U_1742),tc_fun(U_1738,U_1742),U_1738),U_1744)),hAPP(hAPP(c_COMBC(tc_fun(U_1738,U_1742),tc_fun(tc_prod(U_1738,U_1738),tc_HOL_Obool),tc_fun(U_1738,tc_fun(U_1738,U_1742))),c_Recdef_Ocut(U_1738,U_1742)),U_1740)))),c_COMBI(U_1738)),U_1746))
| c_Wellfounded_Owf(U_1738,U_1740) )
& ! [U_1745,U_1743,U_1741,U_1739,U_1737] :
( c_Nitpick_Owfrec_H(U_1737,U_1741,U_1739,U_1743,U_1745) = c_Nitpick_Owf__wfrec_H(U_1737,U_1741,U_1739,U_1743,U_1745)
| ~ c_Wellfounded_Owf(U_1737,U_1739) ) ),
inference(miniscope,[status(thm)],[f_287_2]) ).
fof(f_287_4,plain,
( ! [U_1742,U_1740,U_1738,U_1744,U_1746] :
( c_Nitpick_Owfrec_H(U_1738,U_1742,U_1740,U_1744,U_1746) = c_HOL_OThe(U_1742,c_Recdef_Owfrec__rel(U_1738,U_1742,U_1740,hAPP(hAPP(c_COMBC(tc_fun(U_1738,U_1742),tc_fun(U_1738,U_1738),tc_fun(U_1738,U_1742)),hAPP(hAPP(c_COMBB(tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(tc_fun(U_1738,U_1738),tc_fun(U_1738,U_1742)),tc_fun(U_1738,U_1742)),c_COMBS(U_1738,U_1738,U_1742)),hAPP(hAPP(c_COMBB(tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(U_1738,U_1742)),hAPP(c_COMBB(tc_fun(U_1738,U_1742),tc_fun(U_1738,U_1742),U_1738),U_1744)),hAPP(hAPP(c_COMBC(tc_fun(U_1738,U_1742),tc_fun(tc_prod(U_1738,U_1738),tc_HOL_Obool),tc_fun(U_1738,tc_fun(U_1738,U_1742))),c_Recdef_Ocut(U_1738,U_1742)),U_1740)))),c_COMBI(U_1738)),U_1746))
| c_Wellfounded_Owf(U_1738,U_1740) )
& ! [U_1743,U_1741,U_1745,U_1739,U_1737] :
( c_Nitpick_Owfrec_H(U_1737,U_1741,U_1739,U_1743,U_1745) = c_Nitpick_Owf__wfrec_H(U_1737,U_1741,U_1739,U_1743,U_1745)
| ~ c_Wellfounded_Owf(U_1737,U_1739) ) ),
inference(definitional_conversion,[status(esa)],[f_287_3]) ).
cnf(f_287_5,plain,
( c_Nitpick_Owfrec_H(U_1737,U_1741,U_1739,U_1743,U_1745) = c_Nitpick_Owf__wfrec_H(U_1737,U_1741,U_1739,U_1743,U_1745)
| ~ c_Wellfounded_Owf(U_1737,U_1739) ),
inference(clausify,[status(thm)],[f_287_4]) ).
cnf(f_287_6,plain,
( c_Nitpick_Owfrec_H(U_1738,U_1742,U_1740,U_1744,U_1746) = c_HOL_OThe(U_1742,c_Recdef_Owfrec__rel(U_1738,U_1742,U_1740,hAPP(hAPP(c_COMBC(tc_fun(U_1738,U_1742),tc_fun(U_1738,U_1738),tc_fun(U_1738,U_1742)),hAPP(hAPP(c_COMBB(tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(tc_fun(U_1738,U_1738),tc_fun(U_1738,U_1742)),tc_fun(U_1738,U_1742)),c_COMBS(U_1738,U_1738,U_1742)),hAPP(hAPP(c_COMBB(tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(U_1738,tc_fun(U_1738,U_1742)),tc_fun(U_1738,U_1742)),hAPP(c_COMBB(tc_fun(U_1738,U_1742),tc_fun(U_1738,U_1742),U_1738),U_1744)),hAPP(hAPP(c_COMBC(tc_fun(U_1738,U_1742),tc_fun(tc_prod(U_1738,U_1738),tc_HOL_Obool),tc_fun(U_1738,tc_fun(U_1738,U_1742))),c_Recdef_Ocut(U_1738,U_1742)),U_1740)))),c_COMBI(U_1738)),U_1746))
| c_Wellfounded_Owf(U_1738,U_1740) ),
inference(clausify,[status(thm)],[f_287_4]) ).
fof(f_288_1,plain,
! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_the__sym__eq__trivial]) ).
fof(f_288_2,plain,
! [U_1748,U_1747] : c_HOL_OThe(U_1747,hAPP(c_fequal,U_1748)) = U_1748,
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1748,U_1747] : c_HOL_OThe(U_1747,hAPP(c_fequal,U_1748)) = U_1748,
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
c_HOL_OThe(U_1747,hAPP(c_fequal,U_1748)) = U_1748,
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_1,plain,
! [V_aa_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_aa_2)) = V_aa_2,
inference(fof_nnf,[status(thm)],[fact_the__eq__trivial]) ).
fof(f_289_2,plain,
! [U_1750,U_1749] : c_HOL_OThe(U_1749,hAPP(hAPP(c_COMBC(U_1749,U_1749,tc_HOL_Obool),c_fequal),U_1750)) = U_1750,
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_1750,U_1749] : c_HOL_OThe(U_1749,hAPP(hAPP(c_COMBC(U_1749,U_1749,tc_HOL_Obool),c_fequal),U_1750)) = U_1750,
inference(definitional_conversion,[status(esa)],[f_289_2]) ).
cnf(f_289_4,plain,
c_HOL_OThe(U_1749,hAPP(hAPP(c_COMBC(U_1749,U_1749,tc_HOL_Obool),c_fequal),U_1750)) = U_1750,
inference(clausify,[status(thm)],[f_289_3]) ).
fof(f_290_1,plain,
! [V_x_2,V_Fa_2,V_R_2,T_a,T_b] : c_Nitpick_Owf__wfrec_H(T_b,T_a,V_R_2,V_Fa_2,V_x_2) = hAPP(hAPP(V_Fa_2,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_b,T_a),c_Nitpick_Owf__wfrec(T_b,T_a,V_R_2,V_Fa_2)),V_R_2),V_x_2)),V_x_2),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf__wfrec_H__def]) ).
fof(f_290_2,plain,
! [U_1755,U_1754,U_1753,U_1752,U_1751] : c_Nitpick_Owf__wfrec_H(U_1751,U_1752,U_1753,U_1754,U_1755) = hAPP(hAPP(U_1754,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1751,U_1752),c_Nitpick_Owf__wfrec(U_1751,U_1752,U_1753,U_1754)),U_1753),U_1755)),U_1755),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_1751,U_1752,U_1753,U_1754,U_1755] : c_Nitpick_Owf__wfrec_H(U_1751,U_1752,U_1753,U_1754,U_1755) = hAPP(hAPP(U_1754,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1751,U_1752),c_Nitpick_Owf__wfrec(U_1751,U_1752,U_1753,U_1754)),U_1753),U_1755)),U_1755),
inference(definitional_conversion,[status(esa)],[f_290_2]) ).
cnf(f_290_4,plain,
c_Nitpick_Owf__wfrec_H(U_1751,U_1752,U_1753,U_1754,U_1755) = hAPP(hAPP(U_1754,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1751,U_1752),c_Nitpick_Owf__wfrec(U_1751,U_1752,U_1753,U_1754)),U_1753),U_1755)),U_1755),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_1,plain,
! [V_r_2,T_a] :
( ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) )
& ( c_Wellfounded_Owf(T_a,V_r_2)
| ~ c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq]) ).
fof(f_291_2,plain,
! [U_1757,U_1756] :
( ( c_Wellfounded_OwfP(U_1756,hAPP(hAPP(c_COMBC(U_1756,tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_fun(U_1756,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1756,tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_fun(U_1756,tc_HOL_Obool)),U_1756),c_COMBC(U_1756,tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1756,tc_prod(U_1756,U_1756)),tc_fun(U_1756,tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool)),U_1756),hAPP(c_COMBB(tc_prod(U_1756,U_1756),tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool),U_1756),c_member(tc_prod(U_1756,U_1756)))),c_Product__Type_OPair(U_1756,U_1756)))),U_1757))
| ~ c_Wellfounded_Owf(U_1756,U_1757) )
& ( c_Wellfounded_Owf(U_1756,U_1757)
| ~ c_Wellfounded_OwfP(U_1756,hAPP(hAPP(c_COMBC(U_1756,tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_fun(U_1756,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1756,tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_fun(U_1756,tc_HOL_Obool)),U_1756),c_COMBC(U_1756,tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1756,tc_prod(U_1756,U_1756)),tc_fun(U_1756,tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool)),U_1756),hAPP(c_COMBB(tc_prod(U_1756,U_1756),tc_fun(tc_fun(tc_prod(U_1756,U_1756),tc_HOL_Obool),tc_HOL_Obool),U_1756),c_member(tc_prod(U_1756,U_1756)))),c_Product__Type_OPair(U_1756,U_1756)))),U_1757)) ) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
( ! [U_1761,U_1759] :
( c_Wellfounded_OwfP(U_1759,hAPP(hAPP(c_COMBC(U_1759,tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_fun(U_1759,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1759,tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_fun(U_1759,tc_HOL_Obool)),U_1759),c_COMBC(U_1759,tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1759,tc_prod(U_1759,U_1759)),tc_fun(U_1759,tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),U_1759),hAPP(c_COMBB(tc_prod(U_1759,U_1759),tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool),U_1759),c_member(tc_prod(U_1759,U_1759)))),c_Product__Type_OPair(U_1759,U_1759)))),U_1761))
| ~ c_Wellfounded_Owf(U_1759,U_1761) )
& ! [U_1760,U_1758] :
( c_Wellfounded_Owf(U_1758,U_1760)
| ~ c_Wellfounded_OwfP(U_1758,hAPP(hAPP(c_COMBC(U_1758,tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_fun(U_1758,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1758,tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_fun(U_1758,tc_HOL_Obool)),U_1758),c_COMBC(U_1758,tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1758,tc_prod(U_1758,U_1758)),tc_fun(U_1758,tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),U_1758),hAPP(c_COMBB(tc_prod(U_1758,U_1758),tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool),U_1758),c_member(tc_prod(U_1758,U_1758)))),c_Product__Type_OPair(U_1758,U_1758)))),U_1760)) ) ),
inference(miniscope,[status(thm)],[f_291_2]) ).
fof(f_291_4,plain,
( ! [U_1761,U_1759] :
( c_Wellfounded_OwfP(U_1759,hAPP(hAPP(c_COMBC(U_1759,tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_fun(U_1759,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1759,tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_fun(U_1759,tc_HOL_Obool)),U_1759),c_COMBC(U_1759,tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1759,tc_prod(U_1759,U_1759)),tc_fun(U_1759,tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),U_1759),hAPP(c_COMBB(tc_prod(U_1759,U_1759),tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool),U_1759),c_member(tc_prod(U_1759,U_1759)))),c_Product__Type_OPair(U_1759,U_1759)))),U_1761))
| ~ c_Wellfounded_Owf(U_1759,U_1761) )
& ! [U_1760,U_1758] :
( c_Wellfounded_Owf(U_1758,U_1760)
| ~ c_Wellfounded_OwfP(U_1758,hAPP(hAPP(c_COMBC(U_1758,tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_fun(U_1758,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1758,tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_fun(U_1758,tc_HOL_Obool)),U_1758),c_COMBC(U_1758,tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1758,tc_prod(U_1758,U_1758)),tc_fun(U_1758,tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),U_1758),hAPP(c_COMBB(tc_prod(U_1758,U_1758),tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool),U_1758),c_member(tc_prod(U_1758,U_1758)))),c_Product__Type_OPair(U_1758,U_1758)))),U_1760)) ) ),
inference(definitional_conversion,[status(esa)],[f_291_3]) ).
cnf(f_291_5,plain,
( c_Wellfounded_Owf(U_1758,U_1760)
| ~ c_Wellfounded_OwfP(U_1758,hAPP(hAPP(c_COMBC(U_1758,tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_fun(U_1758,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1758,tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_fun(U_1758,tc_HOL_Obool)),U_1758),c_COMBC(U_1758,tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1758,tc_prod(U_1758,U_1758)),tc_fun(U_1758,tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool)),U_1758),hAPP(c_COMBB(tc_prod(U_1758,U_1758),tc_fun(tc_fun(tc_prod(U_1758,U_1758),tc_HOL_Obool),tc_HOL_Obool),U_1758),c_member(tc_prod(U_1758,U_1758)))),c_Product__Type_OPair(U_1758,U_1758)))),U_1760)) ),
inference(clausify,[status(thm)],[f_291_4]) ).
cnf(f_291_6,plain,
( c_Wellfounded_OwfP(U_1759,hAPP(hAPP(c_COMBC(U_1759,tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_fun(U_1759,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1759,tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_fun(U_1759,tc_HOL_Obool)),U_1759),c_COMBC(U_1759,tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1759,tc_prod(U_1759,U_1759)),tc_fun(U_1759,tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool)),U_1759),hAPP(c_COMBB(tc_prod(U_1759,U_1759),tc_fun(tc_fun(tc_prod(U_1759,U_1759),tc_HOL_Obool),tc_HOL_Obool),U_1759),c_member(tc_prod(U_1759,U_1759)))),c_Product__Type_OPair(U_1759,U_1759)))),U_1761))
| ~ c_Wellfounded_Owf(U_1759,U_1761) ),
inference(clausify,[status(thm)],[f_291_4]) ).
fof(f_292_1,plain,
! [V_r_2,T_a] :
( ( c_Wellfounded_Owf(T_a,V_r_2)
| ? [B_Q] :
( ! [B_x] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) )
& ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) ) )
& ( ! [B_Q] :
( ? [B_x] :
( ! [B_y] :
( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) )
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) )
| ~ c_Wellfounded_Owf(T_a,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__eq__minimal]) ).
fof(f_292_2,plain,
! [U_1771,U_1770] :
( ( c_Wellfounded_Owf(U_1770,U_1771)
| ? [U_1769] :
( ! [U_1768] :
( ? [U_1767] :
( hBOOL(hAPP(hAPP(c_member(U_1770),U_1767),U_1769))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1770,U_1770)),hAPP(hAPP(c_Product__Type_OPair(U_1770,U_1770),U_1767),U_1768)),U_1771)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1770),U_1768),U_1769)) )
& ? [U_1766] : hBOOL(hAPP(hAPP(c_member(U_1770),U_1766),U_1769)) ) )
& ( ! [U_1765] :
( ? [U_1764] :
( ! [U_1763] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1770),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1770,U_1770)),hAPP(hAPP(c_Product__Type_OPair(U_1770,U_1770),U_1763),U_1764)),U_1771)) )
& hBOOL(hAPP(hAPP(c_member(U_1770),U_1764),U_1765)) )
| ! [U_1762] : ~ hBOOL(hAPP(hAPP(c_member(U_1770),U_1762),U_1765)) )
| ~ c_Wellfounded_Owf(U_1770,U_1771) ) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
( ! [U_1775,U_1773] :
( c_Wellfounded_Owf(U_1773,U_1775)
| ? [U_1769] :
( ! [U_1768] :
( ? [U_1767] :
( hBOOL(hAPP(hAPP(c_member(U_1773),U_1767),U_1769))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1773,U_1773)),hAPP(hAPP(c_Product__Type_OPair(U_1773,U_1773),U_1767),U_1768)),U_1775)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1773),U_1768),U_1769)) )
& ? [U_1766] : hBOOL(hAPP(hAPP(c_member(U_1773),U_1766),U_1769)) ) )
& ! [U_1774,U_1772] :
( ! [U_1765] :
( ? [U_1764] :
( ! [U_1763] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1772,U_1772)),hAPP(hAPP(c_Product__Type_OPair(U_1772,U_1772),U_1763),U_1764)),U_1774)) )
& hBOOL(hAPP(hAPP(c_member(U_1772),U_1764),U_1765)) )
| ! [U_1762] : ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1762),U_1765)) )
| ~ c_Wellfounded_Owf(U_1772,U_1774) ) ),
inference(miniscope,[status(thm)],[f_292_2]) ).
fof(f_292_4,plain,
( ! [U_1775,U_1773] :
( c_Wellfounded_Owf(U_1773,U_1775)
| ? [U_1769] :
( ! [U_1768] :
( ? [U_1767] :
( hBOOL(hAPP(hAPP(c_member(U_1773),U_1767),U_1769))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1773,U_1773)),hAPP(hAPP(c_Product__Type_OPair(U_1773,U_1773),U_1767),U_1768)),U_1775)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1773),U_1768),U_1769)) )
& ? [U_1766] : hBOOL(hAPP(hAPP(c_member(U_1773),U_1766),U_1769)) ) )
& ! [U_1774,U_1772] :
( ! [U_1765] :
( ( ! [U_1763] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1772,U_1772)),hAPP(hAPP(c_Product__Type_OPair(U_1772,U_1772),U_1763),sK93(U_1774,U_1772,U_1765))),U_1774)) )
& hBOOL(hAPP(hAPP(c_member(U_1772),sK93(U_1774,U_1772,U_1765)),U_1765)) )
| ! [U_1762] : ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1762),U_1765)) )
| ~ c_Wellfounded_Owf(U_1772,U_1774) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_1764,sK93(U_1774,U_1772,U_1765))],[f_292_3]) ).
fof(f_292_5,plain,
( ! [U_1775,U_1773] :
( c_Wellfounded_Owf(U_1773,U_1775)
| ( ! [U_1768] :
( ? [U_1767] :
( hBOOL(hAPP(hAPP(c_member(U_1773),U_1767),sK94(U_1775,U_1773)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1773,U_1773)),hAPP(hAPP(c_Product__Type_OPair(U_1773,U_1773),U_1767),U_1768)),U_1775)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1773),U_1768),sK94(U_1775,U_1773))) )
& ? [U_1766] : hBOOL(hAPP(hAPP(c_member(U_1773),U_1766),sK94(U_1775,U_1773))) ) )
& ! [U_1774,U_1772] :
( ! [U_1765] :
( ( ! [U_1763] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1772,U_1772)),hAPP(hAPP(c_Product__Type_OPair(U_1772,U_1772),U_1763),sK93(U_1774,U_1772,U_1765))),U_1774)) )
& hBOOL(hAPP(hAPP(c_member(U_1772),sK93(U_1774,U_1772,U_1765)),U_1765)) )
| ! [U_1762] : ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1762),U_1765)) )
| ~ c_Wellfounded_Owf(U_1772,U_1774) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_1769,sK94(U_1775,U_1773))],[f_292_4]) ).
fof(f_292_6,plain,
( ! [U_1775,U_1773] :
( c_Wellfounded_Owf(U_1773,U_1775)
| ( ! [U_1768] :
( ? [U_1767] :
( hBOOL(hAPP(hAPP(c_member(U_1773),U_1767),sK94(U_1775,U_1773)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1773,U_1773)),hAPP(hAPP(c_Product__Type_OPair(U_1773,U_1773),U_1767),U_1768)),U_1775)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1773),U_1768),sK94(U_1775,U_1773))) )
& hBOOL(hAPP(hAPP(c_member(U_1773),sK95(U_1775,U_1773)),sK94(U_1775,U_1773))) ) )
& ! [U_1774,U_1772] :
( ! [U_1765] :
( ( ! [U_1763] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1772,U_1772)),hAPP(hAPP(c_Product__Type_OPair(U_1772,U_1772),U_1763),sK93(U_1774,U_1772,U_1765))),U_1774)) )
& hBOOL(hAPP(hAPP(c_member(U_1772),sK93(U_1774,U_1772,U_1765)),U_1765)) )
| ! [U_1762] : ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1762),U_1765)) )
| ~ c_Wellfounded_Owf(U_1772,U_1774) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_1766,sK95(U_1775,U_1773))],[f_292_5]) ).
fof(f_292_7,plain,
( ! [U_1775,U_1773] :
( c_Wellfounded_Owf(U_1773,U_1775)
| ( ! [U_1768] :
( ( hBOOL(hAPP(hAPP(c_member(U_1773),sK96(U_1775,U_1773,U_1768)),sK94(U_1775,U_1773)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1773,U_1773)),hAPP(hAPP(c_Product__Type_OPair(U_1773,U_1773),sK96(U_1775,U_1773,U_1768)),U_1768)),U_1775)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1773),U_1768),sK94(U_1775,U_1773))) )
& hBOOL(hAPP(hAPP(c_member(U_1773),sK95(U_1775,U_1773)),sK94(U_1775,U_1773))) ) )
& ! [U_1774,U_1772] :
( ! [U_1765] :
( ( ! [U_1763] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1772,U_1772)),hAPP(hAPP(c_Product__Type_OPair(U_1772,U_1772),U_1763),sK93(U_1774,U_1772,U_1765))),U_1774)) )
& hBOOL(hAPP(hAPP(c_member(U_1772),sK93(U_1774,U_1772,U_1765)),U_1765)) )
| ! [U_1762] : ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1762),U_1765)) )
| ~ c_Wellfounded_Owf(U_1772,U_1774) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_1767,sK96(U_1775,U_1773,U_1768))],[f_292_6]) ).
fof(f_292_8,plain,
( ! [U_1773,U_1768,U_1775] :
( hBOOL(hAPP(hAPP(c_member(U_1773),sK96(U_1775,U_1773,U_1768)),sK94(U_1775,U_1773)))
| ~ sP106(U_1773,U_1768,U_1775) )
& ! [U_1773,U_1768,U_1775] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1773,U_1773)),hAPP(hAPP(c_Product__Type_OPair(U_1773,U_1773),sK96(U_1775,U_1773,U_1768)),U_1768)),U_1775))
| ~ sP106(U_1773,U_1768,U_1775) )
& ! [U_1773,U_1768,U_1775] :
( sP106(U_1773,U_1768,U_1775)
| ~ hBOOL(hAPP(hAPP(c_member(U_1773),U_1768),sK94(U_1775,U_1773)))
| ~ sP107(U_1773,U_1768,U_1775) )
& ! [U_1773,U_1768,U_1775] :
( hBOOL(hAPP(hAPP(c_member(U_1773),sK95(U_1775,U_1773)),sK94(U_1775,U_1773)))
| ~ sP107(U_1773,U_1768,U_1775) )
& ! [U_1763,U_1765,U_1772,U_1774] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1772,U_1772)),hAPP(hAPP(c_Product__Type_OPair(U_1772,U_1772),U_1763),sK93(U_1774,U_1772,U_1765))),U_1774))
| ~ sP105(U_1763,U_1765,U_1772,U_1774) )
& ! [U_1763,U_1765,U_1772,U_1774] :
( hBOOL(hAPP(hAPP(c_member(U_1772),sK93(U_1774,U_1772,U_1765)),U_1765))
| ~ sP105(U_1763,U_1765,U_1772,U_1774) )
& ! [U_1773,U_1768,U_1775] :
( c_Wellfounded_Owf(U_1773,U_1775)
| sP107(U_1773,U_1768,U_1775) )
& ! [U_1762,U_1763,U_1765,U_1772,U_1774] :
( sP105(U_1763,U_1765,U_1772,U_1774)
| ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1762),U_1765))
| ~ c_Wellfounded_Owf(U_1772,U_1774) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105,sP106,sP107])],[f_292_7]) ).
cnf(f_292_9,plain,
( sP105(U_1763,U_1765,U_1772,U_1774)
| ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1762),U_1765))
| ~ c_Wellfounded_Owf(U_1772,U_1774) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_10,plain,
( c_Wellfounded_Owf(U_1773,U_1775)
| sP107(U_1773,U_1768,U_1775) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_1772),sK93(U_1774,U_1772,U_1765)),U_1765))
| ~ sP105(U_1763,U_1765,U_1772,U_1774) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_12,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1763),U_1765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1772,U_1772)),hAPP(hAPP(c_Product__Type_OPair(U_1772,U_1772),U_1763),sK93(U_1774,U_1772,U_1765))),U_1774))
| ~ sP105(U_1763,U_1765,U_1772,U_1774) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_13,plain,
( hBOOL(hAPP(hAPP(c_member(U_1773),sK95(U_1775,U_1773)),sK94(U_1775,U_1773)))
| ~ sP107(U_1773,U_1768,U_1775) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_14,plain,
( sP106(U_1773,U_1768,U_1775)
| ~ hBOOL(hAPP(hAPP(c_member(U_1773),U_1768),sK94(U_1775,U_1773)))
| ~ sP107(U_1773,U_1768,U_1775) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_15,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1773,U_1773)),hAPP(hAPP(c_Product__Type_OPair(U_1773,U_1773),sK96(U_1775,U_1773,U_1768)),U_1768)),U_1775))
| ~ sP106(U_1773,U_1768,U_1775) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_16,plain,
( hBOOL(hAPP(hAPP(c_member(U_1773),sK96(U_1775,U_1773,U_1768)),sK94(U_1775,U_1773)))
| ~ sP106(U_1773,U_1768,U_1775) ),
inference(clausify,[status(thm)],[f_292_8]) ).
fof(f_293_1,plain,
! [T_a] : c_Wellfounded_OwfP(T_a,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,c_COMBK(tc_HOL_Obool,T_a,c_fFalse))),
inference(fof_nnf,[status(thm)],[fact_wfP__empty]) ).
fof(f_293_2,plain,
! [U_1776] : c_Wellfounded_OwfP(U_1776,c_COMBK(tc_fun(U_1776,tc_HOL_Obool),U_1776,c_COMBK(tc_HOL_Obool,U_1776,c_fFalse))),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_1776] : c_Wellfounded_OwfP(U_1776,c_COMBK(tc_fun(U_1776,tc_HOL_Obool),U_1776,c_COMBK(tc_HOL_Obool,U_1776,c_fFalse))),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
c_Wellfounded_OwfP(U_1776,c_COMBK(tc_fun(U_1776,tc_HOL_Obool),U_1776,c_COMBK(tc_HOL_Obool,U_1776,c_fFalse))),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_1,plain,
! [V_x_2,V_r_2,T_a] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2))
| ~ c_Wellfounded_OwfP(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_accp__wfPD]) ).
fof(f_294_2,plain,
! [U_1779,U_1778,U_1777] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1777,U_1778),U_1779))
| ~ c_Wellfounded_OwfP(U_1777,U_1778) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_1779,U_1777,U_1778] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1777,U_1778),U_1779))
| ~ c_Wellfounded_OwfP(U_1777,U_1778) ),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1777,U_1778),U_1779))
| ~ c_Wellfounded_OwfP(U_1777,U_1778) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_1,plain,
! [V_r_2,T_a] :
( ( c_Wellfounded_OwfP(T_a,V_r_2)
| ? [B_x1] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) )
& ( ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1))
| ~ c_Wellfounded_OwfP(T_a,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff]) ).
fof(f_295_2,plain,
! [U_1783,U_1782] :
( ( c_Wellfounded_OwfP(U_1782,U_1783)
| ? [U_1781] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1782,U_1783),U_1781)) )
& ( ! [U_1780] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_1782,U_1783),U_1780))
| ~ c_Wellfounded_OwfP(U_1782,U_1783) ) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
( ! [U_1787,U_1785] :
( c_Wellfounded_OwfP(U_1785,U_1787)
| ? [U_1781] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1785,U_1787),U_1781)) )
& ! [U_1786,U_1784] :
( ! [U_1780] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_1784,U_1786),U_1780))
| ~ c_Wellfounded_OwfP(U_1784,U_1786) ) ),
inference(miniscope,[status(thm)],[f_295_2]) ).
fof(f_295_4,plain,
( ! [U_1787,U_1785] :
( c_Wellfounded_OwfP(U_1785,U_1787)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1785,U_1787),sK97(U_1787,U_1785))) )
& ! [U_1786,U_1784] :
( ! [U_1780] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_1784,U_1786),U_1780))
| ~ c_Wellfounded_OwfP(U_1784,U_1786) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_1781,sK97(U_1787,U_1785))],[f_295_3]) ).
fof(f_295_5,plain,
( ! [U_1785,U_1787] :
( c_Wellfounded_OwfP(U_1785,U_1787)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1785,U_1787),sK97(U_1787,U_1785))) )
& ! [U_1780,U_1786,U_1784] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1784,U_1786),U_1780))
| ~ c_Wellfounded_OwfP(U_1784,U_1786) ) ),
inference(definitional_conversion,[status(esa)],[f_295_4]) ).
cnf(f_295_6,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1784,U_1786),U_1780))
| ~ c_Wellfounded_OwfP(U_1784,U_1786) ),
inference(clausify,[status(thm)],[f_295_5]) ).
cnf(f_295_7,plain,
( c_Wellfounded_OwfP(U_1785,U_1787)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1785,U_1787),sK97(U_1787,U_1785))) ),
inference(clausify,[status(thm)],[f_295_5]) ).
fof(f_296_1,plain,
! [V_r_2,T_a] :
( c_Wellfounded_OwfP(T_a,c_Transitive__Closure_Otranclp(T_a,V_r_2))
| ~ c_Wellfounded_OwfP(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wfP__trancl]) ).
fof(f_296_2,plain,
! [U_1789,U_1788] :
( c_Wellfounded_OwfP(U_1788,c_Transitive__Closure_Otranclp(U_1788,U_1789))
| ~ c_Wellfounded_OwfP(U_1788,U_1789) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_1788,U_1789] :
( c_Wellfounded_OwfP(U_1788,c_Transitive__Closure_Otranclp(U_1788,U_1789))
| ~ c_Wellfounded_OwfP(U_1788,U_1789) ),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
( c_Wellfounded_OwfP(U_1788,c_Transitive__Closure_Otranclp(U_1788,U_1789))
| ~ c_Wellfounded_OwfP(U_1788,U_1789) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [V_R_2,T_a] :
( c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2))
| ~ c_Wellfounded_Owf(T_a,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__in__rel]) ).
fof(f_297_2,plain,
! [U_1791,U_1790] :
( c_Wellfounded_OwfP(U_1790,c_FunDef_Oin__rel(U_1790,U_1790,U_1791))
| ~ c_Wellfounded_Owf(U_1790,U_1791) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_1790,U_1791] :
( c_Wellfounded_OwfP(U_1790,c_FunDef_Oin__rel(U_1790,U_1790,U_1791))
| ~ c_Wellfounded_Owf(U_1790,U_1791) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( c_Wellfounded_OwfP(U_1790,c_FunDef_Oin__rel(U_1790,U_1790,U_1791))
| ~ c_Wellfounded_Owf(U_1790,U_1791) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [V_x_2,V_f_2,V_A_2,T_b,T_a] : c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2,V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__def]) ).
fof(f_298_2,plain,
! [U_1796,U_1795,U_1794,U_1793,U_1792] : c_Fun_Othe__inv__into(U_1792,U_1793,U_1794,U_1795,U_1796) = c_HOL_OThe(U_1792,hAPP(hAPP(c_COMBS(U_1792,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_1792),c_fconj),hAPP(hAPP(c_COMBC(U_1792,tc_fun(U_1792,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1792)),U_1794))),hAPP(hAPP(c_COMBC(U_1792,U_1793,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_1793,tc_fun(U_1793,tc_HOL_Obool),U_1792),c_fequal),U_1795)),U_1796))),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_1792,U_1793,U_1794,U_1795,U_1796] : c_Fun_Othe__inv__into(U_1792,U_1793,U_1794,U_1795,U_1796) = c_HOL_OThe(U_1792,hAPP(hAPP(c_COMBS(U_1792,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_1792),c_fconj),hAPP(hAPP(c_COMBC(U_1792,tc_fun(U_1792,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1792)),U_1794))),hAPP(hAPP(c_COMBC(U_1792,U_1793,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_1793,tc_fun(U_1793,tc_HOL_Obool),U_1792),c_fequal),U_1795)),U_1796))),
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
c_Fun_Othe__inv__into(U_1792,U_1793,U_1794,U_1795,U_1796) = c_HOL_OThe(U_1792,hAPP(hAPP(c_COMBS(U_1792,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_1792),c_fconj),hAPP(hAPP(c_COMBC(U_1792,tc_fun(U_1792,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1792)),U_1794))),hAPP(hAPP(c_COMBC(U_1792,U_1793,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_1793,tc_fun(U_1793,tc_HOL_Obool),U_1792),c_fequal),U_1795)),U_1796))),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_1,plain,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_r_2)
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acc__wfI]) ).
fof(f_299_2,plain,
! [U_1799,U_1798] :
( c_Wellfounded_Owf(U_1798,U_1799)
| ? [U_1797] : ~ hBOOL(hAPP(hAPP(c_member(U_1798),U_1797),c_Wellfounded_Oacc(U_1798,U_1799))) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_1799,U_1798] :
( c_Wellfounded_Owf(U_1798,U_1799)
| ~ hBOOL(hAPP(hAPP(c_member(U_1798),sK98(U_1799,U_1798)),c_Wellfounded_Oacc(U_1798,U_1799))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_1797,sK98(U_1799,U_1798))],[f_299_2]) ).
fof(f_299_4,plain,
! [U_1799,U_1798] :
( c_Wellfounded_Owf(U_1798,U_1799)
| ~ hBOOL(hAPP(hAPP(c_member(U_1798),sK98(U_1799,U_1798)),c_Wellfounded_Oacc(U_1798,U_1799))) ),
inference(definitional_conversion,[status(esa)],[f_299_3]) ).
cnf(f_299_5,plain,
( c_Wellfounded_Owf(U_1798,U_1799)
| ~ hBOOL(hAPP(hAPP(c_member(U_1798),sK98(U_1799,U_1798)),c_Wellfounded_Oacc(U_1798,U_1799))) ),
inference(clausify,[status(thm)],[f_299_4]) ).
fof(f_300_1,plain,
! [V_r_2,T_a] :
( c_Relation_Oantisym(T_a,V_r_2)
| ? [B_x,B_y] :
( B_x != B_y
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_antisymI]) ).
fof(f_300_2,plain,
! [U_1803,U_1802] :
( c_Relation_Oantisym(U_1802,U_1803)
| ? [U_1801,U_1800] :
( U_1801 != U_1800
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),U_1800),U_1801)),U_1803))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),U_1801),U_1800)),U_1803)) ) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1803,U_1802] :
( c_Relation_Oantisym(U_1802,U_1803)
| ? [U_1800] :
( sK99(U_1803,U_1802) != U_1800
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),U_1800),sK99(U_1803,U_1802))),U_1803))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),sK99(U_1803,U_1802)),U_1800)),U_1803)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_1801,sK99(U_1803,U_1802))],[f_300_2]) ).
fof(f_300_4,plain,
! [U_1803,U_1802] :
( c_Relation_Oantisym(U_1802,U_1803)
| ( sK99(U_1803,U_1802) != sK100(U_1803,U_1802)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),sK100(U_1803,U_1802)),sK99(U_1803,U_1802))),U_1803))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),sK99(U_1803,U_1802)),sK100(U_1803,U_1802))),U_1803)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_1800,sK100(U_1803,U_1802))],[f_300_3]) ).
fof(f_300_5,plain,
( ! [U_1802,U_1803] :
( sK99(U_1803,U_1802) != sK100(U_1803,U_1802)
| ~ sP108(U_1802,U_1803) )
& ! [U_1802,U_1803] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),sK100(U_1803,U_1802)),sK99(U_1803,U_1802))),U_1803))
| ~ sP108(U_1802,U_1803) )
& ! [U_1802,U_1803] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),sK99(U_1803,U_1802)),sK100(U_1803,U_1802))),U_1803))
| ~ sP108(U_1802,U_1803) )
& ! [U_1802,U_1803] :
( c_Relation_Oantisym(U_1802,U_1803)
| sP108(U_1802,U_1803) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_300_4]) ).
cnf(f_300_6,plain,
( c_Relation_Oantisym(U_1802,U_1803)
| sP108(U_1802,U_1803) ),
inference(clausify,[status(thm)],[f_300_5]) ).
cnf(f_300_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),sK99(U_1803,U_1802)),sK100(U_1803,U_1802))),U_1803))
| ~ sP108(U_1802,U_1803) ),
inference(clausify,[status(thm)],[f_300_5]) ).
cnf(f_300_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1802,U_1802)),hAPP(hAPP(c_Product__Type_OPair(U_1802,U_1802),sK100(U_1803,U_1802)),sK99(U_1803,U_1802))),U_1803))
| ~ sP108(U_1802,U_1803) ),
inference(clausify,[status(thm)],[f_300_5]) ).
cnf(f_300_9,plain,
( sK99(U_1803,U_1802) != sK100(U_1803,U_1802)
| ~ sP108(U_1802,U_1803) ),
inference(clausify,[status(thm)],[f_300_5]) ).
fof(f_301_1,plain,
! [V_f_2,V_y_2,V_x_2,T_a] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) )
& ( 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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__measure]) ).
fof(f_301_2,plain,
! [U_1807,U_1806,U_1805,U_1804] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1804,U_1804)),hAPP(hAPP(c_Product__Type_OPair(U_1804,U_1804),U_1805),U_1806)),hAPP(c_Wellfounded_Omeasure(U_1804),U_1807)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1807,U_1805),hAPP(U_1807,U_1806)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1807,U_1805),hAPP(U_1807,U_1806))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1804,U_1804)),hAPP(hAPP(c_Product__Type_OPair(U_1804,U_1804),U_1805),U_1806)),hAPP(c_Wellfounded_Omeasure(U_1804),U_1807))) ) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
( ! [U_1815,U_1813,U_1811] :
( ! [U_1809] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1809,U_1809)),hAPP(hAPP(c_Product__Type_OPair(U_1809,U_1809),U_1811),U_1813)),hAPP(c_Wellfounded_Omeasure(U_1809),U_1815)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1815,U_1811),hAPP(U_1815,U_1813)) )
& ! [U_1814,U_1812,U_1810] :
( ! [U_1808] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1808,U_1808)),hAPP(hAPP(c_Product__Type_OPair(U_1808,U_1808),U_1810),U_1812)),hAPP(c_Wellfounded_Omeasure(U_1808),U_1814)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1814,U_1810),hAPP(U_1814,U_1812)) ) ),
inference(miniscope,[status(thm)],[f_301_2]) ).
fof(f_301_4,plain,
( ! [U_1809,U_1811,U_1813,U_1815] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1809,U_1809)),hAPP(hAPP(c_Product__Type_OPair(U_1809,U_1809),U_1811),U_1813)),hAPP(c_Wellfounded_Omeasure(U_1809),U_1815)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1815,U_1811),hAPP(U_1815,U_1813)) )
& ! [U_1812,U_1810,U_1814,U_1808] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1808,U_1808)),hAPP(hAPP(c_Product__Type_OPair(U_1808,U_1808),U_1810),U_1812)),hAPP(c_Wellfounded_Omeasure(U_1808),U_1814)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1814,U_1810),hAPP(U_1814,U_1812)) ) ),
inference(definitional_conversion,[status(esa)],[f_301_3]) ).
cnf(f_301_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1808,U_1808)),hAPP(hAPP(c_Product__Type_OPair(U_1808,U_1808),U_1810),U_1812)),hAPP(c_Wellfounded_Omeasure(U_1808),U_1814)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1814,U_1810),hAPP(U_1814,U_1812)) ),
inference(clausify,[status(thm)],[f_301_4]) ).
cnf(f_301_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1809,U_1809)),hAPP(hAPP(c_Product__Type_OPair(U_1809,U_1809),U_1811),U_1813)),hAPP(c_Wellfounded_Omeasure(U_1809),U_1815)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1815,U_1811),hAPP(U_1815,U_1813)) ),
inference(clausify,[status(thm)],[f_301_4]) ).
fof(f_302_1,plain,
! [V_g_2,V_f_2,T_b,V_A_2,V_aa_2,T_a] :
( ( c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_f_2,V_aa_2)
| hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) )
& ( c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_g_2,V_aa_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_override__on__def]) ).
fof(f_302_2,plain,
! [U_1821,U_1820,U_1819,U_1818,U_1817,U_1816] :
( ( c_Fun_Ooverride__on(U_1816,U_1819,U_1820,U_1821,U_1818,U_1817) = hAPP(U_1820,U_1817)
| hBOOL(hAPP(hAPP(c_member(U_1816),U_1817),U_1818)) )
& ( c_Fun_Ooverride__on(U_1816,U_1819,U_1820,U_1821,U_1818,U_1817) = hAPP(U_1821,U_1817)
| ~ hBOOL(hAPP(hAPP(c_member(U_1816),U_1817),U_1818)) ) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
( ! [U_1833,U_1831,U_1829,U_1827,U_1825,U_1823] :
( c_Fun_Ooverride__on(U_1823,U_1829,U_1831,U_1833,U_1827,U_1825) = hAPP(U_1831,U_1825)
| hBOOL(hAPP(hAPP(c_member(U_1823),U_1825),U_1827)) )
& ! [U_1832,U_1830,U_1828,U_1826,U_1824,U_1822] :
( c_Fun_Ooverride__on(U_1822,U_1828,U_1830,U_1832,U_1826,U_1824) = hAPP(U_1832,U_1824)
| ~ hBOOL(hAPP(hAPP(c_member(U_1822),U_1824),U_1826)) ) ),
inference(miniscope,[status(thm)],[f_302_2]) ).
fof(f_302_4,plain,
( ! [U_1831,U_1823,U_1829,U_1825,U_1827,U_1833] :
( c_Fun_Ooverride__on(U_1823,U_1829,U_1831,U_1833,U_1827,U_1825) = hAPP(U_1831,U_1825)
| hBOOL(hAPP(hAPP(c_member(U_1823),U_1825),U_1827)) )
& ! [U_1824,U_1828,U_1822,U_1826,U_1830,U_1832] :
( c_Fun_Ooverride__on(U_1822,U_1828,U_1830,U_1832,U_1826,U_1824) = hAPP(U_1832,U_1824)
| ~ hBOOL(hAPP(hAPP(c_member(U_1822),U_1824),U_1826)) ) ),
inference(definitional_conversion,[status(esa)],[f_302_3]) ).
cnf(f_302_5,plain,
( c_Fun_Ooverride__on(U_1822,U_1828,U_1830,U_1832,U_1826,U_1824) = hAPP(U_1832,U_1824)
| ~ hBOOL(hAPP(hAPP(c_member(U_1822),U_1824),U_1826)) ),
inference(clausify,[status(thm)],[f_302_4]) ).
cnf(f_302_6,plain,
( c_Fun_Ooverride__on(U_1823,U_1829,U_1831,U_1833,U_1827,U_1825) = hAPP(U_1831,U_1825)
| hBOOL(hAPP(hAPP(c_member(U_1823),U_1825),U_1827)) ),
inference(clausify,[status(thm)],[f_302_4]) ).
fof(f_303_1,plain,
! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_measure__def]) ).
fof(f_303_2,plain,
! [U_1834] : c_Wellfounded_Omeasure(U_1834) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_1834),c_Wellfounded_Oless__than),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_1834] : c_Wellfounded_Omeasure(U_1834) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_1834),c_Wellfounded_Oless__than),
inference(definitional_conversion,[status(esa)],[f_303_2]) ).
cnf(f_303_4,plain,
c_Wellfounded_Omeasure(U_1834) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_1834),c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).
fof(f_304_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(definitional_conversion,[status(esa)],[f_304_1]) ).
cnf(f_304_3,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
& ( 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_305_2,plain,
! [U_1836,U_1835] :
( ( 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_1835),U_1836)),c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1835,U_1836) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1835,U_1836)
| ~ 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_1835),U_1836)),c_Wellfounded_Oless__than)) ) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
( ! [U_1840,U_1838] :
( 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_1838),U_1840)),c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1838,U_1840) )
& ! [U_1839,U_1837] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1837,U_1839)
| ~ 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_1837),U_1839)),c_Wellfounded_Oless__than)) ) ),
inference(miniscope,[status(thm)],[f_305_2]) ).
fof(f_305_4,plain,
( ! [U_1838,U_1840] :
( 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_1838),U_1840)),c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1838,U_1840) )
& ! [U_1839,U_1837] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1837,U_1839)
| ~ 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_1837),U_1839)),c_Wellfounded_Oless__than)) ) ),
inference(definitional_conversion,[status(esa)],[f_305_3]) ).
cnf(f_305_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1837,U_1839)
| ~ 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_1837),U_1839)),c_Wellfounded_Oless__than)) ),
inference(clausify,[status(thm)],[f_305_4]) ).
cnf(f_305_6,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_1838),U_1840)),c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1838,U_1840) ),
inference(clausify,[status(thm)],[f_305_4]) ).
fof(f_306_1,plain,
! [V_b,V_x,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)
| ~ 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_306_2,plain,
! [U_1844,U_1843,U_1842,U_1841] :
( c_Orderings_Oord__class_Oless(U_1841,c_Lattices_Osemilattice__inf__class_Oinf(U_1841,U_1842,U_1844),U_1843)
| ~ c_Orderings_Oord__class_Oless(U_1841,U_1842,U_1843)
| ~ class_Lattices_Osemilattice__inf(U_1841) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_1842,U_1844,U_1841,U_1843] :
( c_Orderings_Oord__class_Oless(U_1841,c_Lattices_Osemilattice__inf__class_Oinf(U_1841,U_1842,U_1844),U_1843)
| ~ c_Orderings_Oord__class_Oless(U_1841,U_1842,U_1843)
| ~ class_Lattices_Osemilattice__inf(U_1841) ),
inference(definitional_conversion,[status(esa)],[f_306_2]) ).
cnf(f_306_4,plain,
( c_Orderings_Oord__class_Oless(U_1841,c_Lattices_Osemilattice__inf__class_Oinf(U_1841,U_1842,U_1844),U_1843)
| ~ c_Orderings_Oord__class_Oless(U_1841,U_1842,U_1843)
| ~ class_Lattices_Osemilattice__inf(U_1841) ),
inference(clausify,[status(thm)],[f_306_3]) ).
fof(f_307_1,plain,
! [V_a,V_x,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)
| ~ 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_307_2,plain,
! [U_1848,U_1847,U_1846,U_1845] :
( c_Orderings_Oord__class_Oless(U_1845,c_Lattices_Osemilattice__inf__class_Oinf(U_1845,U_1848,U_1846),U_1847)
| ~ c_Orderings_Oord__class_Oless(U_1845,U_1846,U_1847)
| ~ class_Lattices_Osemilattice__inf(U_1845) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_1846,U_1845,U_1847,U_1848] :
( c_Orderings_Oord__class_Oless(U_1845,c_Lattices_Osemilattice__inf__class_Oinf(U_1845,U_1848,U_1846),U_1847)
| ~ c_Orderings_Oord__class_Oless(U_1845,U_1846,U_1847)
| ~ class_Lattices_Osemilattice__inf(U_1845) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( c_Orderings_Oord__class_Oless(U_1845,c_Lattices_Osemilattice__inf__class_Oinf(U_1845,U_1848,U_1846),U_1847)
| ~ c_Orderings_Oord__class_Oless(U_1845,U_1846,U_1847)
| ~ class_Lattices_Osemilattice__inf(U_1845) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_1,plain,
! [V_g_2,V_f_2,T_b,V_A_2,V_aa_2,T_a] :
( c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_f_2,V_aa_2)
| hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_override__on__apply__notin]) ).
fof(f_308_2,plain,
! [U_1854,U_1853,U_1852,U_1851,U_1850,U_1849] :
( c_Fun_Ooverride__on(U_1849,U_1852,U_1853,U_1854,U_1851,U_1850) = hAPP(U_1853,U_1850)
| hBOOL(hAPP(hAPP(c_member(U_1849),U_1850),U_1851)) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
! [U_1850,U_1849,U_1851,U_1852,U_1853,U_1854] :
( c_Fun_Ooverride__on(U_1849,U_1852,U_1853,U_1854,U_1851,U_1850) = hAPP(U_1853,U_1850)
| hBOOL(hAPP(hAPP(c_member(U_1849),U_1850),U_1851)) ),
inference(definitional_conversion,[status(esa)],[f_308_2]) ).
cnf(f_308_4,plain,
( c_Fun_Ooverride__on(U_1849,U_1852,U_1853,U_1854,U_1851,U_1850) = hAPP(U_1853,U_1850)
| hBOOL(hAPP(hAPP(c_member(U_1849),U_1850),U_1851)) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_1,plain,
! [V_g_2,V_f_2,T_b,V_A_2,V_aa_2,T_a] :
( c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_g_2,V_aa_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_override__on__apply__in]) ).
fof(f_309_2,plain,
! [U_1860,U_1859,U_1858,U_1857,U_1856,U_1855] :
( c_Fun_Ooverride__on(U_1855,U_1858,U_1859,U_1860,U_1857,U_1856) = hAPP(U_1860,U_1856)
| ~ hBOOL(hAPP(hAPP(c_member(U_1855),U_1856),U_1857)) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_1856,U_1855,U_1857,U_1858,U_1859,U_1860] :
( c_Fun_Ooverride__on(U_1855,U_1858,U_1859,U_1860,U_1857,U_1856) = hAPP(U_1860,U_1856)
| ~ hBOOL(hAPP(hAPP(c_member(U_1855),U_1856),U_1857)) ),
inference(definitional_conversion,[status(esa)],[f_309_2]) ).
cnf(f_309_4,plain,
( c_Fun_Ooverride__on(U_1855,U_1858,U_1859,U_1860,U_1857,U_1856) = hAPP(U_1860,U_1856)
| ~ hBOOL(hAPP(hAPP(c_member(U_1855),U_1856),U_1857)) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_1,plain,
! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)))
| ~ 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_310_2,plain,
! [U_1865,U_1864,U_1863,U_1862,U_1861] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1864,U_1864)),hAPP(hAPP(c_Product__Type_OPair(U_1864,U_1864),U_1862),U_1863)),c_Wellfounded_Omlex__prod(U_1864,U_1861,U_1865)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1861,U_1862),hAPP(U_1861,U_1863)) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_1862,U_1861,U_1863,U_1864,U_1865] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1864,U_1864)),hAPP(hAPP(c_Product__Type_OPair(U_1864,U_1864),U_1862),U_1863)),c_Wellfounded_Omlex__prod(U_1864,U_1861,U_1865)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1861,U_1862),hAPP(U_1861,U_1863)) ),
inference(definitional_conversion,[status(esa)],[f_310_2]) ).
cnf(f_310_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1864,U_1864)),hAPP(hAPP(c_Product__Type_OPair(U_1864,U_1864),U_1862),U_1863)),c_Wellfounded_Omlex__prod(U_1864,U_1861,U_1865)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1861,U_1862),hAPP(U_1861,U_1863)) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_1,plain,
! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))),
inference(fof_nnf,[status(thm)],[fact_mlex__prod__def]) ).
fof(f_311_2,plain,
! [U_1868,U_1867,U_1866] : c_Wellfounded_Omlex__prod(U_1866,U_1867,U_1868) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_1866),U_1866),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_1866,c_Wellfounded_Oless__than,U_1868)),hAPP(hAPP(c_COMBS(U_1866,U_1866,tc_prod(tc_Nat_Onat,U_1866)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_1866,tc_prod(tc_Nat_Onat,U_1866)),U_1866),c_Product__Type_OPair(tc_Nat_Onat,U_1866)),U_1867)),c_COMBI(U_1866))),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
! [U_1866,U_1867,U_1868] : c_Wellfounded_Omlex__prod(U_1866,U_1867,U_1868) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_1866),U_1866),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_1866,c_Wellfounded_Oless__than,U_1868)),hAPP(hAPP(c_COMBS(U_1866,U_1866,tc_prod(tc_Nat_Onat,U_1866)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_1866,tc_prod(tc_Nat_Onat,U_1866)),U_1866),c_Product__Type_OPair(tc_Nat_Onat,U_1866)),U_1867)),c_COMBI(U_1866))),
inference(definitional_conversion,[status(esa)],[f_311_2]) ).
cnf(f_311_4,plain,
c_Wellfounded_Omlex__prod(U_1866,U_1867,U_1868) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_1866),U_1866),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_1866,c_Wellfounded_Oless__than,U_1868)),hAPP(hAPP(c_COMBS(U_1866,U_1866,tc_prod(tc_Nat_Onat,U_1866)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_1866,tc_prod(tc_Nat_Onat,U_1866)),U_1866),c_Product__Type_OPair(tc_Nat_Onat,U_1866)),U_1867)),c_COMBI(U_1866))),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_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]) ).
fof(f_312_2,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(definitional_conversion,[status(esa)],[f_312_1]) ).
cnf(f_312_3,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_312_2]) ).
fof(f_313_1,plain,
! [V_ca_2,V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).
fof(f_313_2,plain,
! [U_1872,U_1871,U_1870,U_1869] :
( hBOOL(hAPP(hAPP(c_member(U_1869),U_1872),U_1871))
| ~ hBOOL(hAPP(hAPP(c_member(U_1869),U_1872),U_1870))
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1869,tc_HOL_Obool),U_1870,U_1871) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_1869,U_1870,U_1871,U_1872] :
( hBOOL(hAPP(hAPP(c_member(U_1869),U_1872),U_1871))
| ~ hBOOL(hAPP(hAPP(c_member(U_1869),U_1872),U_1870))
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1869,tc_HOL_Obool),U_1870,U_1871) ),
inference(definitional_conversion,[status(esa)],[f_313_2]) ).
cnf(f_313_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1869),U_1872),U_1871))
| ~ hBOOL(hAPP(hAPP(c_member(U_1869),U_1872),U_1870))
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1869,tc_HOL_Obool),U_1870,U_1871) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).
fof(f_314_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(definitional_conversion,[status(esa)],[f_314_1]) ).
cnf(f_314_3,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_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)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
& ( 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_315_2,plain,
! [U_1874,U_1873] :
( ( 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_1873),U_1874)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1873,U_1874) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1873,U_1874)
| ~ 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_1873),U_1874)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
( ! [U_1878,U_1876] :
( 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_1876),U_1878)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1876,U_1878) )
& ! [U_1877,U_1875] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1875,U_1877)
| ~ 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_1875),U_1877)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(miniscope,[status(thm)],[f_315_2]) ).
fof(f_315_4,plain,
( ! [U_1878,U_1876] :
( 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_1876),U_1878)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1876,U_1878) )
& ! [U_1877,U_1875] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1875,U_1877)
| ~ 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_1875),U_1877)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(definitional_conversion,[status(esa)],[f_315_3]) ).
cnf(f_315_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1875,U_1877)
| ~ 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_1875),U_1877)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(clausify,[status(thm)],[f_315_4]) ).
cnf(f_315_6,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_1876),U_1878)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1876,U_1878) ),
inference(clausify,[status(thm)],[f_315_4]) ).
fof(f_316_1,plain,
! [V_f_2,V_R_2,T_a] :
( c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))
| ~ c_Wellfounded_Owf(T_a,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__mlex]) ).
fof(f_316_2,plain,
! [U_1881,U_1880,U_1879] :
( c_Wellfounded_Owf(U_1879,c_Wellfounded_Omlex__prod(U_1879,U_1881,U_1880))
| ~ c_Wellfounded_Owf(U_1879,U_1880) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
! [U_1879,U_1881,U_1880] :
( c_Wellfounded_Owf(U_1879,c_Wellfounded_Omlex__prod(U_1879,U_1881,U_1880))
| ~ c_Wellfounded_Owf(U_1879,U_1880) ),
inference(definitional_conversion,[status(esa)],[f_316_2]) ).
cnf(f_316_4,plain,
( c_Wellfounded_Owf(U_1879,c_Wellfounded_Omlex__prod(U_1879,U_1881,U_1880))
| ~ c_Wellfounded_Owf(U_1879,U_1880) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_1,plain,
! [V_t_2,V_s_2,V_ba_2,V_aa_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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_ba_2) ),
inference(fof_nnf,[status(thm)],[fact_pair__leqI1]) ).
fof(f_317_2,plain,
! [U_1885,U_1884,U_1883,U_1882] :
( 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_1882),U_1884)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1883),U_1885))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1882,U_1883) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_1882,U_1883,U_1884,U_1885] :
( 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_1882),U_1884)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1883),U_1885))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1882,U_1883) ),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_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)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1882),U_1884)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1883),U_1885))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1882,U_1883) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_1,plain,
! [V_t_2,V_s_2,V_ba_2,V_aa_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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_ba_2) ),
inference(fof_nnf,[status(thm)],[fact_pair__lessI1]) ).
fof(f_318_2,plain,
! [U_1889,U_1888,U_1887,U_1886] :
( 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_1886),U_1888)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1887),U_1889))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1886,U_1887) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_1886,U_1887,U_1888,U_1889] :
( 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_1886),U_1888)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1887),U_1889))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1886,U_1887) ),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_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)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1886),U_1888)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1887),U_1889))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1886,U_1887) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_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)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( 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_319_2,plain,
! [U_1891,U_1890] :
( ( 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_1890),U_1891)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1890,U_1891) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1890,U_1891)
| ~ 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_1890),U_1891)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
( ! [U_1895,U_1893] :
( 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_1893),U_1895)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1893,U_1895) )
& ! [U_1894,U_1892] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1892,U_1894)
| ~ 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_1892),U_1894)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(miniscope,[status(thm)],[f_319_2]) ).
fof(f_319_4,plain,
( ! [U_1893,U_1895] :
( 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_1893),U_1895)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1893,U_1895) )
& ! [U_1894,U_1892] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1892,U_1894)
| ~ 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_1892),U_1894)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(definitional_conversion,[status(esa)],[f_319_3]) ).
cnf(f_319_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1892,U_1894)
| ~ 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_1892),U_1894)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(clausify,[status(thm)],[f_319_4]) ).
cnf(f_319_6,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_1893),U_1895)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1893,U_1895) ),
inference(clausify,[status(thm)],[f_319_4]) ).
fof(f_320_1,plain,
! [V_C_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_psubset__trans]) ).
fof(f_320_2,plain,
! [U_1899,U_1898,U_1897,U_1896] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1897,U_1899)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1898,U_1899)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1897,U_1898) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1899,U_1897,U_1898,U_1896] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1897,U_1899)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1898,U_1899)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1897,U_1898) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1897,U_1899)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1898,U_1899)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1896,tc_HOL_Obool),U_1897,U_1898) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
| ~ 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_321_2,plain,
! [U_1901,U_1900] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1900,U_1901)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1900,U_1901) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1901,U_1900] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1900,U_1901)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1900,U_1901) ),
inference(definitional_conversion,[status(esa)],[f_321_2]) ).
cnf(f_321_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1900,U_1901)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1900,U_1901) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [V_t_2,V_s_2,V_ba_2,V_aa_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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s_2,V_t_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_aa_2,V_ba_2) ),
inference(fof_nnf,[status(thm)],[fact_pair__lessI2]) ).
fof(f_322_2,plain,
! [U_1905,U_1904,U_1903,U_1902] :
( 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_1902),U_1904)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1903),U_1905))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1904,U_1905)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1902,U_1903) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
! [U_1902,U_1903,U_1904,U_1905] :
( 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_1902),U_1904)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1903),U_1905))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1904,U_1905)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1902,U_1903) ),
inference(definitional_conversion,[status(esa)],[f_322_2]) ).
cnf(f_322_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)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1902),U_1904)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1903),U_1905))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1904,U_1905)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1902,U_1903) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_1,plain,
! [V_t_2,V_s_2,V_ba_2,V_aa_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_aa_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_ba_2),V_t_2))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_s_2,V_t_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_aa_2,V_ba_2) ),
inference(fof_nnf,[status(thm)],[fact_pair__leqI2]) ).
fof(f_323_2,plain,
! [U_1909,U_1908,U_1907,U_1906] :
( 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_1906),U_1908)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1907),U_1909))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1908,U_1909)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1906,U_1907) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
! [U_1906,U_1907,U_1908,U_1909] :
( 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_1906),U_1908)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1907),U_1909))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1908,U_1909)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1906,U_1907) ),
inference(definitional_conversion,[status(esa)],[f_323_2]) ).
cnf(f_323_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)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1906),U_1908)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1907),U_1909))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1908,U_1909)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1906,U_1907) ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_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]) ).
fof(f_324_2,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(definitional_conversion,[status(esa)],[f_324_1]) ).
cnf(f_324_3,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_325_2,plain,
! [U_1912,U_1911,U_1910] :
( c_Orderings_Oord__class_Oless__eq(U_1910,c_Lattices_Osemilattice__inf__class_Oinf(U_1910,U_1911,U_1912),U_1911)
| ~ class_Lattices_Olattice(U_1910) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1912,U_1911,U_1910] :
( c_Orderings_Oord__class_Oless__eq(U_1910,c_Lattices_Osemilattice__inf__class_Oinf(U_1910,U_1911,U_1912),U_1911)
| ~ class_Lattices_Olattice(U_1910) ),
inference(definitional_conversion,[status(esa)],[f_325_2]) ).
cnf(f_325_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1910,c_Lattices_Osemilattice__inf__class_Oinf(U_1910,U_1911,U_1912),U_1911)
| ~ class_Lattices_Olattice(U_1910) ),
inference(clausify,[status(thm)],[f_325_3]) ).
fof(f_326_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_326_2,plain,
! [U_1915,U_1914,U_1913] :
( c_Orderings_Oord__class_Oless__eq(U_1913,c_Lattices_Osemilattice__inf__class_Oinf(U_1913,U_1914,U_1915),U_1914)
| ~ class_Lattices_Osemilattice__inf(U_1913) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1913,U_1914,U_1915] :
( c_Orderings_Oord__class_Oless__eq(U_1913,c_Lattices_Osemilattice__inf__class_Oinf(U_1913,U_1914,U_1915),U_1914)
| ~ class_Lattices_Osemilattice__inf(U_1913) ),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1913,c_Lattices_Osemilattice__inf__class_Oinf(U_1913,U_1914,U_1915),U_1914)
| ~ class_Lattices_Osemilattice__inf(U_1913) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_327_2,plain,
! [U_1918,U_1917,U_1916] :
( c_Orderings_Oord__class_Oless__eq(U_1916,c_Lattices_Osemilattice__inf__class_Oinf(U_1916,U_1917,U_1918),U_1918)
| ~ class_Lattices_Olattice(U_1916) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1916,U_1917,U_1918] :
( c_Orderings_Oord__class_Oless__eq(U_1916,c_Lattices_Osemilattice__inf__class_Oinf(U_1916,U_1917,U_1918),U_1918)
| ~ class_Lattices_Olattice(U_1916) ),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1916,c_Lattices_Osemilattice__inf__class_Oinf(U_1916,U_1917,U_1918),U_1918)
| ~ class_Lattices_Olattice(U_1916) ),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_328_2,plain,
! [U_1921,U_1920,U_1919] :
( c_Orderings_Oord__class_Oless__eq(U_1919,c_Lattices_Osemilattice__inf__class_Oinf(U_1919,U_1920,U_1921),U_1921)
| ~ class_Lattices_Osemilattice__inf(U_1919) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
! [U_1920,U_1919,U_1921] :
( c_Orderings_Oord__class_Oless__eq(U_1919,c_Lattices_Osemilattice__inf__class_Oinf(U_1919,U_1920,U_1921),U_1921)
| ~ class_Lattices_Osemilattice__inf(U_1919) ),
inference(definitional_conversion,[status(esa)],[f_328_2]) ).
cnf(f_328_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1919,c_Lattices_Osemilattice__inf__class_Oinf(U_1919,U_1920,U_1921),U_1921)
| ~ class_Lattices_Osemilattice__inf(U_1919) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x_2,V_y_2) != V_x_2 )
& ( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x_2,V_y_2) = V_x_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__inf]) ).
fof(f_329_2,plain,
! [U_1924,U_1923,U_1922] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1922,U_1923,U_1924)
| c_Lattices_Osemilattice__inf__class_Oinf(U_1922,U_1923,U_1924) != U_1923 )
& ( c_Lattices_Osemilattice__inf__class_Oinf(U_1922,U_1923,U_1924) = U_1923
| ~ c_Orderings_Oord__class_Oless__eq(U_1922,U_1923,U_1924) ) )
| ~ class_Lattices_Osemilattice__inf(U_1922) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
( ! [U_1923,U_1922,U_1924] :
( c_Orderings_Oord__class_Oless__eq(U_1922,U_1923,U_1924)
| c_Lattices_Osemilattice__inf__class_Oinf(U_1922,U_1923,U_1924) != U_1923
| ~ sP109(U_1923,U_1922,U_1924) )
& ! [U_1923,U_1922,U_1924] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1922,U_1923,U_1924) = U_1923
| ~ c_Orderings_Oord__class_Oless__eq(U_1922,U_1923,U_1924)
| ~ sP109(U_1923,U_1922,U_1924) )
& ! [U_1923,U_1922,U_1924] :
( sP109(U_1923,U_1922,U_1924)
| ~ class_Lattices_Osemilattice__inf(U_1922) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_329_2]) ).
cnf(f_329_4,plain,
( sP109(U_1923,U_1922,U_1924)
| ~ class_Lattices_Osemilattice__inf(U_1922) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_5,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1922,U_1923,U_1924) = U_1923
| ~ c_Orderings_Oord__class_Oless__eq(U_1922,U_1923,U_1924)
| ~ sP109(U_1923,U_1922,U_1924) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1922,U_1923,U_1924)
| c_Lattices_Osemilattice__inf__class_Oinf(U_1922,U_1923,U_1924) != U_1923
| ~ sP109(U_1923,U_1922,U_1924) ),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_1,plain,
! [V_z_2,V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2)) ) )
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__inf__iff]) ).
fof(f_330_2,plain,
! [U_1928,U_1927,U_1926,U_1925] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,c_Lattices_Osemilattice__inf__class_Oinf(U_1925,U_1927,U_1928))
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1928)
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1927) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1928)
& c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1927) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,c_Lattices_Osemilattice__inf__class_Oinf(U_1925,U_1927,U_1928)) ) )
| ~ class_Lattices_Osemilattice__inf(U_1925) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
( ! [U_1927,U_1925,U_1926,U_1928] :
( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1928)
| ~ sP110(U_1927,U_1925,U_1926,U_1928) )
& ! [U_1927,U_1925,U_1926,U_1928] :
( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1927)
| ~ sP110(U_1927,U_1925,U_1926,U_1928) )
& ! [U_1927,U_1925,U_1926,U_1928] :
( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,c_Lattices_Osemilattice__inf__class_Oinf(U_1925,U_1927,U_1928))
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1928)
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1927)
| ~ sP111(U_1927,U_1925,U_1926,U_1928) )
& ! [U_1927,U_1925,U_1926,U_1928] :
( sP110(U_1927,U_1925,U_1926,U_1928)
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,c_Lattices_Osemilattice__inf__class_Oinf(U_1925,U_1927,U_1928))
| ~ sP111(U_1927,U_1925,U_1926,U_1928) )
& ! [U_1927,U_1925,U_1926,U_1928] :
( sP111(U_1927,U_1925,U_1926,U_1928)
| ~ class_Lattices_Osemilattice__inf(U_1925) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110,sP111])],[f_330_2]) ).
cnf(f_330_4,plain,
( sP111(U_1927,U_1925,U_1926,U_1928)
| ~ class_Lattices_Osemilattice__inf(U_1925) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_5,plain,
( sP110(U_1927,U_1925,U_1926,U_1928)
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,c_Lattices_Osemilattice__inf__class_Oinf(U_1925,U_1927,U_1928))
| ~ sP111(U_1927,U_1925,U_1926,U_1928) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,c_Lattices_Osemilattice__inf__class_Oinf(U_1925,U_1927,U_1928))
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1928)
| ~ c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1927)
| ~ sP111(U_1927,U_1925,U_1926,U_1928) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1927)
| ~ sP110(U_1927,U_1925,U_1926,U_1928) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_1925,U_1926,U_1928)
| ~ sP110(U_1927,U_1925,U_1926,U_1928) ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_1,plain,
! [V_b,V_x,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)
| ~ 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_331_2,plain,
! [U_1932,U_1931,U_1930,U_1929] :
( c_Orderings_Oord__class_Oless__eq(U_1929,c_Lattices_Osemilattice__inf__class_Oinf(U_1929,U_1930,U_1932),U_1931)
| ~ c_Orderings_Oord__class_Oless__eq(U_1929,U_1930,U_1931)
| ~ class_Lattices_Osemilattice__inf(U_1929) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1931,U_1929,U_1930,U_1932] :
( c_Orderings_Oord__class_Oless__eq(U_1929,c_Lattices_Osemilattice__inf__class_Oinf(U_1929,U_1930,U_1932),U_1931)
| ~ c_Orderings_Oord__class_Oless__eq(U_1929,U_1930,U_1931)
| ~ class_Lattices_Osemilattice__inf(U_1929) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1929,c_Lattices_Osemilattice__inf__class_Oinf(U_1929,U_1930,U_1932),U_1931)
| ~ c_Orderings_Oord__class_Oless__eq(U_1929,U_1930,U_1931)
| ~ class_Lattices_Osemilattice__inf(U_1929) ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_1,plain,
! [V_a,V_x,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)
| ~ 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_332_2,plain,
! [U_1936,U_1935,U_1934,U_1933] :
( c_Orderings_Oord__class_Oless__eq(U_1933,c_Lattices_Osemilattice__inf__class_Oinf(U_1933,U_1936,U_1934),U_1935)
| ~ c_Orderings_Oord__class_Oless__eq(U_1933,U_1934,U_1935)
| ~ class_Lattices_Osemilattice__inf(U_1933) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_1933,U_1936,U_1935,U_1934] :
( c_Orderings_Oord__class_Oless__eq(U_1933,c_Lattices_Osemilattice__inf__class_Oinf(U_1933,U_1936,U_1934),U_1935)
| ~ c_Orderings_Oord__class_Oless__eq(U_1933,U_1934,U_1935)
| ~ class_Lattices_Osemilattice__inf(U_1933) ),
inference(definitional_conversion,[status(esa)],[f_332_2]) ).
cnf(f_332_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1933,c_Lattices_Osemilattice__inf__class_Oinf(U_1933,U_1936,U_1934),U_1935)
| ~ c_Orderings_Oord__class_Oless__eq(U_1933,U_1934,U_1935)
| ~ class_Lattices_Osemilattice__inf(U_1933) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_1,plain,
! [V_y,V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_x
| ~ 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_333_2,plain,
! [U_1939,U_1938,U_1937] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1937,U_1938,U_1939) = U_1938
| ~ c_Orderings_Oord__class_Oless__eq(U_1937,U_1938,U_1939)
| ~ class_Lattices_Osemilattice__inf(U_1937) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_1938,U_1939,U_1937] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1937,U_1938,U_1939) = U_1938
| ~ c_Orderings_Oord__class_Oless__eq(U_1937,U_1938,U_1939)
| ~ class_Lattices_Osemilattice__inf(U_1937) ),
inference(definitional_conversion,[status(esa)],[f_333_2]) ).
cnf(f_333_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1937,U_1938,U_1939) = U_1938
| ~ c_Orderings_Oord__class_Oless__eq(U_1937,U_1938,U_1939)
| ~ class_Lattices_Osemilattice__inf(U_1937) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
! [V_x,V_y,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_y
| ~ 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_334_2,plain,
! [U_1942,U_1941,U_1940] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1940,U_1942,U_1941) = U_1941
| ~ c_Orderings_Oord__class_Oless__eq(U_1940,U_1941,U_1942)
| ~ class_Lattices_Osemilattice__inf(U_1940) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1942,U_1940,U_1941] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1940,U_1942,U_1941) = U_1941
| ~ c_Orderings_Oord__class_Oless__eq(U_1940,U_1941,U_1942)
| ~ class_Lattices_Osemilattice__inf(U_1940) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1940,U_1942,U_1941) = U_1941
| ~ c_Orderings_Oord__class_Oless__eq(U_1940,U_1941,U_1942)
| ~ class_Lattices_Osemilattice__inf(U_1940) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_1,plain,
! [V_b,V_a,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b)
| ~ 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_335_2,plain,
! [U_1946,U_1945,U_1944,U_1943] :
( c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,c_Lattices_Osemilattice__inf__class_Oinf(U_1943,U_1945,U_1946))
| ~ c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,U_1946)
| ~ c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,U_1945)
| ~ class_Lattices_Osemilattice__inf(U_1943) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_1944,U_1943,U_1945,U_1946] :
( c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,c_Lattices_Osemilattice__inf__class_Oinf(U_1943,U_1945,U_1946))
| ~ c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,U_1946)
| ~ c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,U_1945)
| ~ class_Lattices_Osemilattice__inf(U_1943) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,c_Lattices_Osemilattice__inf__class_Oinf(U_1943,U_1945,U_1946))
| ~ c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,U_1946)
| ~ c_Orderings_Oord__class_Oless__eq(U_1943,U_1944,U_1945)
| ~ class_Lattices_Osemilattice__inf(U_1943) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z)
| ~ 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_336_2,plain,
! [U_1950,U_1949,U_1948,U_1947] :
( c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,c_Lattices_Osemilattice__inf__class_Oinf(U_1947,U_1949,U_1950))
| ~ c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,U_1950)
| ~ c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,U_1949)
| ~ class_Lattices_Osemilattice__inf(U_1947) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_1949,U_1948,U_1947,U_1950] :
( c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,c_Lattices_Osemilattice__inf__class_Oinf(U_1947,U_1949,U_1950))
| ~ c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,U_1950)
| ~ c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,U_1949)
| ~ class_Lattices_Osemilattice__inf(U_1947) ),
inference(definitional_conversion,[status(esa)],[f_336_2]) ).
cnf(f_336_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,c_Lattices_Osemilattice__inf__class_Oinf(U_1947,U_1949,U_1950))
| ~ c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,U_1950)
| ~ c_Orderings_Oord__class_Oless__eq(U_1947,U_1948,U_1949)
| ~ class_Lattices_Osemilattice__inf(U_1947) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_c,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d)
| ~ 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_337_2,plain,
! [U_1955,U_1954,U_1953,U_1952,U_1951] :
( c_Orderings_Oord__class_Oless__eq(U_1951,c_Lattices_Osemilattice__inf__class_Oinf(U_1951,U_1952,U_1954),c_Lattices_Osemilattice__inf__class_Oinf(U_1951,U_1953,U_1955))
| ~ c_Orderings_Oord__class_Oless__eq(U_1951,U_1954,U_1955)
| ~ c_Orderings_Oord__class_Oless__eq(U_1951,U_1952,U_1953)
| ~ class_Lattices_Osemilattice__inf(U_1951) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_1952,U_1951,U_1953,U_1954,U_1955] :
( c_Orderings_Oord__class_Oless__eq(U_1951,c_Lattices_Osemilattice__inf__class_Oinf(U_1951,U_1952,U_1954),c_Lattices_Osemilattice__inf__class_Oinf(U_1951,U_1953,U_1955))
| ~ c_Orderings_Oord__class_Oless__eq(U_1951,U_1954,U_1955)
| ~ c_Orderings_Oord__class_Oless__eq(U_1951,U_1952,U_1953)
| ~ class_Lattices_Osemilattice__inf(U_1951) ),
inference(definitional_conversion,[status(esa)],[f_337_2]) ).
cnf(f_337_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1951,c_Lattices_Osemilattice__inf__class_Oinf(U_1951,U_1952,U_1954),c_Lattices_Osemilattice__inf__class_Oinf(U_1951,U_1953,U_1955))
| ~ c_Orderings_Oord__class_Oless__eq(U_1951,U_1954,U_1955)
| ~ c_Orderings_Oord__class_Oless__eq(U_1951,U_1952,U_1953)
| ~ class_Lattices_Osemilattice__inf(U_1951) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_1,plain,
! [V_b,V_a,V_x,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,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_338_2,plain,
! [U_1959,U_1958,U_1957,U_1956] :
( ( c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,U_1959)
& c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,U_1958) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,c_Lattices_Osemilattice__inf__class_Oinf(U_1956,U_1958,U_1959))
| ~ class_Lattices_Osemilattice__inf(U_1956) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
( ! [U_1956,U_1957,U_1958,U_1959] :
( c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,U_1959)
| ~ sP112(U_1956,U_1957,U_1958,U_1959) )
& ! [U_1956,U_1957,U_1958,U_1959] :
( c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,U_1958)
| ~ sP112(U_1956,U_1957,U_1958,U_1959) )
& ! [U_1956,U_1957,U_1958,U_1959] :
( sP112(U_1956,U_1957,U_1958,U_1959)
| ~ c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,c_Lattices_Osemilattice__inf__class_Oinf(U_1956,U_1958,U_1959))
| ~ class_Lattices_Osemilattice__inf(U_1956) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_338_2]) ).
cnf(f_338_4,plain,
( sP112(U_1956,U_1957,U_1958,U_1959)
| ~ c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,c_Lattices_Osemilattice__inf__class_Oinf(U_1956,U_1958,U_1959))
| ~ class_Lattices_Osemilattice__inf(U_1956) ),
inference(clausify,[status(thm)],[f_338_3]) ).
cnf(f_338_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,U_1958)
| ~ sP112(U_1956,U_1957,U_1958,U_1959) ),
inference(clausify,[status(thm)],[f_338_3]) ).
cnf(f_338_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1956,U_1957,U_1959)
| ~ sP112(U_1956,U_1957,U_1958,U_1959) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_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]) ).
fof(f_339_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(definitional_conversion,[status(esa)],[f_339_1]) ).
cnf(f_339_3,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_339_2]) ).
fof(f_340_1,plain,
! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
| ~ 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_340_2,plain,
! [U_1964,U_1963,U_1962,U_1961,U_1960] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1961),U_1962)),c_Wellfounded_Omlex__prod(U_1963,U_1960,U_1964)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1961),U_1962)),U_1964))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(U_1960,U_1961),hAPP(U_1960,U_1962)) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
! [U_1960,U_1961,U_1962,U_1963,U_1964] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1961),U_1962)),c_Wellfounded_Omlex__prod(U_1963,U_1960,U_1964)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1961),U_1962)),U_1964))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(U_1960,U_1961),hAPP(U_1960,U_1962)) ),
inference(definitional_conversion,[status(esa)],[f_340_2]) ).
cnf(f_340_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1961),U_1962)),c_Wellfounded_Omlex__prod(U_1963,U_1960,U_1964)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1961),U_1962)),U_1964))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(U_1960,U_1961),hAPP(U_1960,U_1962)) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_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),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_341_2,plain,
! [U_1968,U_1967,U_1966,U_1965] :
( 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_1966),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1967,U_1968))),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_1966),U_1968)),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_1965),U_1967)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1965),U_1966)) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1966,U_1965,U_1967,U_1968] :
( 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_1966),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1967,U_1968))),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_1966),U_1968)),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_1965),U_1967)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1965),U_1966)) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,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_1966),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1967,U_1968))),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_1966),U_1968)),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_1965),U_1967)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1965),U_1966)) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_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)),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_342_2,plain,
! [U_1972,U_1971,U_1970,U_1969] :
( 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_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1971,U_1972)),U_1970)),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_1972),U_1970)),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_1971),U_1969)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1969),U_1970)) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_1970,U_1971,U_1972,U_1969] :
( 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_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1971,U_1972)),U_1970)),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_1972),U_1970)),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_1971),U_1969)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1969),U_1970)) ),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,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_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1971,U_1972)),U_1970)),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_1972),U_1970)),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_1971),U_1969)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1969),U_1970)) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_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),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_343_2,plain,
! [U_1976,U_1975,U_1974,U_1973] :
( 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_1974),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1975,U_1976))),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_1974),U_1976)),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_1973),U_1975)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1973),U_1974)) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_1974,U_1975,U_1973,U_1976] :
( 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_1974),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1975,U_1976))),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_1974),U_1976)),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_1973),U_1975)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1973),U_1974)) ),
inference(definitional_conversion,[status(esa)],[f_343_2]) ).
cnf(f_343_4,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_1974),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_1975,U_1976))),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_1974),U_1976)),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_1973),U_1975)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_1973),U_1974)) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_1,plain,
! [V_ca_2,V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_subsetD]) ).
fof(f_344_2,plain,
! [U_1980,U_1979,U_1978,U_1977] :
( hBOOL(hAPP(hAPP(c_member(U_1977),U_1980),U_1979))
| ~ hBOOL(hAPP(hAPP(c_member(U_1977),U_1980),U_1978))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1977,tc_HOL_Obool),U_1978,U_1979) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_1977,U_1978,U_1979,U_1980] :
( hBOOL(hAPP(hAPP(c_member(U_1977),U_1980),U_1979))
| ~ hBOOL(hAPP(hAPP(c_member(U_1977),U_1980),U_1978))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1977,tc_HOL_Obool),U_1978,U_1979) ),
inference(definitional_conversion,[status(esa)],[f_344_2]) ).
cnf(f_344_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1977),U_1980),U_1979))
| ~ hBOOL(hAPP(hAPP(c_member(U_1977),U_1980),U_1978))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1977,tc_HOL_Obool),U_1978,U_1979) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_1,plain,
! [V_C_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans]) ).
fof(f_345_2,plain,
! [U_1984,U_1983,U_1982,U_1981] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1981,tc_HOL_Obool),U_1982,U_1984)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1981,tc_HOL_Obool),U_1983,U_1984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1981,tc_HOL_Obool),U_1982,U_1983) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_1984,U_1981,U_1983,U_1982] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1981,tc_HOL_Obool),U_1982,U_1984)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1981,tc_HOL_Obool),U_1983,U_1984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1981,tc_HOL_Obool),U_1982,U_1983) ),
inference(definitional_conversion,[status(esa)],[f_345_2]) ).
cnf(f_345_4,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_1981,tc_HOL_Obool),U_1982,U_1984)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1981,tc_HOL_Obool),U_1983,U_1984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1981,tc_HOL_Obool),U_1982,U_1983) ),
inference(clausify,[status(thm)],[f_345_3]) ).
fof(f_346_1,plain,
! [V_C_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans]) ).
fof(f_346_2,plain,
! [U_1988,U_1987,U_1986,U_1985] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1985,tc_HOL_Obool),U_1986,U_1988)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1985,tc_HOL_Obool),U_1987,U_1988)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1985,tc_HOL_Obool),U_1986,U_1987) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_1985,U_1986,U_1987,U_1988] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1985,tc_HOL_Obool),U_1986,U_1988)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1985,tc_HOL_Obool),U_1987,U_1988)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1985,tc_HOL_Obool),U_1986,U_1987) ),
inference(definitional_conversion,[status(esa)],[f_346_2]) ).
cnf(f_346_4,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_1985,tc_HOL_Obool),U_1986,U_1988)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1985,tc_HOL_Obool),U_1987,U_1988)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1985,tc_HOL_Obool),U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_346_3]) ).
fof(f_347_1,plain,
! [V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset]) ).
fof(f_347_2,plain,
! [U_1991,U_1990,U_1989] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1989,tc_HOL_Obool),U_1990,U_1991)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1989,tc_HOL_Obool),U_1990,U_1991) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_1990,U_1989,U_1991] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1989,tc_HOL_Obool),U_1990,U_1991)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1989,tc_HOL_Obool),U_1990,U_1991) ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1989,tc_HOL_Obool),U_1990,U_1991)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1989,tc_HOL_Obool),U_1990,U_1991) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_1,plain,
! [V_B_2,V_A_2,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| ( V_A_2 != V_B_2
& ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) )
& ( V_A_2 = V_B_2
| c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq]) ).
fof(f_348_2,plain,
! [U_1994,U_1993,U_1992] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1992,tc_HOL_Obool),U_1993,U_1994)
| ( U_1993 != U_1994
& ~ c_Orderings_Oord__class_Oless(tc_fun(U_1992,tc_HOL_Obool),U_1993,U_1994) ) )
& ( U_1993 = U_1994
| c_Orderings_Oord__class_Oless(tc_fun(U_1992,tc_HOL_Obool),U_1993,U_1994)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1992,tc_HOL_Obool),U_1993,U_1994) ) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
( ! [U_2000,U_1998,U_1996] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000)
| ( U_1998 != U_2000
& ~ c_Orderings_Oord__class_Oless(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000) ) )
& ! [U_1999,U_1997,U_1995] :
( U_1997 = U_1999
| c_Orderings_Oord__class_Oless(tc_fun(U_1995,tc_HOL_Obool),U_1997,U_1999)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1995,tc_HOL_Obool),U_1997,U_1999) ) ),
inference(miniscope,[status(thm)],[f_348_2]) ).
fof(f_348_4,plain,
( ! [U_1996,U_2000,U_1998] :
( U_1998 != U_2000
| ~ sP113(U_1996,U_2000,U_1998) )
& ! [U_1996,U_2000,U_1998] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000)
| ~ sP113(U_1996,U_2000,U_1998) )
& ! [U_1996,U_2000,U_1998] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000)
| sP113(U_1996,U_2000,U_1998) )
& ! [U_1997,U_1999,U_1995] :
( U_1997 = U_1999
| c_Orderings_Oord__class_Oless(tc_fun(U_1995,tc_HOL_Obool),U_1997,U_1999)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1995,tc_HOL_Obool),U_1997,U_1999) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_348_3]) ).
cnf(f_348_5,plain,
( U_1997 = U_1999
| c_Orderings_Oord__class_Oless(tc_fun(U_1995,tc_HOL_Obool),U_1997,U_1999)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1995,tc_HOL_Obool),U_1997,U_1999) ),
inference(clausify,[status(thm)],[f_348_4]) ).
cnf(f_348_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000)
| sP113(U_1996,U_2000,U_1998) ),
inference(clausify,[status(thm)],[f_348_4]) ).
cnf(f_348_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000)
| ~ sP113(U_1996,U_2000,U_1998) ),
inference(clausify,[status(thm)],[f_348_4]) ).
cnf(f_348_8,plain,
( U_1998 != U_2000
| ~ sP113(U_1996,U_2000,U_1998) ),
inference(clausify,[status(thm)],[f_348_4]) ).
fof(f_349_1,plain,
! [V_B_2,V_A_2,T_a] :
( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| V_A_2 = V_B_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) )
& ( ( V_A_2 != V_B_2
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_psubset__eq]) ).
fof(f_349_2,plain,
! [U_2003,U_2002,U_2001] :
( ( c_Orderings_Oord__class_Oless(tc_fun(U_2001,tc_HOL_Obool),U_2002,U_2003)
| U_2002 = U_2003
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2001,tc_HOL_Obool),U_2002,U_2003) )
& ( ( U_2002 != U_2003
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2001,tc_HOL_Obool),U_2002,U_2003) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2001,tc_HOL_Obool),U_2002,U_2003) ) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
( ! [U_2009,U_2007,U_2005] :
( c_Orderings_Oord__class_Oless(tc_fun(U_2005,tc_HOL_Obool),U_2007,U_2009)
| U_2007 = U_2009
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2005,tc_HOL_Obool),U_2007,U_2009) )
& ! [U_2008,U_2006,U_2004] :
( ( U_2006 != U_2008
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2008) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2008) ) ),
inference(miniscope,[status(thm)],[f_349_2]) ).
fof(f_349_4,plain,
( ! [U_2006,U_2004,U_2008] :
( U_2006 != U_2008
| ~ sP114(U_2006,U_2004,U_2008) )
& ! [U_2006,U_2004,U_2008] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2008)
| ~ sP114(U_2006,U_2004,U_2008) )
& ! [U_2005,U_2007,U_2009] :
( c_Orderings_Oord__class_Oless(tc_fun(U_2005,tc_HOL_Obool),U_2007,U_2009)
| U_2007 = U_2009
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2005,tc_HOL_Obool),U_2007,U_2009) )
& ! [U_2006,U_2004,U_2008] :
( sP114(U_2006,U_2004,U_2008)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2008) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_349_3]) ).
cnf(f_349_5,plain,
( sP114(U_2006,U_2004,U_2008)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2008) ),
inference(clausify,[status(thm)],[f_349_4]) ).
cnf(f_349_6,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_2005,tc_HOL_Obool),U_2007,U_2009)
| U_2007 = U_2009
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2005,tc_HOL_Obool),U_2007,U_2009) ),
inference(clausify,[status(thm)],[f_349_4]) ).
cnf(f_349_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2008)
| ~ sP114(U_2006,U_2004,U_2008) ),
inference(clausify,[status(thm)],[f_349_4]) ).
cnf(f_349_8,plain,
( U_2006 != U_2008
| ~ sP114(U_2006,U_2004,U_2008) ),
inference(clausify,[status(thm)],[f_349_4]) ).
fof(f_350_1,plain,
! [V_S_2,V_R_2,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq]) ).
fof(f_350_2,plain,
! [U_2012,U_2011,U_2010] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2010,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2010,tc_fun(U_2010,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2010)),U_2011),hAPP(hAPP(c_COMBC(U_2010,tc_fun(U_2010,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2010)),U_2012))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2010,tc_HOL_Obool),U_2011,U_2012) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2010,tc_HOL_Obool),U_2011,U_2012)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2010,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2010,tc_fun(U_2010,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2010)),U_2011),hAPP(hAPP(c_COMBC(U_2010,tc_fun(U_2010,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2010)),U_2012)) ) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
( ! [U_2018,U_2016,U_2014] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2014,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2014,tc_fun(U_2014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2014)),U_2016),hAPP(hAPP(c_COMBC(U_2014,tc_fun(U_2014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2014)),U_2018))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2014,tc_HOL_Obool),U_2016,U_2018) )
& ! [U_2017,U_2015,U_2013] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,tc_HOL_Obool),U_2015,U_2017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2013,tc_fun(U_2013,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2013)),U_2015),hAPP(hAPP(c_COMBC(U_2013,tc_fun(U_2013,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2013)),U_2017)) ) ),
inference(miniscope,[status(thm)],[f_350_2]) ).
fof(f_350_4,plain,
( ! [U_2016,U_2018,U_2014] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2014,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2014,tc_fun(U_2014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2014)),U_2016),hAPP(hAPP(c_COMBC(U_2014,tc_fun(U_2014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2014)),U_2018))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2014,tc_HOL_Obool),U_2016,U_2018) )
& ! [U_2013,U_2015,U_2017] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,tc_HOL_Obool),U_2015,U_2017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2013,tc_fun(U_2013,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2013)),U_2015),hAPP(hAPP(c_COMBC(U_2013,tc_fun(U_2013,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2013)),U_2017)) ) ),
inference(definitional_conversion,[status(esa)],[f_350_3]) ).
cnf(f_350_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,tc_HOL_Obool),U_2015,U_2017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2013,tc_fun(U_2013,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2013)),U_2015),hAPP(hAPP(c_COMBC(U_2013,tc_fun(U_2013,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2013)),U_2017)) ),
inference(clausify,[status(thm)],[f_350_4]) ).
cnf(f_350_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2014,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2014,tc_fun(U_2014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2014)),U_2016),hAPP(hAPP(c_COMBC(U_2014,tc_fun(U_2014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2014)),U_2018))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2014,tc_HOL_Obool),U_2016,U_2018) ),
inference(clausify,[status(thm)],[f_350_4]) ).
fof(f_351_1,plain,
! [V_S_2,V_R_2,T_b,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2]) ).
fof(f_351_2,plain,
! [U_2022,U_2021,U_2020,U_2019] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2019,tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2019,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),U_2019),c_COMBC(U_2020,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_prod(U_2019,U_2020)),tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),U_2019),hAPP(c_COMBB(tc_prod(U_2019,U_2020),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool),U_2020),c_member(tc_prod(U_2019,U_2020)))),c_Product__Type_OPair(U_2019,U_2020)))),U_2021),hAPP(hAPP(c_COMBC(U_2019,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),U_2019),c_COMBC(U_2020,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_prod(U_2019,U_2020)),tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),U_2019),hAPP(c_COMBB(tc_prod(U_2019,U_2020),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool),U_2020),c_member(tc_prod(U_2019,U_2020)))),c_Product__Type_OPair(U_2019,U_2020)))),U_2022))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),U_2021,U_2022) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),U_2021,U_2022)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2019,tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2019,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),U_2019),c_COMBC(U_2020,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_prod(U_2019,U_2020)),tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),U_2019),hAPP(c_COMBB(tc_prod(U_2019,U_2020),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool),U_2020),c_member(tc_prod(U_2019,U_2020)))),c_Product__Type_OPair(U_2019,U_2020)))),U_2021),hAPP(hAPP(c_COMBC(U_2019,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_fun(U_2020,tc_HOL_Obool)),U_2019),c_COMBC(U_2020,tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2020,tc_prod(U_2019,U_2020)),tc_fun(U_2020,tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool)),U_2019),hAPP(c_COMBB(tc_prod(U_2019,U_2020),tc_fun(tc_fun(tc_prod(U_2019,U_2020),tc_HOL_Obool),tc_HOL_Obool),U_2020),c_member(tc_prod(U_2019,U_2020)))),c_Product__Type_OPair(U_2019,U_2020)))),U_2022)) ) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
( ! [U_2030,U_2028,U_2026,U_2024] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2024,tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2024,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),U_2024),c_COMBC(U_2026,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_prod(U_2024,U_2026)),tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),U_2024),hAPP(c_COMBB(tc_prod(U_2024,U_2026),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool),U_2026),c_member(tc_prod(U_2024,U_2026)))),c_Product__Type_OPair(U_2024,U_2026)))),U_2028),hAPP(hAPP(c_COMBC(U_2024,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),U_2024),c_COMBC(U_2026,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_prod(U_2024,U_2026)),tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),U_2024),hAPP(c_COMBB(tc_prod(U_2024,U_2026),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool),U_2026),c_member(tc_prod(U_2024,U_2026)))),c_Product__Type_OPair(U_2024,U_2026)))),U_2030))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),U_2028,U_2030) )
& ! [U_2029,U_2027,U_2025,U_2023] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),U_2027,U_2029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2023,tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2023,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),U_2023),c_COMBC(U_2025,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_prod(U_2023,U_2025)),tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),U_2023),hAPP(c_COMBB(tc_prod(U_2023,U_2025),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool),U_2025),c_member(tc_prod(U_2023,U_2025)))),c_Product__Type_OPair(U_2023,U_2025)))),U_2027),hAPP(hAPP(c_COMBC(U_2023,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),U_2023),c_COMBC(U_2025,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_prod(U_2023,U_2025)),tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),U_2023),hAPP(c_COMBB(tc_prod(U_2023,U_2025),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool),U_2025),c_member(tc_prod(U_2023,U_2025)))),c_Product__Type_OPair(U_2023,U_2025)))),U_2029)) ) ),
inference(miniscope,[status(thm)],[f_351_2]) ).
fof(f_351_4,plain,
( ! [U_2028,U_2030,U_2024,U_2026] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2024,tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2024,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),U_2024),c_COMBC(U_2026,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_prod(U_2024,U_2026)),tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),U_2024),hAPP(c_COMBB(tc_prod(U_2024,U_2026),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool),U_2026),c_member(tc_prod(U_2024,U_2026)))),c_Product__Type_OPair(U_2024,U_2026)))),U_2028),hAPP(hAPP(c_COMBC(U_2024,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),U_2024),c_COMBC(U_2026,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_prod(U_2024,U_2026)),tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),U_2024),hAPP(c_COMBB(tc_prod(U_2024,U_2026),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool),U_2026),c_member(tc_prod(U_2024,U_2026)))),c_Product__Type_OPair(U_2024,U_2026)))),U_2030))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),U_2028,U_2030) )
& ! [U_2025,U_2023,U_2027,U_2029] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),U_2027,U_2029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2023,tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2023,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),U_2023),c_COMBC(U_2025,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_prod(U_2023,U_2025)),tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),U_2023),hAPP(c_COMBB(tc_prod(U_2023,U_2025),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool),U_2025),c_member(tc_prod(U_2023,U_2025)))),c_Product__Type_OPair(U_2023,U_2025)))),U_2027),hAPP(hAPP(c_COMBC(U_2023,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),U_2023),c_COMBC(U_2025,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_prod(U_2023,U_2025)),tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),U_2023),hAPP(c_COMBB(tc_prod(U_2023,U_2025),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool),U_2025),c_member(tc_prod(U_2023,U_2025)))),c_Product__Type_OPair(U_2023,U_2025)))),U_2029)) ) ),
inference(definitional_conversion,[status(esa)],[f_351_3]) ).
cnf(f_351_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),U_2027,U_2029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2023,tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2023,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),U_2023),c_COMBC(U_2025,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_prod(U_2023,U_2025)),tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),U_2023),hAPP(c_COMBB(tc_prod(U_2023,U_2025),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool),U_2025),c_member(tc_prod(U_2023,U_2025)))),c_Product__Type_OPair(U_2023,U_2025)))),U_2027),hAPP(hAPP(c_COMBC(U_2023,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_fun(U_2025,tc_HOL_Obool)),U_2023),c_COMBC(U_2025,tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2025,tc_prod(U_2023,U_2025)),tc_fun(U_2025,tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool)),U_2023),hAPP(c_COMBB(tc_prod(U_2023,U_2025),tc_fun(tc_fun(tc_prod(U_2023,U_2025),tc_HOL_Obool),tc_HOL_Obool),U_2025),c_member(tc_prod(U_2023,U_2025)))),c_Product__Type_OPair(U_2023,U_2025)))),U_2029)) ),
inference(clausify,[status(thm)],[f_351_4]) ).
cnf(f_351_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2024,tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2024,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),U_2024),c_COMBC(U_2026,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_prod(U_2024,U_2026)),tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),U_2024),hAPP(c_COMBB(tc_prod(U_2024,U_2026),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool),U_2026),c_member(tc_prod(U_2024,U_2026)))),c_Product__Type_OPair(U_2024,U_2026)))),U_2028),hAPP(hAPP(c_COMBC(U_2024,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_fun(U_2026,tc_HOL_Obool)),U_2024),c_COMBC(U_2026,tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2026,tc_prod(U_2024,U_2026)),tc_fun(U_2026,tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool)),U_2024),hAPP(c_COMBB(tc_prod(U_2024,U_2026),tc_fun(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),tc_HOL_Obool),U_2026),c_member(tc_prod(U_2024,U_2026)))),c_Product__Type_OPair(U_2024,U_2026)))),U_2030))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2024,U_2026),tc_HOL_Obool),U_2028,U_2030) ),
inference(clausify,[status(thm)],[f_351_4]) ).
fof(f_352_1,plain,
! [V_x_2,V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_set__mp]) ).
fof(f_352_2,plain,
! [U_2034,U_2033,U_2032,U_2031] :
( hBOOL(hAPP(hAPP(c_member(U_2031),U_2034),U_2033))
| ~ hBOOL(hAPP(hAPP(c_member(U_2031),U_2034),U_2032))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,tc_HOL_Obool),U_2032,U_2033) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
! [U_2031,U_2033,U_2034,U_2032] :
( hBOOL(hAPP(hAPP(c_member(U_2031),U_2034),U_2033))
| ~ hBOOL(hAPP(hAPP(c_member(U_2031),U_2034),U_2032))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,tc_HOL_Obool),U_2032,U_2033) ),
inference(definitional_conversion,[status(esa)],[f_352_2]) ).
cnf(f_352_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2031),U_2034),U_2033))
| ~ hBOOL(hAPP(hAPP(c_member(U_2031),U_2034),U_2032))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,tc_HOL_Obool),U_2032,U_2033) ),
inference(clausify,[status(thm)],[f_352_3]) ).
fof(f_353_1,plain,
! [V_B_2,V_A_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_set__rev__mp]) ).
fof(f_353_2,plain,
! [U_2038,U_2037,U_2036,U_2035] :
( hBOOL(hAPP(hAPP(c_member(U_2035),U_2036),U_2038))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2035,tc_HOL_Obool),U_2037,U_2038)
| ~ hBOOL(hAPP(hAPP(c_member(U_2035),U_2036),U_2037)) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
! [U_2035,U_2036,U_2037,U_2038] :
( hBOOL(hAPP(hAPP(c_member(U_2035),U_2036),U_2038))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2035,tc_HOL_Obool),U_2037,U_2038)
| ~ hBOOL(hAPP(hAPP(c_member(U_2035),U_2036),U_2037)) ),
inference(definitional_conversion,[status(esa)],[f_353_2]) ).
cnf(f_353_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2035),U_2036),U_2038))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2035,tc_HOL_Obool),U_2037,U_2038)
| ~ hBOOL(hAPP(hAPP(c_member(U_2035),U_2036),U_2037)) ),
inference(clausify,[status(thm)],[f_353_3]) ).
fof(f_354_1,plain,
! [V_x_2,V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_in__mono]) ).
fof(f_354_2,plain,
! [U_2042,U_2041,U_2040,U_2039] :
( hBOOL(hAPP(hAPP(c_member(U_2039),U_2042),U_2041))
| ~ hBOOL(hAPP(hAPP(c_member(U_2039),U_2042),U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2039,tc_HOL_Obool),U_2040,U_2041) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_2039,U_2040,U_2041,U_2042] :
( hBOOL(hAPP(hAPP(c_member(U_2039),U_2042),U_2041))
| ~ hBOOL(hAPP(hAPP(c_member(U_2039),U_2042),U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2039,tc_HOL_Obool),U_2040,U_2041) ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2039),U_2042),U_2041))
| ~ hBOOL(hAPP(hAPP(c_member(U_2039),U_2042),U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2039,tc_HOL_Obool),U_2040,U_2041) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [V_p_2,V_r_2,T_a] :
( c_Wellfounded_Owf(T_a,V_p_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_p_2,V_r_2)
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__subset]) ).
fof(f_355_2,plain,
! [U_2045,U_2044,U_2043] :
( c_Wellfounded_Owf(U_2043,U_2045)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2043,U_2043),tc_HOL_Obool),U_2045,U_2044)
| ~ c_Wellfounded_Owf(U_2043,U_2044) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
! [U_2044,U_2043,U_2045] :
( c_Wellfounded_Owf(U_2043,U_2045)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2043,U_2043),tc_HOL_Obool),U_2045,U_2044)
| ~ c_Wellfounded_Owf(U_2043,U_2044) ),
inference(definitional_conversion,[status(esa)],[f_355_2]) ).
cnf(f_355_4,plain,
( c_Wellfounded_Owf(U_2043,U_2045)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2043,U_2043),tc_HOL_Obool),U_2045,U_2044)
| ~ c_Wellfounded_Owf(U_2043,U_2044) ),
inference(clausify,[status(thm)],[f_355_3]) ).
fof(f_356_1,plain,
! [V_s_2,V_r_2,T_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_r_2),c_Relation_ODomain(T_a,T_b,V_s_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) ),
inference(fof_nnf,[status(thm)],[fact_Domain__mono]) ).
fof(f_356_2,plain,
! [U_2049,U_2048,U_2047,U_2046] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2046,tc_HOL_Obool),c_Relation_ODomain(U_2046,U_2047,U_2048),c_Relation_ODomain(U_2046,U_2047,U_2049))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2046,U_2047),tc_HOL_Obool),U_2048,U_2049) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
! [U_2046,U_2047,U_2048,U_2049] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2046,tc_HOL_Obool),c_Relation_ODomain(U_2046,U_2047,U_2048),c_Relation_ODomain(U_2046,U_2047,U_2049))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2046,U_2047),tc_HOL_Obool),U_2048,U_2049) ),
inference(definitional_conversion,[status(esa)],[f_356_2]) ).
cnf(f_356_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2046,tc_HOL_Obool),c_Relation_ODomain(U_2046,U_2047,U_2048),c_Relation_ODomain(U_2046,U_2047,U_2049))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2046,U_2047),tc_HOL_Obool),U_2048,U_2049) ),
inference(clausify,[status(thm)],[f_356_3]) ).
fof(f_357_1,plain,
! [V_R2_2,V_R1_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2) ),
inference(fof_nnf,[status(thm)],[fact_acc__subset]) ).
fof(f_357_2,plain,
! [U_2052,U_2051,U_2050] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2050,tc_HOL_Obool),c_Wellfounded_Oacc(U_2050,U_2052),c_Wellfounded_Oacc(U_2050,U_2051))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2050,U_2050),tc_HOL_Obool),U_2051,U_2052) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
! [U_2050,U_2051,U_2052] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2050,tc_HOL_Obool),c_Wellfounded_Oacc(U_2050,U_2052),c_Wellfounded_Oacc(U_2050,U_2051))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2050,U_2050),tc_HOL_Obool),U_2051,U_2052) ),
inference(definitional_conversion,[status(esa)],[f_357_2]) ).
cnf(f_357_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2050,tc_HOL_Obool),c_Wellfounded_Oacc(U_2050,U_2052),c_Wellfounded_Oacc(U_2050,U_2051))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2050,U_2050),tc_HOL_Obool),U_2051,U_2052) ),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_1,plain,
! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono]) ).
fof(f_358_2,plain,
! [U_2057,U_2056,U_2055,U_2054,U_2053] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2053,U_2056),tc_HOL_Obool),c_FuncSet_OPi(U_2053,U_2056,U_2055,U_2057),c_FuncSet_OPi(U_2053,U_2056,U_2054,U_2057))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2053,tc_HOL_Obool),U_2054,U_2055) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_2053,U_2054,U_2055,U_2056,U_2057] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2053,U_2056),tc_HOL_Obool),c_FuncSet_OPi(U_2053,U_2056,U_2055,U_2057),c_FuncSet_OPi(U_2053,U_2056,U_2054,U_2057))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2053,tc_HOL_Obool),U_2054,U_2055) ),
inference(definitional_conversion,[status(esa)],[f_358_2]) ).
cnf(f_358_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2053,U_2056),tc_HOL_Obool),c_FuncSet_OPi(U_2053,U_2056,U_2055,U_2057),c_FuncSet_OPi(U_2053,U_2056,U_2054,U_2057))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2053,tc_HOL_Obool),U_2054,U_2055) ),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_1,plain,
! [V_R2_2,V_R1_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oaccp(T_a,V_R2_2),c_Wellfounded_Oaccp(T_a,V_R1_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_R1_2,V_R2_2) ),
inference(fof_nnf,[status(thm)],[fact_accp__subset]) ).
fof(f_359_2,plain,
! [U_2060,U_2059,U_2058] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2058,tc_HOL_Obool),c_Wellfounded_Oaccp(U_2058,U_2060),c_Wellfounded_Oaccp(U_2058,U_2059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2058,tc_fun(U_2058,tc_HOL_Obool)),U_2059,U_2060) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_2058,U_2059,U_2060] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2058,tc_HOL_Obool),c_Wellfounded_Oaccp(U_2058,U_2060),c_Wellfounded_Oaccp(U_2058,U_2059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2058,tc_fun(U_2058,tc_HOL_Obool)),U_2059,U_2060) ),
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2058,tc_HOL_Obool),c_Wellfounded_Oaccp(U_2058,U_2060),c_Wellfounded_Oaccp(U_2058,U_2059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2058,tc_fun(U_2058,tc_HOL_Obool)),U_2059,U_2060) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_s_2,V_r_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__mono]) ).
fof(f_360_2,plain,
! [U_2063,U_2062,U_2061] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2061,U_2061),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2061,U_2062),c_Transitive__Closure_Ortrancl(U_2061,U_2063))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2061,U_2061),tc_HOL_Obool),U_2062,U_2063) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_2061,U_2062,U_2063] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2061,U_2061),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2061,U_2062),c_Transitive__Closure_Ortrancl(U_2061,U_2063))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2061,U_2061),tc_HOL_Obool),U_2062,U_2063) ),
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2061,U_2061),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2061,U_2062),c_Transitive__Closure_Ortrancl(U_2061,U_2063))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2061,U_2061),tc_HOL_Obool),U_2062,U_2063) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_S_2,V_R_2,T_a] :
( c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__subset]) ).
fof(f_361_2,plain,
! [U_2066,U_2065,U_2064] :
( c_Transitive__Closure_Ortrancl(U_2064,U_2066) = c_Transitive__Closure_Ortrancl(U_2064,U_2065)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2066,c_Transitive__Closure_Ortrancl(U_2064,U_2065))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2065,U_2066) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_2064,U_2065,U_2066] :
( c_Transitive__Closure_Ortrancl(U_2064,U_2066) = c_Transitive__Closure_Ortrancl(U_2064,U_2065)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2066,c_Transitive__Closure_Ortrancl(U_2064,U_2065))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2065,U_2066) ),
inference(definitional_conversion,[status(esa)],[f_361_2]) ).
cnf(f_361_4,plain,
( c_Transitive__Closure_Ortrancl(U_2064,U_2066) = c_Transitive__Closure_Ortrancl(U_2064,U_2065)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2066,c_Transitive__Closure_Ortrancl(U_2064,U_2065))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2065,U_2066) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_s_2,V_r_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl]) ).
fof(f_362_2,plain,
! [U_2069,U_2068,U_2067] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2067,U_2068),c_Transitive__Closure_Ortrancl(U_2067,U_2069))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),U_2068,c_Transitive__Closure_Ortrancl(U_2067,U_2069)) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
! [U_2067,U_2068,U_2069] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2067,U_2068),c_Transitive__Closure_Ortrancl(U_2067,U_2069))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),U_2068,c_Transitive__Closure_Ortrancl(U_2067,U_2069)) ),
inference(definitional_conversion,[status(esa)],[f_362_2]) ).
cnf(f_362_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2067,U_2068),c_Transitive__Closure_Ortrancl(U_2067,U_2069))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),U_2068,c_Transitive__Closure_Ortrancl(U_2067,U_2069)) ),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_1,plain,
! [V_s_2,V_r_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(T_a,V_r_2),c_Transitive__Closure_Ortranclp(T_a,V_s_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_r_2,V_s_2) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp__mono]) ).
fof(f_363_2,plain,
! [U_2072,U_2071,U_2070] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2070,tc_fun(U_2070,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(U_2070,U_2071),c_Transitive__Closure_Ortranclp(U_2070,U_2072))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2070,tc_fun(U_2070,tc_HOL_Obool)),U_2071,U_2072) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
! [U_2070,U_2071,U_2072] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2070,tc_fun(U_2070,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(U_2070,U_2071),c_Transitive__Closure_Ortranclp(U_2070,U_2072))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2070,tc_fun(U_2070,tc_HOL_Obool)),U_2071,U_2072) ),
inference(definitional_conversion,[status(esa)],[f_363_2]) ).
cnf(f_363_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2070,tc_fun(U_2070,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(U_2070,U_2071),c_Transitive__Closure_Ortranclp(U_2070,U_2072))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2070,tc_fun(U_2070,tc_HOL_Obool)),U_2071,U_2072) ),
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_1,plain,
! [V_S_2,V_R_2,T_a] :
( c_Transitive__Closure_Ortranclp(T_a,V_S_2) = c_Transitive__Closure_Ortranclp(T_a,V_R_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_S_2,c_Transitive__Closure_Ortranclp(T_a,V_R_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_R_2,V_S_2) ),
inference(fof_nnf,[status(thm)],[fact_rtranclp__subset]) ).
fof(f_364_2,plain,
! [U_2075,U_2074,U_2073] :
( c_Transitive__Closure_Ortranclp(U_2073,U_2075) = c_Transitive__Closure_Ortranclp(U_2073,U_2074)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2073,tc_fun(U_2073,tc_HOL_Obool)),U_2075,c_Transitive__Closure_Ortranclp(U_2073,U_2074))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2073,tc_fun(U_2073,tc_HOL_Obool)),U_2074,U_2075) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
! [U_2073,U_2074,U_2075] :
( c_Transitive__Closure_Ortranclp(U_2073,U_2075) = c_Transitive__Closure_Ortranclp(U_2073,U_2074)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2073,tc_fun(U_2073,tc_HOL_Obool)),U_2075,c_Transitive__Closure_Ortranclp(U_2073,U_2074))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2073,tc_fun(U_2073,tc_HOL_Obool)),U_2074,U_2075) ),
inference(definitional_conversion,[status(esa)],[f_364_2]) ).
cnf(f_364_4,plain,
( c_Transitive__Closure_Ortranclp(U_2073,U_2075) = c_Transitive__Closure_Ortranclp(U_2073,U_2074)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2073,tc_fun(U_2073,tc_HOL_Obool)),U_2075,c_Transitive__Closure_Ortranclp(U_2073,U_2074))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2073,tc_fun(U_2073,tc_HOL_Obool)),U_2074,U_2075) ),
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [V_B_2,V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Int__lower1]) ).
fof(f_365_2,plain,
! [U_2078,U_2077,U_2076] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2076,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2076,tc_HOL_Obool),U_2077,U_2078),U_2077),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
! [U_2077,U_2078,U_2076] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2076,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2076,tc_HOL_Obool),U_2077,U_2078),U_2077),
inference(definitional_conversion,[status(esa)],[f_365_2]) ).
cnf(f_365_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2076,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2076,tc_HOL_Obool),U_2077,U_2078),U_2077),
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [V_B_2,V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Int__lower2]) ).
fof(f_366_2,plain,
! [U_2081,U_2080,U_2079] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2079,tc_HOL_Obool),U_2080,U_2081),U_2081),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
! [U_2079,U_2080,U_2081] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2079,tc_HOL_Obool),U_2080,U_2081),U_2081),
inference(definitional_conversion,[status(esa)],[f_366_2]) ).
cnf(f_366_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2079,tc_HOL_Obool),U_2080,U_2081),U_2081),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [V_B_2,V_A_2,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_A_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb2]) ).
fof(f_367_2,plain,
! [U_2084,U_2083,U_2082] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2082,tc_HOL_Obool),U_2083,U_2084) = U_2083
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2082,tc_HOL_Obool),U_2083,U_2084) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_2083,U_2082,U_2084] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2082,tc_HOL_Obool),U_2083,U_2084) = U_2083
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2082,tc_HOL_Obool),U_2083,U_2084) ),
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2082,tc_HOL_Obool),U_2083,U_2084) = U_2083
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2082,tc_HOL_Obool),U_2083,U_2084) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [V_A_2,V_B_2,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb1]) ).
fof(f_368_2,plain,
! [U_2087,U_2086,U_2085] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2085,tc_HOL_Obool),U_2087,U_2086) = U_2086
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2085,tc_HOL_Obool),U_2086,U_2087) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_2085,U_2086,U_2087] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2085,tc_HOL_Obool),U_2087,U_2086) = U_2086
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2085,tc_HOL_Obool),U_2086,U_2087) ),
inference(definitional_conversion,[status(esa)],[f_368_2]) ).
cnf(f_368_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2085,tc_HOL_Obool),U_2087,U_2086) = U_2086
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2085,tc_HOL_Obool),U_2086,U_2087) ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_1,plain,
! [V_B_2,V_A_2,V_C_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Int__greatest]) ).
fof(f_369_2,plain,
! [U_2091,U_2090,U_2089,U_2088] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2088,tc_HOL_Obool),U_2090,U_2091))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2091)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2090) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
! [U_2088,U_2089,U_2090,U_2091] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2088,tc_HOL_Obool),U_2090,U_2091))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2091)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2090) ),
inference(definitional_conversion,[status(esa)],[f_369_2]) ).
cnf(f_369_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2088,tc_HOL_Obool),U_2090,U_2091))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2091)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2090) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_1,plain,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) ),
inference(fof_nnf,[status(thm)],[fact_Int__mono]) ).
fof(f_370_2,plain,
! [U_2096,U_2095,U_2094,U_2093,U_2092] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool),U_2093,U_2095),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool),U_2094,U_2096))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),U_2095,U_2096)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),U_2093,U_2094) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
! [U_2094,U_2093,U_2092,U_2095,U_2096] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool),U_2093,U_2095),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool),U_2094,U_2096))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),U_2095,U_2096)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),U_2093,U_2094) ),
inference(definitional_conversion,[status(esa)],[f_370_2]) ).
cnf(f_370_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool),U_2093,U_2095),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool),U_2094,U_2096))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),U_2095,U_2096)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2092,tc_HOL_Obool),U_2093,U_2094) ),
inference(clausify,[status(thm)],[f_370_3]) ).
fof(f_371_1,plain,
! [V_s_2,V_r_2,T_b,T_a] :
( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
| ~ c_Relation_Osingle__valued(T_a,T_b,V_s_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__subset]) ).
fof(f_371_2,plain,
! [U_2100,U_2099,U_2098,U_2097] :
( c_Relation_Osingle__valued(U_2097,U_2098,U_2099)
| ~ c_Relation_Osingle__valued(U_2097,U_2098,U_2100)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2097,U_2098),tc_HOL_Obool),U_2099,U_2100) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
! [U_2098,U_2097,U_2099,U_2100] :
( c_Relation_Osingle__valued(U_2097,U_2098,U_2099)
| ~ c_Relation_Osingle__valued(U_2097,U_2098,U_2100)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2097,U_2098),tc_HOL_Obool),U_2099,U_2100) ),
inference(definitional_conversion,[status(esa)],[f_371_2]) ).
cnf(f_371_4,plain,
( c_Relation_Osingle__valued(U_2097,U_2098,U_2099)
| ~ c_Relation_Osingle__valued(U_2097,U_2098,U_2100)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2097,U_2098),tc_HOL_Obool),U_2099,U_2100) ),
inference(clausify,[status(thm)],[f_371_3]) ).
fof(f_372_1,plain,
! [V_r_2,V_s_2,T_a] :
( c_Wellfounded_Oacyclic(T_a,V_r_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)
| ~ c_Wellfounded_Oacyclic(T_a,V_s_2) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__subset]) ).
fof(f_372_2,plain,
! [U_2103,U_2102,U_2101] :
( c_Wellfounded_Oacyclic(U_2101,U_2103)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2101,U_2101),tc_HOL_Obool),U_2103,U_2102)
| ~ c_Wellfounded_Oacyclic(U_2101,U_2102) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
! [U_2103,U_2102,U_2101] :
( c_Wellfounded_Oacyclic(U_2101,U_2103)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2101,U_2101),tc_HOL_Obool),U_2103,U_2102)
| ~ c_Wellfounded_Oacyclic(U_2101,U_2102) ),
inference(definitional_conversion,[status(esa)],[f_372_2]) ).
cnf(f_372_4,plain,
( c_Wellfounded_Oacyclic(U_2101,U_2103)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2101,U_2101),tc_HOL_Obool),U_2103,U_2102)
| ~ c_Wellfounded_Oacyclic(U_2101,U_2102) ),
inference(clausify,[status(thm)],[f_372_3]) ).
fof(f_373_1,plain,
! [V_s_2,V_r_2,T_a] :
( c_Relation_Oantisym(T_a,V_r_2)
| ~ c_Relation_Oantisym(T_a,V_s_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) ),
inference(fof_nnf,[status(thm)],[fact_antisym__subset]) ).
fof(f_373_2,plain,
! [U_2106,U_2105,U_2104] :
( c_Relation_Oantisym(U_2104,U_2105)
| ~ c_Relation_Oantisym(U_2104,U_2106)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2104,U_2104),tc_HOL_Obool),U_2105,U_2106) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
! [U_2104,U_2105,U_2106] :
( c_Relation_Oantisym(U_2104,U_2105)
| ~ c_Relation_Oantisym(U_2104,U_2106)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2104,U_2104),tc_HOL_Obool),U_2105,U_2106) ),
inference(definitional_conversion,[status(esa)],[f_373_2]) ).
cnf(f_373_4,plain,
( c_Relation_Oantisym(U_2104,U_2105)
| ~ c_Relation_Oantisym(U_2104,U_2106)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2104,U_2104),tc_HOL_Obool),U_2105,U_2106) ),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_1,plain,
! [V_aa_2,V_D_2,V_C_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2),c_Set_Oinsert(T_a,V_aa_2,V_D_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2) ),
inference(fof_nnf,[status(thm)],[fact_insert__mono]) ).
fof(f_374_2,plain,
! [U_2110,U_2109,U_2108,U_2107] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2107,tc_HOL_Obool),c_Set_Oinsert(U_2107,U_2110,U_2108),c_Set_Oinsert(U_2107,U_2110,U_2109))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2107,tc_HOL_Obool),U_2108,U_2109) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
! [U_2108,U_2107,U_2109,U_2110] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2107,tc_HOL_Obool),c_Set_Oinsert(U_2107,U_2110,U_2108),c_Set_Oinsert(U_2107,U_2110,U_2109))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2107,tc_HOL_Obool),U_2108,U_2109) ),
inference(definitional_conversion,[status(esa)],[f_374_2]) ).
cnf(f_374_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2107,tc_HOL_Obool),c_Set_Oinsert(U_2107,U_2110,U_2108),c_Set_Oinsert(U_2107,U_2110,U_2109))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2107,tc_HOL_Obool),U_2108,U_2109) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
! [V_ba_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_ba_2,V_B_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_subset__insertI2]) ).
fof(f_375_2,plain,
! [U_2114,U_2113,U_2112,U_2111] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2111,tc_HOL_Obool),U_2112,c_Set_Oinsert(U_2111,U_2114,U_2113))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2111,tc_HOL_Obool),U_2112,U_2113) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
! [U_2112,U_2111,U_2113,U_2114] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2111,tc_HOL_Obool),U_2112,c_Set_Oinsert(U_2111,U_2114,U_2113))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2111,tc_HOL_Obool),U_2112,U_2113) ),
inference(definitional_conversion,[status(esa)],[f_375_2]) ).
cnf(f_375_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2111,tc_HOL_Obool),U_2112,c_Set_Oinsert(U_2111,U_2114,U_2113))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2111,tc_HOL_Obool),U_2112,U_2113) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_1,plain,
! [V_aa_2,V_B_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)),
inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).
fof(f_376_2,plain,
! [U_2117,U_2116,U_2115] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2115,tc_HOL_Obool),U_2116,c_Set_Oinsert(U_2115,U_2117,U_2116)),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
! [U_2115,U_2116,U_2117] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2115,tc_HOL_Obool),U_2116,c_Set_Oinsert(U_2115,U_2117,U_2116)),
inference(definitional_conversion,[status(esa)],[f_376_2]) ).
cnf(f_376_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2115,tc_HOL_Obool),U_2116,c_Set_Oinsert(U_2115,U_2117,U_2116)),
inference(clausify,[status(thm)],[f_376_3]) ).
fof(f_377_1,plain,
! [V_p_2,V_r_2,T_a] :
( c_Wellfounded_OwfP(T_a,V_p_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_p_2,V_r_2)
| ~ c_Wellfounded_OwfP(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wfP__subset]) ).
fof(f_377_2,plain,
! [U_2120,U_2119,U_2118] :
( c_Wellfounded_OwfP(U_2118,U_2120)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2118,tc_fun(U_2118,tc_HOL_Obool)),U_2120,U_2119)
| ~ c_Wellfounded_OwfP(U_2118,U_2119) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
! [U_2118,U_2119,U_2120] :
( c_Wellfounded_OwfP(U_2118,U_2120)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2118,tc_fun(U_2118,tc_HOL_Obool)),U_2120,U_2119)
| ~ c_Wellfounded_OwfP(U_2118,U_2119) ),
inference(definitional_conversion,[status(esa)],[f_377_2]) ).
cnf(f_377_4,plain,
( c_Wellfounded_OwfP(U_2118,U_2120)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2118,tc_fun(U_2118,tc_HOL_Obool)),U_2120,U_2119)
| ~ c_Wellfounded_OwfP(U_2118,U_2119) ),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_1,plain,
! [V_B_2,V_A_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2)) ) )
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__insert]) ).
fof(f_378_2,plain,
! [U_2124,U_2123,U_2122,U_2121] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,c_Set_Oinsert(U_2121,U_2122,U_2124))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,U_2124) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,U_2124)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,c_Set_Oinsert(U_2121,U_2122,U_2124)) ) )
| hBOOL(hAPP(hAPP(c_member(U_2121),U_2122),U_2123)) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
( ! [U_2121,U_2122,U_2123,U_2124] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,c_Set_Oinsert(U_2121,U_2122,U_2124))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,U_2124)
| ~ sP115(U_2121,U_2122,U_2123,U_2124) )
& ! [U_2121,U_2122,U_2123,U_2124] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,U_2124)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,c_Set_Oinsert(U_2121,U_2122,U_2124))
| ~ sP115(U_2121,U_2122,U_2123,U_2124) )
& ! [U_2121,U_2122,U_2123,U_2124] :
( sP115(U_2121,U_2122,U_2123,U_2124)
| hBOOL(hAPP(hAPP(c_member(U_2121),U_2122),U_2123)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_378_2]) ).
cnf(f_378_4,plain,
( sP115(U_2121,U_2122,U_2123,U_2124)
| hBOOL(hAPP(hAPP(c_member(U_2121),U_2122),U_2123)) ),
inference(clausify,[status(thm)],[f_378_3]) ).
cnf(f_378_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,U_2124)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,c_Set_Oinsert(U_2121,U_2122,U_2124))
| ~ sP115(U_2121,U_2122,U_2123,U_2124) ),
inference(clausify,[status(thm)],[f_378_3]) ).
cnf(f_378_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,c_Set_Oinsert(U_2121,U_2122,U_2124))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2121,tc_HOL_Obool),U_2123,U_2124)
| ~ sP115(U_2121,U_2122,U_2123,U_2124) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [V_B_2,V_A_2,V_x_2,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
& hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__subset]) ).
fof(f_379_2,plain,
! [U_2128,U_2127,U_2126,U_2125] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2125,tc_HOL_Obool),c_Set_Oinsert(U_2125,U_2126,U_2127),U_2128)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2125,tc_HOL_Obool),U_2127,U_2128)
| ~ hBOOL(hAPP(hAPP(c_member(U_2125),U_2126),U_2128)) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2125,tc_HOL_Obool),U_2127,U_2128)
& hBOOL(hAPP(hAPP(c_member(U_2125),U_2126),U_2128)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2125,tc_HOL_Obool),c_Set_Oinsert(U_2125,U_2126,U_2127),U_2128) ) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
( ! [U_2136,U_2134,U_2132,U_2130] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2130,tc_HOL_Obool),c_Set_Oinsert(U_2130,U_2132,U_2134),U_2136)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2130,tc_HOL_Obool),U_2134,U_2136)
| ~ hBOOL(hAPP(hAPP(c_member(U_2130),U_2132),U_2136)) )
& ! [U_2135,U_2133,U_2131,U_2129] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2129,tc_HOL_Obool),U_2133,U_2135)
& hBOOL(hAPP(hAPP(c_member(U_2129),U_2131),U_2135)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2129,tc_HOL_Obool),c_Set_Oinsert(U_2129,U_2131,U_2133),U_2135) ) ),
inference(miniscope,[status(thm)],[f_379_2]) ).
fof(f_379_4,plain,
( ! [U_2129,U_2135,U_2131,U_2133] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2129,tc_HOL_Obool),U_2133,U_2135)
| ~ sP116(U_2129,U_2135,U_2131,U_2133) )
& ! [U_2129,U_2135,U_2131,U_2133] :
( hBOOL(hAPP(hAPP(c_member(U_2129),U_2131),U_2135))
| ~ sP116(U_2129,U_2135,U_2131,U_2133) )
& ! [U_2134,U_2130,U_2132,U_2136] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2130,tc_HOL_Obool),c_Set_Oinsert(U_2130,U_2132,U_2134),U_2136)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2130,tc_HOL_Obool),U_2134,U_2136)
| ~ hBOOL(hAPP(hAPP(c_member(U_2130),U_2132),U_2136)) )
& ! [U_2129,U_2135,U_2131,U_2133] :
( sP116(U_2129,U_2135,U_2131,U_2133)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2129,tc_HOL_Obool),c_Set_Oinsert(U_2129,U_2131,U_2133),U_2135) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_379_3]) ).
cnf(f_379_5,plain,
( sP116(U_2129,U_2135,U_2131,U_2133)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2129,tc_HOL_Obool),c_Set_Oinsert(U_2129,U_2131,U_2133),U_2135) ),
inference(clausify,[status(thm)],[f_379_4]) ).
cnf(f_379_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2130,tc_HOL_Obool),c_Set_Oinsert(U_2130,U_2132,U_2134),U_2136)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2130,tc_HOL_Obool),U_2134,U_2136)
| ~ hBOOL(hAPP(hAPP(c_member(U_2130),U_2132),U_2136)) ),
inference(clausify,[status(thm)],[f_379_4]) ).
cnf(f_379_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_2129),U_2131),U_2135))
| ~ sP116(U_2129,U_2135,U_2131,U_2133) ),
inference(clausify,[status(thm)],[f_379_4]) ).
cnf(f_379_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2129,tc_HOL_Obool),U_2133,U_2135)
| ~ sP116(U_2129,U_2135,U_2131,U_2133) ),
inference(clausify,[status(thm)],[f_379_4]) ).
fof(f_380_1,plain,
! [V_s_2,V_r_2,V_p_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__mono]) ).
fof(f_380_2,plain,
! [U_2140,U_2139,U_2138,U_2137] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2137,U_2137)),U_2138),c_Transitive__Closure_Otrancl(U_2137,U_2140)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2137,U_2137),tc_HOL_Obool),U_2139,U_2140)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2137,U_2137)),U_2138),c_Transitive__Closure_Otrancl(U_2137,U_2139))) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
! [U_2137,U_2140,U_2139,U_2138] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2137,U_2137)),U_2138),c_Transitive__Closure_Otrancl(U_2137,U_2140)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2137,U_2137),tc_HOL_Obool),U_2139,U_2140)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2137,U_2137)),U_2138),c_Transitive__Closure_Otrancl(U_2137,U_2139))) ),
inference(definitional_conversion,[status(esa)],[f_380_2]) ).
cnf(f_380_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2137,U_2137)),U_2138),c_Transitive__Closure_Otrancl(U_2137,U_2140)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2137,U_2137),tc_HOL_Obool),U_2139,U_2140)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2137,U_2137)),U_2138),c_Transitive__Closure_Otrancl(U_2137,U_2139))) ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_B_2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_extensional__subset]) ).
fof(f_381_2,plain,
! [U_2145,U_2144,U_2143,U_2142,U_2141] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2141,U_2142)),U_2143),c_FuncSet_Oextensional(U_2141,U_2142,U_2145)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2141,tc_HOL_Obool),U_2144,U_2145)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2141,U_2142)),U_2143),c_FuncSet_Oextensional(U_2141,U_2142,U_2144))) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
! [U_2141,U_2142,U_2143,U_2144,U_2145] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2141,U_2142)),U_2143),c_FuncSet_Oextensional(U_2141,U_2142,U_2145)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2141,tc_HOL_Obool),U_2144,U_2145)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2141,U_2142)),U_2143),c_FuncSet_Oextensional(U_2141,U_2142,U_2144))) ),
inference(definitional_conversion,[status(esa)],[f_381_2]) ).
cnf(f_381_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2141,U_2142)),U_2143),c_FuncSet_Oextensional(U_2141,U_2142,U_2145)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2141,tc_HOL_Obool),U_2144,U_2145)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2141,U_2142)),U_2143),c_FuncSet_Oextensional(U_2141,U_2142,U_2144))) ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_1,plain,
! [V_B_2,V_A_2,T_b,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Domain__Int__subset]) ).
fof(f_382_2,plain,
! [U_2149,U_2148,U_2147,U_2146] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2146,tc_HOL_Obool),c_Relation_ODomain(U_2146,U_2147,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2146,U_2147),tc_HOL_Obool),U_2148,U_2149)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2146,tc_HOL_Obool),c_Relation_ODomain(U_2146,U_2147,U_2148),c_Relation_ODomain(U_2146,U_2147,U_2149))),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_2146,U_2147,U_2148,U_2149] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2146,tc_HOL_Obool),c_Relation_ODomain(U_2146,U_2147,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2146,U_2147),tc_HOL_Obool),U_2148,U_2149)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2146,tc_HOL_Obool),c_Relation_ODomain(U_2146,U_2147,U_2148),c_Relation_ODomain(U_2146,U_2147,U_2149))),
inference(definitional_conversion,[status(esa)],[f_382_2]) ).
cnf(f_382_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2146,tc_HOL_Obool),c_Relation_ODomain(U_2146,U_2147,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2146,U_2147),tc_HOL_Obool),U_2148,U_2149)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2146,tc_HOL_Obool),c_Relation_ODomain(U_2146,U_2147,U_2148),c_Relation_ODomain(U_2146,U_2147,U_2149))),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_1,plain,
! [V_B_2,V_A_2,T_b,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Range__Int__subset]) ).
fof(f_383_2,plain,
! [U_2153,U_2152,U_2151,U_2150] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2150,tc_HOL_Obool),c_Relation_ORange(U_2151,U_2150,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2151,U_2150),tc_HOL_Obool),U_2152,U_2153)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2150,tc_HOL_Obool),c_Relation_ORange(U_2151,U_2150,U_2152),c_Relation_ORange(U_2151,U_2150,U_2153))),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_2151,U_2150,U_2152,U_2153] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2150,tc_HOL_Obool),c_Relation_ORange(U_2151,U_2150,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2151,U_2150),tc_HOL_Obool),U_2152,U_2153)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2150,tc_HOL_Obool),c_Relation_ORange(U_2151,U_2150,U_2152),c_Relation_ORange(U_2151,U_2150,U_2153))),
inference(definitional_conversion,[status(esa)],[f_383_2]) ).
cnf(f_383_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2150,tc_HOL_Obool),c_Relation_ORange(U_2151,U_2150,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2151,U_2150),tc_HOL_Obool),U_2152,U_2153)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2150,tc_HOL_Obool),c_Relation_ORange(U_2151,U_2150,U_2152),c_Relation_ORange(U_2151,U_2150,U_2153))),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_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)),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_384_2,plain,
! [U_2157,U_2156,U_2155,U_2154] :
( 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_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2156,U_2157)),U_2155)),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_2157),U_2155)),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_2156),U_2154)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2154),U_2155)) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
! [U_2154,U_2155,U_2156,U_2157] :
( 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_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2156,U_2157)),U_2155)),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_2157),U_2155)),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_2156),U_2154)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2154),U_2155)) ),
inference(definitional_conversion,[status(esa)],[f_384_2]) ).
cnf(f_384_4,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_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2156,U_2157)),U_2155)),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_2157),U_2155)),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_2156),U_2154)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2154),U_2155)) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_1,plain,
! [V_x,T_a] :
( 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_385_2,plain,
! [U_2159,U_2158] :
( c_Orderings_Oord__class_Oless__eq(U_2158,U_2159,U_2159)
| ~ class_Orderings_Opreorder(U_2158) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
! [U_2159,U_2158] :
( c_Orderings_Oord__class_Oless__eq(U_2158,U_2159,U_2159)
| ~ class_Orderings_Opreorder(U_2158) ),
inference(definitional_conversion,[status(esa)],[f_385_2]) ).
cnf(f_385_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2158,U_2159,U_2159)
| ~ class_Orderings_Opreorder(U_2158) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_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]) ).
fof(f_386_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(definitional_conversion,[status(esa)],[f_386_1]) ).
cnf(f_386_3,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_386_2]) ).
fof(f_387_1,plain,
! [V_B_2,V_A_2,T_a] :
( V_A_2 = V_B_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_equalityI]) ).
fof(f_387_2,plain,
! [U_2162,U_2161,U_2160] :
( U_2161 = U_2162
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool),U_2162,U_2161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool),U_2161,U_2162) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
! [U_2160,U_2161,U_2162] :
( U_2161 = U_2162
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool),U_2162,U_2161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool),U_2161,U_2162) ),
inference(definitional_conversion,[status(esa)],[f_387_2]) ).
cnf(f_387_4,plain,
( U_2161 = U_2162
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool),U_2162,U_2161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool),U_2161,U_2162) ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_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]) ).
fof(f_388_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(definitional_conversion,[status(esa)],[f_388_1]) ).
cnf(f_388_3,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_388_2]) ).
fof(f_389_1,plain,
! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2,V_Q_2)
| ~ hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).
fof(f_389_2,plain,
! [U_2168,U_2167,U_2166,U_2165,U_2164,U_2163] :
( hBOOL(hAPP(hAPP(U_2168,U_2164),U_2165))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2166,tc_fun(U_2167,tc_HOL_Obool)),U_2163,U_2168)
| ~ hBOOL(hAPP(hAPP(U_2163,U_2164),U_2165)) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
! [U_2164,U_2163,U_2165,U_2166,U_2167,U_2168] :
( hBOOL(hAPP(hAPP(U_2168,U_2164),U_2165))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2166,tc_fun(U_2167,tc_HOL_Obool)),U_2163,U_2168)
| ~ hBOOL(hAPP(hAPP(U_2163,U_2164),U_2165)) ),
inference(definitional_conversion,[status(esa)],[f_389_2]) ).
cnf(f_389_4,plain,
( hBOOL(hAPP(hAPP(U_2168,U_2164),U_2165))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2166,tc_fun(U_2167,tc_HOL_Obool)),U_2163,U_2168)
| ~ hBOOL(hAPP(hAPP(U_2163,U_2164),U_2165)) ),
inference(clausify,[status(thm)],[f_389_3]) ).
fof(f_390_1,plain,
! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2,V_Q_2) ),
inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).
fof(f_390_2,plain,
! [U_2174,U_2173,U_2172,U_2171,U_2170,U_2169] :
( hBOOL(hAPP(hAPP(U_2172,U_2173),U_2174))
| ~ hBOOL(hAPP(hAPP(U_2171,U_2173),U_2174))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2169,tc_fun(U_2170,tc_HOL_Obool)),U_2171,U_2172) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
! [U_2174,U_2173,U_2172,U_2171] :
( ! [U_2170,U_2169] : ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2169,tc_fun(U_2170,tc_HOL_Obool)),U_2171,U_2172)
| hBOOL(hAPP(hAPP(U_2172,U_2173),U_2174))
| ~ hBOOL(hAPP(hAPP(U_2171,U_2173),U_2174)) ),
inference(miniscope,[status(thm)],[f_390_2]) ).
fof(f_390_4,plain,
! [U_2171,U_2170,U_2169,U_2172,U_2173,U_2174] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2169,tc_fun(U_2170,tc_HOL_Obool)),U_2171,U_2172)
| hBOOL(hAPP(hAPP(U_2172,U_2173),U_2174))
| ~ hBOOL(hAPP(hAPP(U_2171,U_2173),U_2174)) ),
inference(definitional_conversion,[status(esa)],[f_390_3]) ).
cnf(f_390_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2169,tc_fun(U_2170,tc_HOL_Obool)),U_2171,U_2172)
| hBOOL(hAPP(hAPP(U_2172,U_2173),U_2174))
| ~ hBOOL(hAPP(hAPP(U_2171,U_2173),U_2174)) ),
inference(clausify,[status(thm)],[f_390_4]) ).
fof(f_391_1,plain,
! [V_x_2,V_Q_2,V_Pa_2,T_a] :
( hBOOL(hAPP(V_Q_2,V_x_2))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2) ),
inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).
fof(f_391_2,plain,
! [U_2178,U_2177,U_2176,U_2175] :
( hBOOL(hAPP(U_2177,U_2178))
| ~ hBOOL(hAPP(U_2176,U_2178))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2175,tc_HOL_Obool),U_2176,U_2177) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_2178,U_2177,U_2176] :
( ! [U_2175] : ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2175,tc_HOL_Obool),U_2176,U_2177)
| hBOOL(hAPP(U_2177,U_2178))
| ~ hBOOL(hAPP(U_2176,U_2178)) ),
inference(miniscope,[status(thm)],[f_391_2]) ).
fof(f_391_4,plain,
! [U_2177,U_2176,U_2175,U_2178] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2175,tc_HOL_Obool),U_2176,U_2177)
| hBOOL(hAPP(U_2177,U_2178))
| ~ hBOOL(hAPP(U_2176,U_2178)) ),
inference(definitional_conversion,[status(esa)],[f_391_3]) ).
cnf(f_391_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2175,tc_HOL_Obool),U_2176,U_2177)
| hBOOL(hAPP(U_2177,U_2178))
| ~ hBOOL(hAPP(U_2176,U_2178)) ),
inference(clausify,[status(thm)],[f_391_4]) ).
fof(f_392_1,plain,
! [V_Q_2,T_a,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Q_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2)
| ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).
fof(f_392_2,plain,
! [U_2182,U_2181,U_2180,U_2179] :
( hBOOL(hAPP(U_2182,U_2180))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2181,tc_HOL_Obool),U_2179,U_2182)
| ~ hBOOL(hAPP(U_2179,U_2180)) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
! [U_2180,U_2179,U_2181,U_2182] :
( hBOOL(hAPP(U_2182,U_2180))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2181,tc_HOL_Obool),U_2179,U_2182)
| ~ hBOOL(hAPP(U_2179,U_2180)) ),
inference(definitional_conversion,[status(esa)],[f_392_2]) ).
cnf(f_392_4,plain,
( hBOOL(hAPP(U_2182,U_2180))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2181,tc_HOL_Obool),U_2179,U_2182)
| ~ hBOOL(hAPP(U_2179,U_2180)) ),
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_1,plain,
! [T_a,V_B_2,V_A_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityE]) ).
fof(f_393_2,plain,
! [U_2185,U_2184,U_2183] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2185,tc_HOL_Obool),U_2184,U_2183)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2185,tc_HOL_Obool),U_2183,U_2184) )
| U_2183 != U_2184 ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
( ! [U_2183,U_2185,U_2184] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2185,tc_HOL_Obool),U_2184,U_2183)
| ~ sP117(U_2183,U_2185,U_2184) )
& ! [U_2183,U_2185,U_2184] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2185,tc_HOL_Obool),U_2183,U_2184)
| ~ sP117(U_2183,U_2185,U_2184) )
& ! [U_2183,U_2185,U_2184] :
( sP117(U_2183,U_2185,U_2184)
| U_2183 != U_2184 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_393_2]) ).
cnf(f_393_4,plain,
( sP117(U_2183,U_2185,U_2184)
| U_2183 != U_2184 ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2185,tc_HOL_Obool),U_2183,U_2184)
| ~ sP117(U_2183,U_2185,U_2184) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2185,tc_HOL_Obool),U_2184,U_2183)
| ~ sP117(U_2183,U_2185,U_2184) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_1,plain,
! [V_C_2,V_B_2,V_A_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_subset__trans]) ).
fof(f_394_2,plain,
! [U_2189,U_2188,U_2187,U_2186] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2187,U_2189)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2188,U_2189)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2187,U_2188) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_2186,U_2187,U_2189,U_2188] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2187,U_2189)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2188,U_2189)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2187,U_2188) ),
inference(definitional_conversion,[status(esa)],[f_394_2]) ).
cnf(f_394_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2187,U_2189)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2188,U_2189)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2186,tc_HOL_Obool),U_2187,U_2188) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_1,plain,
! [T_a,V_B_2,V_A_2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD2]) ).
fof(f_395_2,plain,
! [U_2192,U_2191,U_2190] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2192,tc_HOL_Obool),U_2191,U_2190)
| U_2190 != U_2191 ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_2190,U_2192,U_2191] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2192,tc_HOL_Obool),U_2191,U_2190)
| U_2190 != U_2191 ),
inference(definitional_conversion,[status(esa)],[f_395_2]) ).
cnf(f_395_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2192,tc_HOL_Obool),U_2191,U_2190)
| U_2190 != U_2191 ),
inference(clausify,[status(thm)],[f_395_3]) ).
fof(f_396_1,plain,
! [T_a,V_B_2,V_A_2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD1]) ).
fof(f_396_2,plain,
! [U_2195,U_2194,U_2193] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2195,tc_HOL_Obool),U_2193,U_2194)
| U_2193 != U_2194 ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
! [U_2193,U_2194,U_2195] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2195,tc_HOL_Obool),U_2193,U_2194)
| U_2193 != U_2194 ),
inference(definitional_conversion,[status(esa)],[f_396_2]) ).
cnf(f_396_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2195,tc_HOL_Obool),U_2193,U_2194)
| U_2193 != U_2194 ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [T_a,V_B_2,V_A_2] :
( ( V_A_2 = V_B_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_397_2,plain,
! [U_2198,U_2197,U_2196] :
( ( U_2196 = U_2197
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2198,tc_HOL_Obool),U_2197,U_2196)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2198,tc_HOL_Obool),U_2196,U_2197) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2198,tc_HOL_Obool),U_2197,U_2196)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2198,tc_HOL_Obool),U_2196,U_2197) )
| U_2196 != U_2197 ) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
( ! [U_2204,U_2202,U_2200] :
( U_2200 = U_2202
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2204,tc_HOL_Obool),U_2202,U_2200)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2204,tc_HOL_Obool),U_2200,U_2202) )
& ! [U_2203,U_2201,U_2199] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool),U_2201,U_2199)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool),U_2199,U_2201) )
| U_2199 != U_2201 ) ),
inference(miniscope,[status(thm)],[f_397_2]) ).
fof(f_397_4,plain,
( ! [U_2201,U_2199,U_2203] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool),U_2201,U_2199)
| ~ sP118(U_2201,U_2199,U_2203) )
& ! [U_2201,U_2199,U_2203] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool),U_2199,U_2201)
| ~ sP118(U_2201,U_2199,U_2203) )
& ! [U_2202,U_2204,U_2200] :
( U_2200 = U_2202
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2204,tc_HOL_Obool),U_2202,U_2200)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2204,tc_HOL_Obool),U_2200,U_2202) )
& ! [U_2201,U_2199,U_2203] :
( sP118(U_2201,U_2199,U_2203)
| U_2199 != U_2201 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_397_3]) ).
cnf(f_397_5,plain,
( sP118(U_2201,U_2199,U_2203)
| U_2199 != U_2201 ),
inference(clausify,[status(thm)],[f_397_4]) ).
cnf(f_397_6,plain,
( U_2200 = U_2202
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2204,tc_HOL_Obool),U_2202,U_2200)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2204,tc_HOL_Obool),U_2200,U_2202) ),
inference(clausify,[status(thm)],[f_397_4]) ).
cnf(f_397_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool),U_2199,U_2201)
| ~ sP118(U_2201,U_2199,U_2203) ),
inference(clausify,[status(thm)],[f_397_4]) ).
cnf(f_397_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool),U_2201,U_2199)
| ~ sP118(U_2201,U_2199,U_2203) ),
inference(clausify,[status(thm)],[f_397_4]) ).
fof(f_398_1,plain,
! [V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2),
inference(fof_nnf,[status(thm)],[fact_subset__refl]) ).
fof(f_398_2,plain,
! [U_2206,U_2205] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2205,tc_HOL_Obool),U_2206,U_2206),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
! [U_2205,U_2206] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2205,tc_HOL_Obool),U_2206,U_2206),
inference(definitional_conversion,[status(esa)],[f_398_2]) ).
cnf(f_398_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2205,tc_HOL_Obool),U_2206,U_2206),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ? [B_x] : ~ c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) )
& ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_399_2,plain,
! [U_2212,U_2211,U_2210,U_2209] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212)
| ? [U_2208] : ~ c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,U_2208),hAPP(U_2212,U_2208)) )
& ( ! [U_2207] : c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,U_2207),hAPP(U_2212,U_2207))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212) ) )
| ~ class_Orderings_Oord(U_2209) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_2212,U_2211,U_2210,U_2209] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212)
| ~ c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,sK101(U_2212,U_2211,U_2210,U_2209)),hAPP(U_2212,sK101(U_2212,U_2211,U_2210,U_2209))) )
& ( ! [U_2207] : c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,U_2207),hAPP(U_2212,U_2207))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212) ) )
| ~ class_Orderings_Oord(U_2209) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_2208,sK101(U_2212,U_2211,U_2210,U_2209))],[f_399_2]) ).
fof(f_399_4,plain,
( ! [U_2207,U_2209,U_2210,U_2211,U_2212] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212)
| ~ c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,sK101(U_2212,U_2211,U_2210,U_2209)),hAPP(U_2212,sK101(U_2212,U_2211,U_2210,U_2209)))
| ~ sP119(U_2207,U_2209,U_2210,U_2211,U_2212) )
& ! [U_2207,U_2209,U_2210,U_2211,U_2212] :
( c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,U_2207),hAPP(U_2212,U_2207))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212)
| ~ sP119(U_2207,U_2209,U_2210,U_2211,U_2212) )
& ! [U_2207,U_2209,U_2210,U_2211,U_2212] :
( sP119(U_2207,U_2209,U_2210,U_2211,U_2212)
| ~ class_Orderings_Oord(U_2209) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_399_3]) ).
cnf(f_399_5,plain,
( sP119(U_2207,U_2209,U_2210,U_2211,U_2212)
| ~ class_Orderings_Oord(U_2209) ),
inference(clausify,[status(thm)],[f_399_4]) ).
cnf(f_399_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,U_2207),hAPP(U_2212,U_2207))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212)
| ~ sP119(U_2207,U_2209,U_2210,U_2211,U_2212) ),
inference(clausify,[status(thm)],[f_399_4]) ).
cnf(f_399_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2210,U_2209),U_2211,U_2212)
| ~ c_Orderings_Oord__class_Oless__eq(U_2209,hAPP(U_2211,sK101(U_2212,U_2211,U_2210,U_2209)),hAPP(U_2212,sK101(U_2212,U_2211,U_2210,U_2209)))
| ~ sP119(U_2207,U_2209,U_2210,U_2211,U_2212) ),
inference(clausify,[status(thm)],[f_399_4]) ).
fof(f_400_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| 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_400_2,plain,
! [U_2215,U_2214,U_2213] :
( c_Orderings_Oord__class_Oless__eq(U_2213,U_2215,U_2214)
| c_Orderings_Oord__class_Oless__eq(U_2213,U_2214,U_2215)
| ~ class_Orderings_Olinorder(U_2213) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
! [U_2215,U_2214,U_2213] :
( c_Orderings_Oord__class_Oless__eq(U_2213,U_2215,U_2214)
| c_Orderings_Oord__class_Oless__eq(U_2213,U_2214,U_2215)
| ~ class_Orderings_Olinorder(U_2213) ),
inference(definitional_conversion,[status(esa)],[f_400_2]) ).
cnf(f_400_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2213,U_2215,U_2214)
| c_Orderings_Oord__class_Oless__eq(U_2213,U_2214,U_2215)
| ~ class_Orderings_Olinorder(U_2213) ),
inference(clausify,[status(thm)],[f_400_3]) ).
fof(f_401_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_401_2,plain,
! [U_2218,U_2217,U_2216] :
( ( ( U_2217 = U_2218
| ~ c_Orderings_Oord__class_Oless__eq(U_2216,U_2218,U_2217)
| ~ c_Orderings_Oord__class_Oless__eq(U_2216,U_2217,U_2218) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_2216,U_2218,U_2217)
& c_Orderings_Oord__class_Oless__eq(U_2216,U_2217,U_2218) )
| U_2217 != U_2218 ) )
| ~ class_Orderings_Oorder(U_2216) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
( ! [U_2217,U_2218,U_2216] :
( c_Orderings_Oord__class_Oless__eq(U_2216,U_2218,U_2217)
| ~ sP120(U_2217,U_2218,U_2216) )
& ! [U_2217,U_2218,U_2216] :
( c_Orderings_Oord__class_Oless__eq(U_2216,U_2217,U_2218)
| ~ sP120(U_2217,U_2218,U_2216) )
& ! [U_2217,U_2218,U_2216] :
( U_2217 = U_2218
| ~ c_Orderings_Oord__class_Oless__eq(U_2216,U_2218,U_2217)
| ~ c_Orderings_Oord__class_Oless__eq(U_2216,U_2217,U_2218)
| ~ sP121(U_2217,U_2218,U_2216) )
& ! [U_2217,U_2218,U_2216] :
( sP120(U_2217,U_2218,U_2216)
| U_2217 != U_2218
| ~ sP121(U_2217,U_2218,U_2216) )
& ! [U_2217,U_2218,U_2216] :
( sP121(U_2217,U_2218,U_2216)
| ~ class_Orderings_Oorder(U_2216) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120,sP121])],[f_401_2]) ).
cnf(f_401_4,plain,
( sP121(U_2217,U_2218,U_2216)
| ~ class_Orderings_Oorder(U_2216) ),
inference(clausify,[status(thm)],[f_401_3]) ).
cnf(f_401_5,plain,
( sP120(U_2217,U_2218,U_2216)
| U_2217 != U_2218
| ~ sP121(U_2217,U_2218,U_2216) ),
inference(clausify,[status(thm)],[f_401_3]) ).
cnf(f_401_6,plain,
( U_2217 = U_2218
| ~ c_Orderings_Oord__class_Oless__eq(U_2216,U_2218,U_2217)
| ~ c_Orderings_Oord__class_Oless__eq(U_2216,U_2217,U_2218)
| ~ sP121(U_2217,U_2218,U_2216) ),
inference(clausify,[status(thm)],[f_401_3]) ).
cnf(f_401_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2216,U_2217,U_2218)
| ~ sP120(U_2217,U_2218,U_2216) ),
inference(clausify,[status(thm)],[f_401_3]) ).
cnf(f_401_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_2216,U_2218,U_2217)
| ~ sP120(U_2217,U_2218,U_2216) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_1,plain,
! [V_y,V_x,T_a] :
( 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_402_2,plain,
! [U_2221,U_2220,U_2219] :
( c_Orderings_Oord__class_Oless__eq(U_2219,U_2220,U_2221)
| U_2220 != U_2221
| ~ class_Orderings_Opreorder(U_2219) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
! [U_2219,U_2220,U_2221] :
( c_Orderings_Oord__class_Oless__eq(U_2219,U_2220,U_2221)
| U_2220 != U_2221
| ~ class_Orderings_Opreorder(U_2219) ),
inference(definitional_conversion,[status(esa)],[f_402_2]) ).
cnf(f_402_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2219,U_2220,U_2221)
| U_2220 != U_2221
| ~ class_Orderings_Opreorder(U_2219) ),
inference(clausify,[status(thm)],[f_402_3]) ).
fof(f_403_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_403_2,plain,
! [U_2226,U_2225,U_2224,U_2223,U_2222] :
( c_Orderings_Oord__class_Oless__eq(U_2222,hAPP(U_2224,U_2226),hAPP(U_2225,U_2226))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2223,U_2222),U_2224,U_2225)
| ~ class_Orderings_Oord(U_2222) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
! [U_2222,U_2225,U_2223,U_2224,U_2226] :
( c_Orderings_Oord__class_Oless__eq(U_2222,hAPP(U_2224,U_2226),hAPP(U_2225,U_2226))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2223,U_2222),U_2224,U_2225)
| ~ class_Orderings_Oord(U_2222) ),
inference(definitional_conversion,[status(esa)],[f_403_2]) ).
cnf(f_403_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2222,hAPP(U_2224,U_2226),hAPP(U_2225,U_2226))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2223,U_2222),U_2224,U_2225)
| ~ class_Orderings_Oord(U_2222) ),
inference(clausify,[status(thm)],[f_403_3]) ).
fof(f_404_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_404_2,plain,
! [U_2229,U_2228,U_2227] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2227,U_2229,U_2228)
| U_2229 != U_2228 )
& ( U_2229 = U_2228
| ~ c_Orderings_Oord__class_Oless__eq(U_2227,U_2229,U_2228) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2227,U_2228,U_2229)
| ~ class_Orderings_Oorder(U_2227) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
( ! [U_2228,U_2229,U_2227] :
( c_Orderings_Oord__class_Oless__eq(U_2227,U_2229,U_2228)
| U_2229 != U_2228
| ~ sP122(U_2228,U_2229,U_2227) )
& ! [U_2228,U_2229,U_2227] :
( U_2229 = U_2228
| ~ c_Orderings_Oord__class_Oless__eq(U_2227,U_2229,U_2228)
| ~ sP122(U_2228,U_2229,U_2227) )
& ! [U_2228,U_2229,U_2227] :
( sP122(U_2228,U_2229,U_2227)
| ~ c_Orderings_Oord__class_Oless__eq(U_2227,U_2228,U_2229)
| ~ class_Orderings_Oorder(U_2227) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_404_2]) ).
cnf(f_404_4,plain,
( sP122(U_2228,U_2229,U_2227)
| ~ c_Orderings_Oord__class_Oless__eq(U_2227,U_2228,U_2229)
| ~ class_Orderings_Oorder(U_2227) ),
inference(clausify,[status(thm)],[f_404_3]) ).
cnf(f_404_5,plain,
( U_2229 = U_2228
| ~ c_Orderings_Oord__class_Oless__eq(U_2227,U_2229,U_2228)
| ~ sP122(U_2228,U_2229,U_2227) ),
inference(clausify,[status(thm)],[f_404_3]) ).
cnf(f_404_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2227,U_2229,U_2228)
| U_2229 != U_2228
| ~ sP122(U_2228,U_2229,U_2227) ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ 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_405_2,plain,
! [U_2233,U_2232,U_2231,U_2230] :
( c_Orderings_Oord__class_Oless__eq(U_2230,U_2231,U_2233)
| ~ c_Orderings_Oord__class_Oless__eq(U_2230,U_2232,U_2233)
| U_2231 != U_2232
| ~ class_Orderings_Oord(U_2230) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
! [U_2233,U_2231,U_2232,U_2230] :
( c_Orderings_Oord__class_Oless__eq(U_2230,U_2231,U_2233)
| ~ c_Orderings_Oord__class_Oless__eq(U_2230,U_2232,U_2233)
| U_2231 != U_2232
| ~ class_Orderings_Oord(U_2230) ),
inference(definitional_conversion,[status(esa)],[f_405_2]) ).
cnf(f_405_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2230,U_2231,U_2233)
| ~ c_Orderings_Oord__class_Oless__eq(U_2230,U_2232,U_2233)
| U_2231 != U_2232
| ~ class_Orderings_Oord(U_2230) ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ 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_406_2,plain,
! [U_2237,U_2236,U_2235,U_2234] :
( c_Orderings_Oord__class_Oless__eq(U_2234,U_2237,U_2235)
| ~ c_Orderings_Oord__class_Oless__eq(U_2234,U_2237,U_2236)
| U_2235 != U_2236
| ~ class_Orderings_Oorder(U_2234) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
fof(f_406_3,plain,
! [U_2237,U_2235,U_2234,U_2236] :
( c_Orderings_Oord__class_Oless__eq(U_2234,U_2237,U_2235)
| ~ c_Orderings_Oord__class_Oless__eq(U_2234,U_2237,U_2236)
| U_2235 != U_2236
| ~ class_Orderings_Oorder(U_2234) ),
inference(definitional_conversion,[status(esa)],[f_406_2]) ).
cnf(f_406_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2234,U_2237,U_2235)
| ~ c_Orderings_Oord__class_Oless__eq(U_2234,U_2237,U_2236)
| U_2235 != U_2236
| ~ class_Orderings_Oorder(U_2234) ),
inference(clausify,[status(thm)],[f_406_3]) ).
fof(f_407_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| V_b != V_c
| ~ 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_407_2,plain,
! [U_2241,U_2240,U_2239,U_2238] :
( c_Orderings_Oord__class_Oless__eq(U_2238,U_2239,U_2241)
| U_2240 != U_2241
| ~ c_Orderings_Oord__class_Oless__eq(U_2238,U_2239,U_2240)
| ~ class_Orderings_Oord(U_2238) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_2241,U_2240,U_2239,U_2238] :
( c_Orderings_Oord__class_Oless__eq(U_2238,U_2239,U_2241)
| U_2240 != U_2241
| ~ c_Orderings_Oord__class_Oless__eq(U_2238,U_2239,U_2240)
| ~ class_Orderings_Oord(U_2238) ),
inference(definitional_conversion,[status(esa)],[f_407_2]) ).
cnf(f_407_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2238,U_2239,U_2241)
| U_2240 != U_2241
| ~ c_Orderings_Oord__class_Oless__eq(U_2238,U_2239,U_2240)
| ~ class_Orderings_Oord(U_2238) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| V_b != V_c
| ~ 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_408_2,plain,
! [U_2245,U_2244,U_2243,U_2242] :
( c_Orderings_Oord__class_Oless__eq(U_2242,U_2245,U_2244)
| U_2243 != U_2245
| ~ c_Orderings_Oord__class_Oless__eq(U_2242,U_2243,U_2244)
| ~ class_Orderings_Oorder(U_2242) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
! [U_2244,U_2245,U_2242,U_2243] :
( c_Orderings_Oord__class_Oless__eq(U_2242,U_2245,U_2244)
| U_2243 != U_2245
| ~ c_Orderings_Oord__class_Oless__eq(U_2242,U_2243,U_2244)
| ~ class_Orderings_Oorder(U_2242) ),
inference(definitional_conversion,[status(esa)],[f_408_2]) ).
cnf(f_408_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2242,U_2245,U_2244)
| U_2243 != U_2245
| ~ c_Orderings_Oord__class_Oless__eq(U_2242,U_2243,U_2244)
| ~ class_Orderings_Oorder(U_2242) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ 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_409_2,plain,
! [U_2248,U_2247,U_2246] :
( U_2247 = U_2248
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,U_2248,U_2247)
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,U_2247,U_2248)
| ~ class_Orderings_Oorder(U_2246) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
! [U_2248,U_2246,U_2247] :
( U_2247 = U_2248
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,U_2248,U_2247)
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,U_2247,U_2248)
| ~ class_Orderings_Oorder(U_2246) ),
inference(definitional_conversion,[status(esa)],[f_409_2]) ).
cnf(f_409_4,plain,
( U_2247 = U_2248
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,U_2248,U_2247)
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,U_2247,U_2248)
| ~ class_Orderings_Oorder(U_2246) ),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ 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_410_2,plain,
! [U_2252,U_2251,U_2250,U_2249] :
( c_Orderings_Oord__class_Oless__eq(U_2249,U_2250,U_2252)
| ~ c_Orderings_Oord__class_Oless__eq(U_2249,U_2251,U_2252)
| ~ c_Orderings_Oord__class_Oless__eq(U_2249,U_2250,U_2251)
| ~ class_Orderings_Opreorder(U_2249) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
! [U_2250,U_2249,U_2251,U_2252] :
( c_Orderings_Oord__class_Oless__eq(U_2249,U_2250,U_2252)
| ~ c_Orderings_Oord__class_Oless__eq(U_2249,U_2251,U_2252)
| ~ c_Orderings_Oord__class_Oless__eq(U_2249,U_2250,U_2251)
| ~ class_Orderings_Opreorder(U_2249) ),
inference(definitional_conversion,[status(esa)],[f_410_2]) ).
cnf(f_410_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2249,U_2250,U_2252)
| ~ c_Orderings_Oord__class_Oless__eq(U_2249,U_2251,U_2252)
| ~ c_Orderings_Oord__class_Oless__eq(U_2249,U_2250,U_2251)
| ~ class_Orderings_Opreorder(U_2249) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [V_x,V_y,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ 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_411_2,plain,
! [U_2255,U_2254,U_2253] :
( U_2255 = U_2254
| ~ c_Orderings_Oord__class_Oless__eq(U_2253,U_2255,U_2254)
| ~ c_Orderings_Oord__class_Oless__eq(U_2253,U_2254,U_2255)
| ~ class_Orderings_Oorder(U_2253) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
fof(f_411_3,plain,
! [U_2253,U_2255,U_2254] :
( U_2255 = U_2254
| ~ c_Orderings_Oord__class_Oless__eq(U_2253,U_2255,U_2254)
| ~ c_Orderings_Oord__class_Oless__eq(U_2253,U_2254,U_2255)
| ~ class_Orderings_Oorder(U_2253) ),
inference(definitional_conversion,[status(esa)],[f_411_2]) ).
cnf(f_411_4,plain,
( U_2255 = U_2254
| ~ c_Orderings_Oord__class_Oless__eq(U_2253,U_2255,U_2254)
| ~ c_Orderings_Oord__class_Oless__eq(U_2253,U_2254,U_2255)
| ~ class_Orderings_Oorder(U_2253) ),
inference(clausify,[status(thm)],[f_411_3]) ).
fof(f_412_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ 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_412_2,plain,
! [U_2259,U_2258,U_2257,U_2256] :
( c_Orderings_Oord__class_Oless__eq(U_2256,U_2259,U_2258)
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,U_2259,U_2257)
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,U_2257,U_2258)
| ~ class_Orderings_Oorder(U_2256) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
! [U_2257,U_2256,U_2258,U_2259] :
( c_Orderings_Oord__class_Oless__eq(U_2256,U_2259,U_2258)
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,U_2259,U_2257)
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,U_2257,U_2258)
| ~ class_Orderings_Oorder(U_2256) ),
inference(definitional_conversion,[status(esa)],[f_412_2]) ).
cnf(f_412_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2256,U_2259,U_2258)
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,U_2259,U_2257)
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,U_2257,U_2258)
| ~ class_Orderings_Oorder(U_2256) ),
inference(clausify,[status(thm)],[f_412_3]) ).
fof(f_413_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_413_2,plain,
! [U_2264,U_2263,U_2262,U_2261,U_2260] :
( c_Orderings_Oord__class_Oless__eq(U_2260,hAPP(U_2262,U_2264),hAPP(U_2263,U_2264))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2261,U_2260),U_2262,U_2263)
| ~ class_Orderings_Oord(U_2260) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
! [U_2260,U_2261,U_2262,U_2263,U_2264] :
( c_Orderings_Oord__class_Oless__eq(U_2260,hAPP(U_2262,U_2264),hAPP(U_2263,U_2264))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2261,U_2260),U_2262,U_2263)
| ~ class_Orderings_Oord(U_2260) ),
inference(definitional_conversion,[status(esa)],[f_413_2]) ).
cnf(f_413_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2260,hAPP(U_2262,U_2264),hAPP(U_2263,U_2264))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2261,U_2260),U_2262,U_2263)
| ~ class_Orderings_Oord(U_2260) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| 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_414_2,plain,
! [U_2267,U_2266,U_2265] :
( c_Orderings_Oord__class_Oless__eq(U_2265,U_2267,U_2266)
| c_Orderings_Oord__class_Oless__eq(U_2265,U_2266,U_2267)
| ~ class_Orderings_Olinorder(U_2265) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
! [U_2267,U_2265,U_2266] :
( c_Orderings_Oord__class_Oless__eq(U_2265,U_2267,U_2266)
| c_Orderings_Oord__class_Oless__eq(U_2265,U_2266,U_2267)
| ~ class_Orderings_Olinorder(U_2265) ),
inference(definitional_conversion,[status(esa)],[f_414_2]) ).
cnf(f_414_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2265,U_2267,U_2266)
| c_Orderings_Oord__class_Oless__eq(U_2265,U_2266,U_2267)
| ~ class_Orderings_Olinorder(U_2265) ),
inference(clausify,[status(thm)],[f_414_3]) ).
fof(f_415_1,plain,
! [V_x,T_a] :
( ~ 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_415_2,plain,
! [U_2269,U_2268] :
( ~ c_Orderings_Oord__class_Oless(U_2268,U_2269,U_2269)
| ~ class_Orderings_Opreorder(U_2268) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
! [U_2268,U_2269] :
( ~ c_Orderings_Oord__class_Oless(U_2268,U_2269,U_2269)
| ~ class_Orderings_Opreorder(U_2268) ),
inference(definitional_conversion,[status(esa)],[f_415_2]) ).
cnf(f_415_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2268,U_2269,U_2269)
| ~ class_Orderings_Opreorder(U_2268) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 != V_y_2
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_416_2,plain,
! [U_2272,U_2271,U_2270] :
( ( ( U_2271 != U_2272
| ( ~ c_Orderings_Oord__class_Oless(U_2270,U_2272,U_2271)
& ~ c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272) ) )
& ( c_Orderings_Oord__class_Oless(U_2270,U_2272,U_2271)
| c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| U_2271 = U_2272 ) )
| ~ class_Orderings_Olinorder(U_2270) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
( ! [U_2270,U_2272,U_2271] :
( ~ c_Orderings_Oord__class_Oless(U_2270,U_2272,U_2271)
| ~ sP123(U_2270,U_2272,U_2271) )
& ! [U_2270,U_2272,U_2271] :
( ~ c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| ~ sP123(U_2270,U_2272,U_2271) )
& ! [U_2270,U_2272,U_2271] :
( U_2271 != U_2272
| sP123(U_2270,U_2272,U_2271)
| ~ sP124(U_2270,U_2272,U_2271) )
& ! [U_2270,U_2272,U_2271] :
( c_Orderings_Oord__class_Oless(U_2270,U_2272,U_2271)
| c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| U_2271 = U_2272
| ~ sP124(U_2270,U_2272,U_2271) )
& ! [U_2270,U_2272,U_2271] :
( sP124(U_2270,U_2272,U_2271)
| ~ class_Orderings_Olinorder(U_2270) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123,sP124])],[f_416_2]) ).
cnf(f_416_4,plain,
( sP124(U_2270,U_2272,U_2271)
| ~ class_Orderings_Olinorder(U_2270) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_5,plain,
( c_Orderings_Oord__class_Oless(U_2270,U_2272,U_2271)
| c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| U_2271 = U_2272
| ~ sP124(U_2270,U_2272,U_2271) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_6,plain,
( U_2271 != U_2272
| sP123(U_2270,U_2272,U_2271)
| ~ sP124(U_2270,U_2272,U_2271) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| ~ sP123(U_2270,U_2272,U_2271) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_2270,U_2272,U_2271)
| ~ sP123(U_2270,U_2272,U_2271) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_417_2,plain,
! [U_2275,U_2274,U_2273] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2273,U_2274,U_2275)
| ( U_2274 != U_2275
& ~ c_Orderings_Oord__class_Oless(U_2273,U_2275,U_2274) ) )
& ( U_2274 = U_2275
| c_Orderings_Oord__class_Oless(U_2273,U_2275,U_2274)
| c_Orderings_Oord__class_Oless(U_2273,U_2274,U_2275) ) )
| ~ class_Orderings_Olinorder(U_2273) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
( ! [U_2273,U_2275,U_2274] :
( U_2274 != U_2275
| ~ sP125(U_2273,U_2275,U_2274) )
& ! [U_2273,U_2275,U_2274] :
( ~ c_Orderings_Oord__class_Oless(U_2273,U_2275,U_2274)
| ~ sP125(U_2273,U_2275,U_2274) )
& ! [U_2273,U_2275,U_2274] :
( ~ c_Orderings_Oord__class_Oless(U_2273,U_2274,U_2275)
| sP125(U_2273,U_2275,U_2274)
| ~ sP126(U_2273,U_2275,U_2274) )
& ! [U_2273,U_2275,U_2274] :
( U_2274 = U_2275
| c_Orderings_Oord__class_Oless(U_2273,U_2275,U_2274)
| c_Orderings_Oord__class_Oless(U_2273,U_2274,U_2275)
| ~ sP126(U_2273,U_2275,U_2274) )
& ! [U_2273,U_2275,U_2274] :
( sP126(U_2273,U_2275,U_2274)
| ~ class_Orderings_Olinorder(U_2273) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125,sP126])],[f_417_2]) ).
cnf(f_417_4,plain,
( sP126(U_2273,U_2275,U_2274)
| ~ class_Orderings_Olinorder(U_2273) ),
inference(clausify,[status(thm)],[f_417_3]) ).
cnf(f_417_5,plain,
( U_2274 = U_2275
| c_Orderings_Oord__class_Oless(U_2273,U_2275,U_2274)
| c_Orderings_Oord__class_Oless(U_2273,U_2274,U_2275)
| ~ sP126(U_2273,U_2275,U_2274) ),
inference(clausify,[status(thm)],[f_417_3]) ).
cnf(f_417_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2273,U_2274,U_2275)
| sP125(U_2273,U_2275,U_2274)
| ~ sP126(U_2273,U_2275,U_2274) ),
inference(clausify,[status(thm)],[f_417_3]) ).
cnf(f_417_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2273,U_2275,U_2274)
| ~ sP125(U_2273,U_2275,U_2274) ),
inference(clausify,[status(thm)],[f_417_3]) ).
cnf(f_417_8,plain,
( U_2274 != U_2275
| ~ sP125(U_2273,U_2275,U_2274) ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| 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_418_2,plain,
! [U_2278,U_2277,U_2276] :
( c_Orderings_Oord__class_Oless(U_2276,U_2278,U_2277)
| U_2277 = U_2278
| c_Orderings_Oord__class_Oless(U_2276,U_2277,U_2278)
| ~ class_Orderings_Olinorder(U_2276) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
! [U_2278,U_2276,U_2277] :
( c_Orderings_Oord__class_Oless(U_2276,U_2278,U_2277)
| U_2277 = U_2278
| c_Orderings_Oord__class_Oless(U_2276,U_2277,U_2278)
| ~ class_Orderings_Olinorder(U_2276) ),
inference(definitional_conversion,[status(esa)],[f_418_2]) ).
cnf(f_418_4,plain,
( c_Orderings_Oord__class_Oless(U_2276,U_2278,U_2277)
| U_2277 = U_2278
| c_Orderings_Oord__class_Oless(U_2276,U_2277,U_2278)
| ~ class_Orderings_Olinorder(U_2276) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_419_2,plain,
! [U_2281,U_2280,U_2279] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2279,U_2281,U_2280)
| U_2281 != U_2280 )
& ( U_2281 = U_2280
| c_Orderings_Oord__class_Oless(U_2279,U_2281,U_2280) ) )
| c_Orderings_Oord__class_Oless(U_2279,U_2280,U_2281)
| ~ class_Orderings_Olinorder(U_2279) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
fof(f_419_3,plain,
( ! [U_2280,U_2281,U_2279] :
( ~ c_Orderings_Oord__class_Oless(U_2279,U_2281,U_2280)
| U_2281 != U_2280
| ~ sP127(U_2280,U_2281,U_2279) )
& ! [U_2280,U_2281,U_2279] :
( U_2281 = U_2280
| c_Orderings_Oord__class_Oless(U_2279,U_2281,U_2280)
| ~ sP127(U_2280,U_2281,U_2279) )
& ! [U_2280,U_2281,U_2279] :
( sP127(U_2280,U_2281,U_2279)
| c_Orderings_Oord__class_Oless(U_2279,U_2280,U_2281)
| ~ class_Orderings_Olinorder(U_2279) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_419_2]) ).
cnf(f_419_4,plain,
( sP127(U_2280,U_2281,U_2279)
| c_Orderings_Oord__class_Oless(U_2279,U_2280,U_2281)
| ~ class_Orderings_Olinorder(U_2279) ),
inference(clausify,[status(thm)],[f_419_3]) ).
cnf(f_419_5,plain,
( U_2281 = U_2280
| c_Orderings_Oord__class_Oless(U_2279,U_2281,U_2280)
| ~ sP127(U_2280,U_2281,U_2279) ),
inference(clausify,[status(thm)],[f_419_3]) ).
cnf(f_419_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2279,U_2281,U_2280)
| U_2281 != U_2280
| ~ sP127(U_2280,U_2281,U_2279) ),
inference(clausify,[status(thm)],[f_419_3]) ).
fof(f_420_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| 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_420_2,plain,
! [U_2284,U_2283,U_2282] :
( c_Orderings_Oord__class_Oless(U_2282,U_2284,U_2283)
| c_Orderings_Oord__class_Oless(U_2282,U_2283,U_2284)
| U_2283 = U_2284
| ~ class_Orderings_Olinorder(U_2282) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
! [U_2284,U_2282,U_2283] :
( c_Orderings_Oord__class_Oless(U_2282,U_2284,U_2283)
| c_Orderings_Oord__class_Oless(U_2282,U_2283,U_2284)
| U_2283 = U_2284
| ~ class_Orderings_Olinorder(U_2282) ),
inference(definitional_conversion,[status(esa)],[f_420_2]) ).
cnf(f_420_4,plain,
( c_Orderings_Oord__class_Oless(U_2282,U_2284,U_2283)
| c_Orderings_Oord__class_Oless(U_2282,U_2283,U_2284)
| U_2283 = U_2284
| ~ class_Orderings_Olinorder(U_2282) ),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ 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_421_2,plain,
! [U_2287,U_2286,U_2285] :
( U_2286 != U_2287
| ~ c_Orderings_Oord__class_Oless(U_2285,U_2286,U_2287)
| ~ class_Orderings_Oorder(U_2285) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
! [U_2287,U_2286,U_2285] :
( U_2286 != U_2287
| ~ c_Orderings_Oord__class_Oless(U_2285,U_2286,U_2287)
| ~ class_Orderings_Oorder(U_2285) ),
inference(definitional_conversion,[status(esa)],[f_421_2]) ).
cnf(f_421_4,plain,
( U_2286 != U_2287
| ~ c_Orderings_Oord__class_Oless(U_2285,U_2286,U_2287)
| ~ class_Orderings_Oorder(U_2285) ),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ 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_422_2,plain,
! [U_2290,U_2289,U_2288] :
( ~ c_Orderings_Oord__class_Oless(U_2288,U_2290,U_2289)
| ~ c_Orderings_Oord__class_Oless(U_2288,U_2289,U_2290)
| ~ class_Orderings_Opreorder(U_2288) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
! [U_2289,U_2290,U_2288] :
( ~ c_Orderings_Oord__class_Oless(U_2288,U_2290,U_2289)
| ~ c_Orderings_Oord__class_Oless(U_2288,U_2289,U_2290)
| ~ class_Orderings_Opreorder(U_2288) ),
inference(definitional_conversion,[status(esa)],[f_422_2]) ).
cnf(f_422_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2288,U_2290,U_2289)
| ~ c_Orderings_Oord__class_Oless(U_2288,U_2289,U_2290)
| ~ class_Orderings_Opreorder(U_2288) ),
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ 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_423_2,plain,
! [U_2293,U_2292,U_2291] :
( ~ c_Orderings_Oord__class_Oless(U_2291,U_2293,U_2292)
| ~ c_Orderings_Oord__class_Oless(U_2291,U_2292,U_2293)
| ~ class_Orderings_Opreorder(U_2291) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
! [U_2293,U_2291,U_2292] :
( ~ c_Orderings_Oord__class_Oless(U_2291,U_2293,U_2292)
| ~ c_Orderings_Oord__class_Oless(U_2291,U_2292,U_2293)
| ~ class_Orderings_Opreorder(U_2291) ),
inference(definitional_conversion,[status(esa)],[f_423_2]) ).
cnf(f_423_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2291,U_2293,U_2292)
| ~ c_Orderings_Oord__class_Oless(U_2291,U_2292,U_2293)
| ~ class_Orderings_Opreorder(U_2291) ),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ 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_424_2,plain,
! [U_2296,U_2295,U_2294] :
( U_2295 != U_2296
| ~ c_Orderings_Oord__class_Oless(U_2294,U_2295,U_2296)
| ~ class_Orderings_Oorder(U_2294) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
! [U_2295,U_2294,U_2296] :
( U_2295 != U_2296
| ~ c_Orderings_Oord__class_Oless(U_2294,U_2295,U_2296)
| ~ class_Orderings_Oorder(U_2294) ),
inference(definitional_conversion,[status(esa)],[f_424_2]) ).
cnf(f_424_4,plain,
( U_2295 != U_2296
| ~ c_Orderings_Oord__class_Oless(U_2294,U_2295,U_2296)
| ~ class_Orderings_Oorder(U_2294) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_1,plain,
! [V_y,V_x,T_a] :
( V_y != V_x
| ~ 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_425_2,plain,
! [U_2299,U_2298,U_2297] :
( U_2299 != U_2298
| ~ c_Orderings_Oord__class_Oless(U_2297,U_2298,U_2299)
| ~ class_Orderings_Oorder(U_2297) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
! [U_2297,U_2298,U_2299] :
( U_2299 != U_2298
| ~ c_Orderings_Oord__class_Oless(U_2297,U_2298,U_2299)
| ~ class_Orderings_Oorder(U_2297) ),
inference(definitional_conversion,[status(esa)],[f_425_2]) ).
cnf(f_425_4,plain,
( U_2299 != U_2298
| ~ c_Orderings_Oord__class_Oless(U_2297,U_2298,U_2299)
| ~ class_Orderings_Oorder(U_2297) ),
inference(clausify,[status(thm)],[f_425_3]) ).
fof(f_426_1,plain,
! [V_b,V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ 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_426_2,plain,
! [U_2302,U_2301,U_2300] :
( ~ c_Orderings_Oord__class_Oless(U_2300,U_2302,U_2301)
| ~ c_Orderings_Oord__class_Oless(U_2300,U_2301,U_2302)
| ~ class_Orderings_Opreorder(U_2300) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
! [U_2302,U_2301,U_2300] :
( ~ c_Orderings_Oord__class_Oless(U_2300,U_2302,U_2301)
| ~ c_Orderings_Oord__class_Oless(U_2300,U_2301,U_2302)
| ~ class_Orderings_Opreorder(U_2300) ),
inference(definitional_conversion,[status(esa)],[f_426_2]) ).
cnf(f_426_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2300,U_2302,U_2301)
| ~ c_Orderings_Oord__class_Oless(U_2300,U_2301,U_2302)
| ~ class_Orderings_Opreorder(U_2300) ),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_1,plain,
! [V_a,V_b,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ 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_427_2,plain,
! [U_2305,U_2304,U_2303] :
( ~ c_Orderings_Oord__class_Oless(U_2303,U_2305,U_2304)
| ~ c_Orderings_Oord__class_Oless(U_2303,U_2304,U_2305)
| ~ class_Orderings_Oorder(U_2303) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
! [U_2305,U_2303,U_2304] :
( ~ c_Orderings_Oord__class_Oless(U_2303,U_2305,U_2304)
| ~ c_Orderings_Oord__class_Oless(U_2303,U_2304,U_2305)
| ~ class_Orderings_Oorder(U_2303) ),
inference(definitional_conversion,[status(esa)],[f_427_2]) ).
cnf(f_427_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2303,U_2305,U_2304)
| ~ c_Orderings_Oord__class_Oless(U_2303,U_2304,U_2305)
| ~ class_Orderings_Oorder(U_2303) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| ~ 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_428_2,plain,
! [U_2309,U_2308,U_2307,U_2306] :
( c_Orderings_Oord__class_Oless(U_2306,U_2307,U_2309)
| ~ c_Orderings_Oord__class_Oless(U_2306,U_2308,U_2309)
| U_2307 != U_2308
| ~ class_Orderings_Oord(U_2306) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_2309,U_2308,U_2306,U_2307] :
( c_Orderings_Oord__class_Oless(U_2306,U_2307,U_2309)
| ~ c_Orderings_Oord__class_Oless(U_2306,U_2308,U_2309)
| U_2307 != U_2308
| ~ class_Orderings_Oord(U_2306) ),
inference(definitional_conversion,[status(esa)],[f_428_2]) ).
cnf(f_428_4,plain,
( c_Orderings_Oord__class_Oless(U_2306,U_2307,U_2309)
| ~ c_Orderings_Oord__class_Oless(U_2306,U_2308,U_2309)
| U_2307 != U_2308
| ~ class_Orderings_Oord(U_2306) ),
inference(clausify,[status(thm)],[f_428_3]) ).
fof(f_429_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ 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_429_2,plain,
! [U_2313,U_2312,U_2311,U_2310] :
( c_Orderings_Oord__class_Oless(U_2310,U_2313,U_2311)
| ~ c_Orderings_Oord__class_Oless(U_2310,U_2313,U_2312)
| U_2311 != U_2312
| ~ class_Orderings_Oorder(U_2310) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_2312,U_2313,U_2310,U_2311] :
( c_Orderings_Oord__class_Oless(U_2310,U_2313,U_2311)
| ~ c_Orderings_Oord__class_Oless(U_2310,U_2313,U_2312)
| U_2311 != U_2312
| ~ class_Orderings_Oorder(U_2310) ),
inference(definitional_conversion,[status(esa)],[f_429_2]) ).
cnf(f_429_4,plain,
( c_Orderings_Oord__class_Oless(U_2310,U_2313,U_2311)
| ~ c_Orderings_Oord__class_Oless(U_2310,U_2313,U_2312)
| U_2311 != U_2312
| ~ class_Orderings_Oorder(U_2310) ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| V_b != V_c
| ~ 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_430_2,plain,
! [U_2317,U_2316,U_2315,U_2314] :
( c_Orderings_Oord__class_Oless(U_2314,U_2315,U_2317)
| U_2316 != U_2317
| ~ c_Orderings_Oord__class_Oless(U_2314,U_2315,U_2316)
| ~ class_Orderings_Oord(U_2314) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
! [U_2315,U_2316,U_2317,U_2314] :
( c_Orderings_Oord__class_Oless(U_2314,U_2315,U_2317)
| U_2316 != U_2317
| ~ c_Orderings_Oord__class_Oless(U_2314,U_2315,U_2316)
| ~ class_Orderings_Oord(U_2314) ),
inference(definitional_conversion,[status(esa)],[f_430_2]) ).
cnf(f_430_4,plain,
( c_Orderings_Oord__class_Oless(U_2314,U_2315,U_2317)
| U_2316 != U_2317
| ~ c_Orderings_Oord__class_Oless(U_2314,U_2315,U_2316)
| ~ class_Orderings_Oord(U_2314) ),
inference(clausify,[status(thm)],[f_430_3]) ).
fof(f_431_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| V_b != V_c
| ~ 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_431_2,plain,
! [U_2321,U_2320,U_2319,U_2318] :
( c_Orderings_Oord__class_Oless(U_2318,U_2321,U_2320)
| U_2319 != U_2321
| ~ c_Orderings_Oord__class_Oless(U_2318,U_2319,U_2320)
| ~ class_Orderings_Oorder(U_2318) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
! [U_2321,U_2318,U_2319,U_2320] :
( c_Orderings_Oord__class_Oless(U_2318,U_2321,U_2320)
| U_2319 != U_2321
| ~ c_Orderings_Oord__class_Oless(U_2318,U_2319,U_2320)
| ~ class_Orderings_Oorder(U_2318) ),
inference(definitional_conversion,[status(esa)],[f_431_2]) ).
cnf(f_431_4,plain,
( c_Orderings_Oord__class_Oless(U_2318,U_2321,U_2320)
| U_2319 != U_2321
| ~ c_Orderings_Oord__class_Oless(U_2318,U_2319,U_2320)
| ~ class_Orderings_Oorder(U_2318) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ 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_432_2,plain,
! [U_2325,U_2324,U_2323,U_2322] :
( c_Orderings_Oord__class_Oless(U_2322,U_2323,U_2325)
| ~ c_Orderings_Oord__class_Oless(U_2322,U_2324,U_2325)
| ~ c_Orderings_Oord__class_Oless(U_2322,U_2323,U_2324)
| ~ class_Orderings_Opreorder(U_2322) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_2323,U_2325,U_2322,U_2324] :
( c_Orderings_Oord__class_Oless(U_2322,U_2323,U_2325)
| ~ c_Orderings_Oord__class_Oless(U_2322,U_2324,U_2325)
| ~ c_Orderings_Oord__class_Oless(U_2322,U_2323,U_2324)
| ~ class_Orderings_Opreorder(U_2322) ),
inference(definitional_conversion,[status(esa)],[f_432_2]) ).
cnf(f_432_4,plain,
( c_Orderings_Oord__class_Oless(U_2322,U_2323,U_2325)
| ~ c_Orderings_Oord__class_Oless(U_2322,U_2324,U_2325)
| ~ c_Orderings_Oord__class_Oless(U_2322,U_2323,U_2324)
| ~ class_Orderings_Opreorder(U_2322) ),
inference(clausify,[status(thm)],[f_432_3]) ).
fof(f_433_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ 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_433_2,plain,
! [U_2329,U_2328,U_2327,U_2326] :
( c_Orderings_Oord__class_Oless(U_2326,U_2329,U_2328)
| ~ c_Orderings_Oord__class_Oless(U_2326,U_2329,U_2327)
| ~ c_Orderings_Oord__class_Oless(U_2326,U_2327,U_2328)
| ~ class_Orderings_Oorder(U_2326) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_2328,U_2329,U_2326,U_2327] :
( c_Orderings_Oord__class_Oless(U_2326,U_2329,U_2328)
| ~ c_Orderings_Oord__class_Oless(U_2326,U_2329,U_2327)
| ~ c_Orderings_Oord__class_Oless(U_2326,U_2327,U_2328)
| ~ class_Orderings_Oorder(U_2326) ),
inference(definitional_conversion,[status(esa)],[f_433_2]) ).
cnf(f_433_4,plain,
( c_Orderings_Oord__class_Oless(U_2326,U_2329,U_2328)
| ~ c_Orderings_Oord__class_Oless(U_2326,U_2329,U_2327)
| ~ c_Orderings_Oord__class_Oless(U_2326,U_2327,U_2328)
| ~ class_Orderings_Oorder(U_2326) ),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ 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_434_2,plain,
! [U_2332,U_2331,U_2330] :
( ~ c_Orderings_Oord__class_Oless(U_2330,U_2332,U_2331)
| ~ c_Orderings_Oord__class_Oless(U_2330,U_2331,U_2332)
| ~ class_Orderings_Opreorder(U_2330) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_2332,U_2331,U_2330] :
( ~ c_Orderings_Oord__class_Oless(U_2330,U_2332,U_2331)
| ~ c_Orderings_Oord__class_Oless(U_2330,U_2331,U_2332)
| ~ class_Orderings_Opreorder(U_2330) ),
inference(definitional_conversion,[status(esa)],[f_434_2]) ).
cnf(f_434_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2330,U_2332,U_2331)
| ~ c_Orderings_Oord__class_Oless(U_2330,U_2331,U_2332)
| ~ class_Orderings_Opreorder(U_2330) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| 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_435_2,plain,
! [U_2335,U_2334,U_2333] :
( c_Orderings_Oord__class_Oless(U_2333,U_2335,U_2334)
| U_2334 = U_2335
| c_Orderings_Oord__class_Oless(U_2333,U_2334,U_2335)
| ~ class_Orderings_Olinorder(U_2333) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
! [U_2335,U_2333,U_2334] :
( c_Orderings_Oord__class_Oless(U_2333,U_2335,U_2334)
| U_2334 = U_2335
| c_Orderings_Oord__class_Oless(U_2333,U_2334,U_2335)
| ~ class_Orderings_Olinorder(U_2333) ),
inference(definitional_conversion,[status(esa)],[f_435_2]) ).
cnf(f_435_4,plain,
( c_Orderings_Oord__class_Oless(U_2333,U_2335,U_2334)
| U_2334 = U_2335
| c_Orderings_Oord__class_Oless(U_2333,U_2334,U_2335)
| ~ class_Orderings_Olinorder(U_2333) ),
inference(clausify,[status(thm)],[f_435_3]) ).
fof(f_436_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
| c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_436_2,plain,
! [U_2339,U_2338,U_2337,U_2336] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_2337,U_2336),U_2338,U_2339)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2339,U_2338)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2338,U_2339) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2339,U_2338)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2338,U_2339) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2337,U_2336),U_2338,U_2339) ) )
| ~ class_Orderings_Oord(U_2336) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
( ! [U_2337,U_2336,U_2338,U_2339] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2339,U_2338)
| ~ sP128(U_2337,U_2336,U_2338,U_2339) )
& ! [U_2337,U_2336,U_2338,U_2339] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2338,U_2339)
| ~ sP128(U_2337,U_2336,U_2338,U_2339) )
& ! [U_2337,U_2336,U_2338,U_2339] :
( c_Orderings_Oord__class_Oless(tc_fun(U_2337,U_2336),U_2338,U_2339)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2339,U_2338)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2338,U_2339)
| ~ sP129(U_2337,U_2336,U_2338,U_2339) )
& ! [U_2337,U_2336,U_2338,U_2339] :
( sP128(U_2337,U_2336,U_2338,U_2339)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2337,U_2336),U_2338,U_2339)
| ~ sP129(U_2337,U_2336,U_2338,U_2339) )
& ! [U_2337,U_2336,U_2338,U_2339] :
( sP129(U_2337,U_2336,U_2338,U_2339)
| ~ class_Orderings_Oord(U_2336) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128,sP129])],[f_436_2]) ).
cnf(f_436_4,plain,
( sP129(U_2337,U_2336,U_2338,U_2339)
| ~ class_Orderings_Oord(U_2336) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_5,plain,
( sP128(U_2337,U_2336,U_2338,U_2339)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2337,U_2336),U_2338,U_2339)
| ~ sP129(U_2337,U_2336,U_2338,U_2339) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_6,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_2337,U_2336),U_2338,U_2339)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2339,U_2338)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2338,U_2339)
| ~ sP129(U_2337,U_2336,U_2338,U_2339) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2338,U_2339)
| ~ sP128(U_2337,U_2336,U_2338,U_2339) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2337,U_2336),U_2339,U_2338)
| ~ sP128(U_2337,U_2336,U_2338,U_2339) ),
inference(clausify,[status(thm)],[f_436_3]) ).
fof(f_437_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_437_2,plain,
! [U_2342,U_2341,U_2340] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ c_Orderings_Oord__class_Oless__eq(U_2340,U_2342,U_2341) )
& ( c_Orderings_Oord__class_Oless__eq(U_2340,U_2342,U_2341)
| c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342) ) )
| ~ class_Orderings_Olinorder(U_2340) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
( ! [U_2340,U_2341,U_2342] :
( ~ c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ c_Orderings_Oord__class_Oless__eq(U_2340,U_2342,U_2341)
| ~ sP130(U_2340,U_2341,U_2342) )
& ! [U_2340,U_2341,U_2342] :
( c_Orderings_Oord__class_Oless__eq(U_2340,U_2342,U_2341)
| c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ sP130(U_2340,U_2341,U_2342) )
& ! [U_2340,U_2341,U_2342] :
( sP130(U_2340,U_2341,U_2342)
| ~ class_Orderings_Olinorder(U_2340) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_437_2]) ).
cnf(f_437_4,plain,
( sP130(U_2340,U_2341,U_2342)
| ~ class_Orderings_Olinorder(U_2340) ),
inference(clausify,[status(thm)],[f_437_3]) ).
cnf(f_437_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2340,U_2342,U_2341)
| c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ sP130(U_2340,U_2341,U_2342) ),
inference(clausify,[status(thm)],[f_437_3]) ).
cnf(f_437_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ c_Orderings_Oord__class_Oless__eq(U_2340,U_2342,U_2341)
| ~ sP130(U_2340,U_2341,U_2342) ),
inference(clausify,[status(thm)],[f_437_3]) ).
fof(f_438_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_438_2,plain,
! [U_2345,U_2344,U_2343] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345)
| ~ c_Orderings_Oord__class_Oless(U_2343,U_2345,U_2344) )
& ( c_Orderings_Oord__class_Oless(U_2343,U_2345,U_2344)
| c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345) ) )
| ~ class_Orderings_Olinorder(U_2343) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
( ! [U_2344,U_2343,U_2345] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345)
| ~ c_Orderings_Oord__class_Oless(U_2343,U_2345,U_2344)
| ~ sP131(U_2344,U_2343,U_2345) )
& ! [U_2344,U_2343,U_2345] :
( c_Orderings_Oord__class_Oless(U_2343,U_2345,U_2344)
| c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345)
| ~ sP131(U_2344,U_2343,U_2345) )
& ! [U_2344,U_2343,U_2345] :
( sP131(U_2344,U_2343,U_2345)
| ~ class_Orderings_Olinorder(U_2343) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_438_2]) ).
cnf(f_438_4,plain,
( sP131(U_2344,U_2343,U_2345)
| ~ class_Orderings_Olinorder(U_2343) ),
inference(clausify,[status(thm)],[f_438_3]) ).
cnf(f_438_5,plain,
( c_Orderings_Oord__class_Oless(U_2343,U_2345,U_2344)
| c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345)
| ~ sP131(U_2344,U_2343,U_2345) ),
inference(clausify,[status(thm)],[f_438_3]) ).
cnf(f_438_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345)
| ~ c_Orderings_Oord__class_Oless(U_2343,U_2345,U_2344)
| ~ sP131(U_2344,U_2343,U_2345) ),
inference(clausify,[status(thm)],[f_438_3]) ).
fof(f_439_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| 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_439_2,plain,
! [U_2348,U_2347,U_2346] :
( c_Orderings_Oord__class_Oless(U_2346,U_2348,U_2347)
| c_Orderings_Oord__class_Oless__eq(U_2346,U_2347,U_2348)
| ~ class_Orderings_Olinorder(U_2346) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
! [U_2347,U_2348,U_2346] :
( c_Orderings_Oord__class_Oless(U_2346,U_2348,U_2347)
| c_Orderings_Oord__class_Oless__eq(U_2346,U_2347,U_2348)
| ~ class_Orderings_Olinorder(U_2346) ),
inference(definitional_conversion,[status(esa)],[f_439_2]) ).
cnf(f_439_4,plain,
( c_Orderings_Oord__class_Oless(U_2346,U_2348,U_2347)
| c_Orderings_Oord__class_Oless__eq(U_2346,U_2347,U_2348)
| ~ class_Orderings_Olinorder(U_2346) ),
inference(clausify,[status(thm)],[f_439_3]) ).
fof(f_440_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_440_2,plain,
! [U_2351,U_2350,U_2349] :
( ( ( c_Orderings_Oord__class_Oless(U_2349,U_2350,U_2351)
| U_2350 = U_2351
| ~ c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351) )
& ( ( U_2350 != U_2351
& c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351) )
| ~ c_Orderings_Oord__class_Oless(U_2349,U_2350,U_2351) ) )
| ~ class_Orderings_Oorder(U_2349) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
( ! [U_2349,U_2351,U_2350] :
( U_2350 != U_2351
| ~ sP132(U_2349,U_2351,U_2350) )
& ! [U_2349,U_2351,U_2350] :
( c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351)
| ~ sP132(U_2349,U_2351,U_2350) )
& ! [U_2349,U_2351,U_2350] :
( c_Orderings_Oord__class_Oless(U_2349,U_2350,U_2351)
| U_2350 = U_2351
| ~ c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351)
| ~ sP133(U_2349,U_2351,U_2350) )
& ! [U_2349,U_2351,U_2350] :
( sP132(U_2349,U_2351,U_2350)
| ~ c_Orderings_Oord__class_Oless(U_2349,U_2350,U_2351)
| ~ sP133(U_2349,U_2351,U_2350) )
& ! [U_2349,U_2351,U_2350] :
( sP133(U_2349,U_2351,U_2350)
| ~ class_Orderings_Oorder(U_2349) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132,sP133])],[f_440_2]) ).
cnf(f_440_4,plain,
( sP133(U_2349,U_2351,U_2350)
| ~ class_Orderings_Oorder(U_2349) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_5,plain,
( sP132(U_2349,U_2351,U_2350)
| ~ c_Orderings_Oord__class_Oless(U_2349,U_2350,U_2351)
| ~ sP133(U_2349,U_2351,U_2350) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_6,plain,
( c_Orderings_Oord__class_Oless(U_2349,U_2350,U_2351)
| U_2350 = U_2351
| ~ c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351)
| ~ sP133(U_2349,U_2351,U_2350) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351)
| ~ sP132(U_2349,U_2351,U_2350) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_8,plain,
( U_2350 != U_2351
| ~ sP132(U_2349,U_2351,U_2350) ),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_441_2,plain,
! [U_2354,U_2353,U_2352] :
( ( ( c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| c_Orderings_Oord__class_Oless__eq(U_2352,U_2354,U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2353,U_2354) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2354,U_2353)
& c_Orderings_Oord__class_Oless__eq(U_2352,U_2353,U_2354) )
| ~ c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354) ) )
| ~ class_Orderings_Opreorder(U_2352) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
( ! [U_2354,U_2353,U_2352] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2354,U_2353)
| ~ sP134(U_2354,U_2353,U_2352) )
& ! [U_2354,U_2353,U_2352] :
( c_Orderings_Oord__class_Oless__eq(U_2352,U_2353,U_2354)
| ~ sP134(U_2354,U_2353,U_2352) )
& ! [U_2354,U_2353,U_2352] :
( c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| c_Orderings_Oord__class_Oless__eq(U_2352,U_2354,U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2353,U_2354)
| ~ sP135(U_2354,U_2353,U_2352) )
& ! [U_2354,U_2353,U_2352] :
( sP134(U_2354,U_2353,U_2352)
| ~ c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| ~ sP135(U_2354,U_2353,U_2352) )
& ! [U_2354,U_2353,U_2352] :
( sP135(U_2354,U_2353,U_2352)
| ~ class_Orderings_Opreorder(U_2352) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134,sP135])],[f_441_2]) ).
cnf(f_441_4,plain,
( sP135(U_2354,U_2353,U_2352)
| ~ class_Orderings_Opreorder(U_2352) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_5,plain,
( sP134(U_2354,U_2353,U_2352)
| ~ c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| ~ sP135(U_2354,U_2353,U_2352) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_6,plain,
( c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| c_Orderings_Oord__class_Oless__eq(U_2352,U_2354,U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2353,U_2354)
| ~ sP135(U_2354,U_2353,U_2352) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2352,U_2353,U_2354)
| ~ sP134(U_2354,U_2353,U_2352) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2354,U_2353)
| ~ sP134(U_2354,U_2353,U_2352) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_442_2,plain,
! [U_2357,U_2356,U_2355] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2355,U_2356,U_2357)
| ( U_2356 != U_2357
& ~ c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357) ) )
& ( U_2356 = U_2357
| c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357)
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,U_2356,U_2357) ) )
| ~ class_Orderings_Oorder(U_2355) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
( ! [U_2355,U_2356,U_2357] :
( U_2356 != U_2357
| ~ sP136(U_2355,U_2356,U_2357) )
& ! [U_2355,U_2356,U_2357] :
( ~ c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357)
| ~ sP136(U_2355,U_2356,U_2357) )
& ! [U_2355,U_2356,U_2357] :
( c_Orderings_Oord__class_Oless__eq(U_2355,U_2356,U_2357)
| sP136(U_2355,U_2356,U_2357)
| ~ sP137(U_2355,U_2356,U_2357) )
& ! [U_2355,U_2356,U_2357] :
( U_2356 = U_2357
| c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357)
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,U_2356,U_2357)
| ~ sP137(U_2355,U_2356,U_2357) )
& ! [U_2355,U_2356,U_2357] :
( sP137(U_2355,U_2356,U_2357)
| ~ class_Orderings_Oorder(U_2355) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136,sP137])],[f_442_2]) ).
cnf(f_442_4,plain,
( sP137(U_2355,U_2356,U_2357)
| ~ class_Orderings_Oorder(U_2355) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_5,plain,
( U_2356 = U_2357
| c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357)
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,U_2356,U_2357)
| ~ sP137(U_2355,U_2356,U_2357) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2355,U_2356,U_2357)
| sP136(U_2355,U_2356,U_2357)
| ~ sP137(U_2355,U_2356,U_2357) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357)
| ~ sP136(U_2355,U_2356,U_2357) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_8,plain,
( U_2356 != U_2357
| ~ sP136(U_2355,U_2356,U_2357) ),
inference(clausify,[status(thm)],[f_442_3]) ).
fof(f_443_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| 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_443_2,plain,
! [U_2360,U_2359,U_2358] :
( c_Orderings_Oord__class_Oless__eq(U_2358,U_2360,U_2359)
| c_Orderings_Oord__class_Oless(U_2358,U_2359,U_2360)
| ~ class_Orderings_Olinorder(U_2358) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
! [U_2359,U_2358,U_2360] :
( c_Orderings_Oord__class_Oless__eq(U_2358,U_2360,U_2359)
| c_Orderings_Oord__class_Oless(U_2358,U_2359,U_2360)
| ~ class_Orderings_Olinorder(U_2358) ),
inference(definitional_conversion,[status(esa)],[f_443_2]) ).
cnf(f_443_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2358,U_2360,U_2359)
| c_Orderings_Oord__class_Oless(U_2358,U_2359,U_2360)
| ~ class_Orderings_Olinorder(U_2358) ),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_1,plain,
! [V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| 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_444_2,plain,
! [U_2363,U_2362,U_2361] :
( c_Orderings_Oord__class_Oless(U_2361,U_2363,U_2362)
| c_Orderings_Oord__class_Oless__eq(U_2361,U_2362,U_2363)
| ~ class_Orderings_Olinorder(U_2361) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
! [U_2361,U_2363,U_2362] :
( c_Orderings_Oord__class_Oless(U_2361,U_2363,U_2362)
| c_Orderings_Oord__class_Oless__eq(U_2361,U_2362,U_2363)
| ~ class_Orderings_Olinorder(U_2361) ),
inference(definitional_conversion,[status(esa)],[f_444_2]) ).
cnf(f_444_4,plain,
( c_Orderings_Oord__class_Oless(U_2361,U_2363,U_2362)
| c_Orderings_Oord__class_Oless__eq(U_2361,U_2362,U_2363)
| ~ class_Orderings_Olinorder(U_2361) ),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_445_2,plain,
! [U_2366,U_2365,U_2364] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366)
| U_2365 != U_2366 )
& ( U_2365 = U_2366
| ~ c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366) ) )
| c_Orderings_Oord__class_Oless(U_2364,U_2365,U_2366)
| ~ class_Orderings_Olinorder(U_2364) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
( ! [U_2365,U_2366,U_2364] :
( c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366)
| U_2365 != U_2366
| ~ sP138(U_2365,U_2366,U_2364) )
& ! [U_2365,U_2366,U_2364] :
( U_2365 = U_2366
| ~ c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366)
| ~ sP138(U_2365,U_2366,U_2364) )
& ! [U_2365,U_2366,U_2364] :
( sP138(U_2365,U_2366,U_2364)
| c_Orderings_Oord__class_Oless(U_2364,U_2365,U_2366)
| ~ class_Orderings_Olinorder(U_2364) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_445_2]) ).
cnf(f_445_4,plain,
( sP138(U_2365,U_2366,U_2364)
| c_Orderings_Oord__class_Oless(U_2364,U_2365,U_2366)
| ~ class_Orderings_Olinorder(U_2364) ),
inference(clausify,[status(thm)],[f_445_3]) ).
cnf(f_445_5,plain,
( U_2365 = U_2366
| ~ c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366)
| ~ sP138(U_2365,U_2366,U_2364) ),
inference(clausify,[status(thm)],[f_445_3]) ).
cnf(f_445_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366)
| U_2365 != U_2366
| ~ sP138(U_2365,U_2366,U_2364) ),
inference(clausify,[status(thm)],[f_445_3]) ).
fof(f_446_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ 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_446_2,plain,
! [U_2369,U_2368,U_2367] :
( c_Orderings_Oord__class_Oless(U_2367,U_2368,U_2369)
| ~ c_Orderings_Oord__class_Oless__eq(U_2367,U_2368,U_2369)
| U_2368 = U_2369
| ~ class_Orderings_Oorder(U_2367) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
! [U_2369,U_2368,U_2367] :
( c_Orderings_Oord__class_Oless(U_2367,U_2368,U_2369)
| ~ c_Orderings_Oord__class_Oless__eq(U_2367,U_2368,U_2369)
| U_2368 = U_2369
| ~ class_Orderings_Oorder(U_2367) ),
inference(definitional_conversion,[status(esa)],[f_446_2]) ).
cnf(f_446_4,plain,
( c_Orderings_Oord__class_Oless(U_2367,U_2368,U_2369)
| ~ c_Orderings_Oord__class_Oless__eq(U_2367,U_2368,U_2369)
| U_2368 = U_2369
| ~ class_Orderings_Oorder(U_2367) ),
inference(clausify,[status(thm)],[f_446_3]) ).
fof(f_447_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ 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_447_2,plain,
! [U_2372,U_2371,U_2370] :
( c_Orderings_Oord__class_Oless(U_2370,U_2372,U_2371)
| ~ c_Orderings_Oord__class_Oless__eq(U_2370,U_2372,U_2371)
| U_2371 = U_2372
| ~ class_Orderings_Oorder(U_2370) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
! [U_2370,U_2372,U_2371] :
( c_Orderings_Oord__class_Oless(U_2370,U_2372,U_2371)
| ~ c_Orderings_Oord__class_Oless__eq(U_2370,U_2372,U_2371)
| U_2371 = U_2372
| ~ class_Orderings_Oorder(U_2370) ),
inference(definitional_conversion,[status(esa)],[f_447_2]) ).
cnf(f_447_4,plain,
( c_Orderings_Oord__class_Oless(U_2370,U_2372,U_2371)
| ~ c_Orderings_Oord__class_Oless__eq(U_2370,U_2372,U_2371)
| U_2371 = U_2372
| ~ class_Orderings_Oorder(U_2370) ),
inference(clausify,[status(thm)],[f_447_3]) ).
fof(f_448_1,plain,
! [V_x,V_y,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ 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_448_2,plain,
! [U_2375,U_2374,U_2373] :
( ~ c_Orderings_Oord__class_Oless(U_2373,U_2375,U_2374)
| ~ c_Orderings_Oord__class_Oless__eq(U_2373,U_2374,U_2375)
| ~ class_Orderings_Olinorder(U_2373) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
! [U_2374,U_2375,U_2373] :
( ~ c_Orderings_Oord__class_Oless(U_2373,U_2375,U_2374)
| ~ c_Orderings_Oord__class_Oless__eq(U_2373,U_2374,U_2375)
| ~ class_Orderings_Olinorder(U_2373) ),
inference(definitional_conversion,[status(esa)],[f_448_2]) ).
cnf(f_448_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2373,U_2375,U_2374)
| ~ c_Orderings_Oord__class_Oless__eq(U_2373,U_2374,U_2375)
| ~ class_Orderings_Olinorder(U_2373) ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ 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_449_2,plain,
! [U_2378,U_2377,U_2376] :
( c_Orderings_Oord__class_Oless__eq(U_2376,U_2377,U_2378)
| ~ c_Orderings_Oord__class_Oless(U_2376,U_2377,U_2378)
| ~ class_Orderings_Opreorder(U_2376) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
! [U_2378,U_2376,U_2377] :
( c_Orderings_Oord__class_Oless__eq(U_2376,U_2377,U_2378)
| ~ c_Orderings_Oord__class_Oless(U_2376,U_2377,U_2378)
| ~ class_Orderings_Opreorder(U_2376) ),
inference(definitional_conversion,[status(esa)],[f_449_2]) ).
cnf(f_449_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2376,U_2377,U_2378)
| ~ c_Orderings_Oord__class_Oless(U_2376,U_2377,U_2378)
| ~ class_Orderings_Opreorder(U_2376) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_450_2,plain,
! [U_2381,U_2380,U_2379] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2379,U_2380,U_2381)
| U_2380 != U_2381 )
& ( U_2380 = U_2381
| c_Orderings_Oord__class_Oless(U_2379,U_2380,U_2381) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2379,U_2380,U_2381)
| ~ class_Orderings_Olinorder(U_2379) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
( ! [U_2380,U_2379,U_2381] :
( ~ c_Orderings_Oord__class_Oless(U_2379,U_2380,U_2381)
| U_2380 != U_2381
| ~ sP139(U_2380,U_2379,U_2381) )
& ! [U_2380,U_2379,U_2381] :
( U_2380 = U_2381
| c_Orderings_Oord__class_Oless(U_2379,U_2380,U_2381)
| ~ sP139(U_2380,U_2379,U_2381) )
& ! [U_2380,U_2379,U_2381] :
( sP139(U_2380,U_2379,U_2381)
| ~ c_Orderings_Oord__class_Oless__eq(U_2379,U_2380,U_2381)
| ~ class_Orderings_Olinorder(U_2379) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_450_2]) ).
cnf(f_450_4,plain,
( sP139(U_2380,U_2379,U_2381)
| ~ c_Orderings_Oord__class_Oless__eq(U_2379,U_2380,U_2381)
| ~ class_Orderings_Olinorder(U_2379) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_5,plain,
( U_2380 = U_2381
| c_Orderings_Oord__class_Oless(U_2379,U_2380,U_2381)
| ~ sP139(U_2380,U_2379,U_2381) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2379,U_2380,U_2381)
| U_2380 != U_2381
| ~ sP139(U_2380,U_2379,U_2381) ),
inference(clausify,[status(thm)],[f_450_3]) ).
fof(f_451_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ 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_451_2,plain,
! [U_2384,U_2383,U_2382] :
( U_2383 = U_2384
| c_Orderings_Oord__class_Oless(U_2382,U_2383,U_2384)
| ~ c_Orderings_Oord__class_Oless__eq(U_2382,U_2383,U_2384)
| ~ class_Orderings_Oorder(U_2382) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
! [U_2384,U_2383,U_2382] :
( U_2383 = U_2384
| c_Orderings_Oord__class_Oless(U_2382,U_2383,U_2384)
| ~ c_Orderings_Oord__class_Oless__eq(U_2382,U_2383,U_2384)
| ~ class_Orderings_Oorder(U_2382) ),
inference(definitional_conversion,[status(esa)],[f_451_2]) ).
cnf(f_451_4,plain,
( U_2383 = U_2384
| c_Orderings_Oord__class_Oless(U_2382,U_2383,U_2384)
| ~ c_Orderings_Oord__class_Oless__eq(U_2382,U_2383,U_2384)
| ~ class_Orderings_Oorder(U_2382) ),
inference(clausify,[status(thm)],[f_451_3]) ).
fof(f_452_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| V_a = V_b
| ~ 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_452_2,plain,
! [U_2387,U_2386,U_2385] :
( c_Orderings_Oord__class_Oless(U_2385,U_2386,U_2387)
| U_2386 = U_2387
| ~ c_Orderings_Oord__class_Oless__eq(U_2385,U_2386,U_2387)
| ~ class_Orderings_Oorder(U_2385) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
! [U_2385,U_2386,U_2387] :
( c_Orderings_Oord__class_Oless(U_2385,U_2386,U_2387)
| U_2386 = U_2387
| ~ c_Orderings_Oord__class_Oless__eq(U_2385,U_2386,U_2387)
| ~ class_Orderings_Oorder(U_2385) ),
inference(definitional_conversion,[status(esa)],[f_452_2]) ).
cnf(f_452_4,plain,
( c_Orderings_Oord__class_Oless(U_2385,U_2386,U_2387)
| U_2386 = U_2387
| ~ c_Orderings_Oord__class_Oless__eq(U_2385,U_2386,U_2387)
| ~ class_Orderings_Oorder(U_2385) ),
inference(clausify,[status(thm)],[f_452_3]) ).
fof(f_453_1,plain,
! [V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| V_a = V_b
| ~ 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_453_2,plain,
! [U_2390,U_2389,U_2388] :
( c_Orderings_Oord__class_Oless(U_2388,U_2389,U_2390)
| U_2390 = U_2389
| ~ c_Orderings_Oord__class_Oless__eq(U_2388,U_2389,U_2390)
| ~ class_Orderings_Oorder(U_2388) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
! [U_2388,U_2390,U_2389] :
( c_Orderings_Oord__class_Oless(U_2388,U_2389,U_2390)
| U_2390 = U_2389
| ~ c_Orderings_Oord__class_Oless__eq(U_2388,U_2389,U_2390)
| ~ class_Orderings_Oorder(U_2388) ),
inference(definitional_conversion,[status(esa)],[f_453_2]) ).
cnf(f_453_4,plain,
( c_Orderings_Oord__class_Oless(U_2388,U_2389,U_2390)
| U_2390 = U_2389
| ~ c_Orderings_Oord__class_Oless__eq(U_2388,U_2389,U_2390)
| ~ class_Orderings_Oorder(U_2388) ),
inference(clausify,[status(thm)],[f_453_3]) ).
fof(f_454_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ 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_454_2,plain,
! [U_2394,U_2393,U_2392,U_2391] :
( c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2394)
| ~ c_Orderings_Oord__class_Oless__eq(U_2391,U_2393,U_2394)
| ~ c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2393)
| ~ class_Orderings_Opreorder(U_2391) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
! [U_2391,U_2393,U_2394,U_2392] :
( c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2394)
| ~ c_Orderings_Oord__class_Oless__eq(U_2391,U_2393,U_2394)
| ~ c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2393)
| ~ class_Orderings_Opreorder(U_2391) ),
inference(definitional_conversion,[status(esa)],[f_454_2]) ).
cnf(f_454_4,plain,
( c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2394)
| ~ c_Orderings_Oord__class_Oless__eq(U_2391,U_2393,U_2394)
| ~ c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2393)
| ~ class_Orderings_Opreorder(U_2391) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ 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_455_2,plain,
! [U_2398,U_2397,U_2396,U_2395] :
( c_Orderings_Oord__class_Oless(U_2395,U_2398,U_2397)
| ~ c_Orderings_Oord__class_Oless__eq(U_2395,U_2398,U_2396)
| ~ c_Orderings_Oord__class_Oless(U_2395,U_2396,U_2397)
| ~ class_Orderings_Oorder(U_2395) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
! [U_2395,U_2397,U_2398,U_2396] :
( c_Orderings_Oord__class_Oless(U_2395,U_2398,U_2397)
| ~ c_Orderings_Oord__class_Oless__eq(U_2395,U_2398,U_2396)
| ~ c_Orderings_Oord__class_Oless(U_2395,U_2396,U_2397)
| ~ class_Orderings_Oorder(U_2395) ),
inference(definitional_conversion,[status(esa)],[f_455_2]) ).
cnf(f_455_4,plain,
( c_Orderings_Oord__class_Oless(U_2395,U_2398,U_2397)
| ~ c_Orderings_Oord__class_Oless__eq(U_2395,U_2398,U_2396)
| ~ c_Orderings_Oord__class_Oless(U_2395,U_2396,U_2397)
| ~ class_Orderings_Oorder(U_2395) ),
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ 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_456_2,plain,
! [U_2402,U_2401,U_2400,U_2399] :
( c_Orderings_Oord__class_Oless(U_2399,U_2400,U_2402)
| ~ c_Orderings_Oord__class_Oless(U_2399,U_2401,U_2402)
| ~ c_Orderings_Oord__class_Oless__eq(U_2399,U_2400,U_2401)
| ~ class_Orderings_Opreorder(U_2399) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
! [U_2401,U_2399,U_2400,U_2402] :
( c_Orderings_Oord__class_Oless(U_2399,U_2400,U_2402)
| ~ c_Orderings_Oord__class_Oless(U_2399,U_2401,U_2402)
| ~ c_Orderings_Oord__class_Oless__eq(U_2399,U_2400,U_2401)
| ~ class_Orderings_Opreorder(U_2399) ),
inference(definitional_conversion,[status(esa)],[f_456_2]) ).
cnf(f_456_4,plain,
( c_Orderings_Oord__class_Oless(U_2399,U_2400,U_2402)
| ~ c_Orderings_Oord__class_Oless(U_2399,U_2401,U_2402)
| ~ c_Orderings_Oord__class_Oless__eq(U_2399,U_2400,U_2401)
| ~ class_Orderings_Opreorder(U_2399) ),
inference(clausify,[status(thm)],[f_456_3]) ).
fof(f_457_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ 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_457_2,plain,
! [U_2406,U_2405,U_2404,U_2403] :
( c_Orderings_Oord__class_Oless(U_2403,U_2406,U_2405)
| ~ c_Orderings_Oord__class_Oless(U_2403,U_2406,U_2404)
| ~ c_Orderings_Oord__class_Oless__eq(U_2403,U_2404,U_2405)
| ~ class_Orderings_Oorder(U_2403) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
! [U_2403,U_2405,U_2406,U_2404] :
( c_Orderings_Oord__class_Oless(U_2403,U_2406,U_2405)
| ~ c_Orderings_Oord__class_Oless(U_2403,U_2406,U_2404)
| ~ c_Orderings_Oord__class_Oless__eq(U_2403,U_2404,U_2405)
| ~ class_Orderings_Oorder(U_2403) ),
inference(definitional_conversion,[status(esa)],[f_457_2]) ).
cnf(f_457_4,plain,
( c_Orderings_Oord__class_Oless(U_2403,U_2406,U_2405)
| ~ c_Orderings_Oord__class_Oless(U_2403,U_2406,U_2404)
| ~ c_Orderings_Oord__class_Oless__eq(U_2403,U_2404,U_2405)
| ~ class_Orderings_Oorder(U_2403) ),
inference(clausify,[status(thm)],[f_457_3]) ).
fof(f_458_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| V_m_2 = V_n_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( ( V_m_2 != V_n_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
| ~ 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_458_2,plain,
! [U_2408,U_2407] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2407,U_2408)
| U_2407 = U_2408
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2407,U_2408) )
& ( ( U_2407 != U_2408
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2407,U_2408) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2407,U_2408) ) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
( ! [U_2412,U_2410] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2410,U_2412)
| U_2410 = U_2412
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2410,U_2412) )
& ! [U_2411,U_2409] :
( ( U_2409 != U_2411
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2409,U_2411) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2409,U_2411) ) ),
inference(miniscope,[status(thm)],[f_458_2]) ).
fof(f_458_4,plain,
( ! [U_2411,U_2409] :
( U_2409 != U_2411
| ~ sP140(U_2411,U_2409) )
& ! [U_2411,U_2409] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2409,U_2411)
| ~ sP140(U_2411,U_2409) )
& ! [U_2410,U_2412] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2410,U_2412)
| U_2410 = U_2412
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2410,U_2412) )
& ! [U_2411,U_2409] :
( sP140(U_2411,U_2409)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2409,U_2411) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_458_3]) ).
cnf(f_458_5,plain,
( sP140(U_2411,U_2409)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2409,U_2411) ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2410,U_2412)
| U_2410 = U_2412
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2410,U_2412) ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2409,U_2411)
| ~ sP140(U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_8,plain,
( U_2409 != U_2411
| ~ sP140(U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_458_4]) ).
fof(f_459_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ( V_m_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
& ( V_m_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ 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_459_2,plain,
! [U_2414,U_2413] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413,U_2414)
| ( U_2413 != U_2414
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2413,U_2414) ) )
& ( U_2413 = U_2414
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2413,U_2414)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413,U_2414) ) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
( ! [U_2418,U_2416] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2416,U_2418)
| ( U_2416 != U_2418
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2416,U_2418) ) )
& ! [U_2417,U_2415] :
( U_2415 = U_2417
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2415,U_2417)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2415,U_2417) ) ),
inference(miniscope,[status(thm)],[f_459_2]) ).
fof(f_459_4,plain,
( ! [U_2416,U_2418] :
( U_2416 != U_2418
| ~ sP141(U_2416,U_2418) )
& ! [U_2416,U_2418] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2416,U_2418)
| ~ sP141(U_2416,U_2418) )
& ! [U_2416,U_2418] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2416,U_2418)
| sP141(U_2416,U_2418) )
& ! [U_2415,U_2417] :
( U_2415 = U_2417
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2415,U_2417)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2415,U_2417) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_459_3]) ).
cnf(f_459_5,plain,
( U_2415 = U_2417
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2415,U_2417)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2415,U_2417) ),
inference(clausify,[status(thm)],[f_459_4]) ).
cnf(f_459_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2416,U_2418)
| sP141(U_2416,U_2418) ),
inference(clausify,[status(thm)],[f_459_4]) ).
cnf(f_459_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2416,U_2418)
| ~ sP141(U_2416,U_2418) ),
inference(clausify,[status(thm)],[f_459_4]) ).
cnf(f_459_8,plain,
( U_2416 != U_2418
| ~ sP141(U_2416,U_2418) ),
inference(clausify,[status(thm)],[f_459_4]) ).
fof(f_460_1,plain,
! [V_Pa_2,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
| ( ~ hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) )
| ( ~ hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
& V_m_2 = V_n_2 )
| ( ~ hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
& 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_460_2,plain,
! [U_2421,U_2420,U_2419] :
( hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| ( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2420,U_2419) )
| ( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
& U_2419 = U_2420 )
| ( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420) ) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
( ! [U_2419,U_2420,U_2421] :
( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| ~ sP144(U_2419,U_2420,U_2421) )
& ! [U_2419,U_2420,U_2421] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2420,U_2419)
| ~ sP144(U_2419,U_2420,U_2421) )
& ! [U_2419,U_2420,U_2421] :
( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| ~ sP143(U_2419,U_2420,U_2421) )
& ! [U_2419,U_2420,U_2421] :
( U_2419 = U_2420
| ~ sP143(U_2419,U_2420,U_2421) )
& ! [U_2419,U_2420,U_2421] :
( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| ~ sP142(U_2419,U_2420,U_2421) )
& ! [U_2419,U_2420,U_2421] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420)
| ~ sP142(U_2419,U_2420,U_2421) )
& ! [U_2419,U_2420,U_2421] :
( hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| sP144(U_2419,U_2420,U_2421)
| sP143(U_2419,U_2420,U_2421)
| sP142(U_2419,U_2420,U_2421) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142,sP143,sP144])],[f_460_2]) ).
cnf(f_460_4,plain,
( hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| sP144(U_2419,U_2420,U_2421)
| sP143(U_2419,U_2420,U_2421)
| sP142(U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420)
| ~ sP142(U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_6,plain,
( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| ~ sP142(U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_7,plain,
( U_2419 = U_2420
| ~ sP143(U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_8,plain,
( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| ~ sP143(U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2420,U_2419)
| ~ sP144(U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_10,plain,
( ~ hBOOL(hAPP(hAPP(U_2421,U_2420),U_2419))
| ~ sP144(U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [V_t,V_s] :
( V_s != V_t
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).
fof(f_461_2,plain,
! [U_2423,U_2422] :
( U_2422 != U_2423
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2422,U_2423) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
! [U_2422,U_2423] :
( U_2422 != U_2423
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2422,U_2423) ),
inference(definitional_conversion,[status(esa)],[f_461_2]) ).
cnf(f_461_4,plain,
( U_2422 != U_2423
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2422,U_2423) ),
inference(clausify,[status(thm)],[f_461_3]) ).
fof(f_462_1,plain,
! [V_m,V_n] :
( V_m != V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).
fof(f_462_2,plain,
! [U_2425,U_2424] :
( U_2425 != U_2424
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424,U_2425) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_2425,U_2424] :
( U_2425 != U_2424
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424,U_2425) ),
inference(definitional_conversion,[status(esa)],[f_462_2]) ).
cnf(f_462_4,plain,
( U_2425 != U_2424
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424,U_2425) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).
fof(f_463_2,plain,
! [U_2426] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2426,U_2426),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
! [U_2426] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2426,U_2426),
inference(definitional_conversion,[status(esa)],[f_463_2]) ).
cnf(f_463_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2426,U_2426),
inference(clausify,[status(thm)],[f_463_3]) ).
fof(f_464_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)
| 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_464_2,plain,
! [U_2428,U_2427] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2428,U_2427)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2427,U_2428)
| U_2427 = U_2428 ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
! [U_2427,U_2428] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2428,U_2427)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2427,U_2428)
| U_2427 = U_2428 ),
inference(definitional_conversion,[status(esa)],[f_464_2]) ).
cnf(f_464_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2428,U_2427)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2427,U_2428)
| U_2427 = U_2428 ),
inference(clausify,[status(thm)],[f_464_3]) ).
fof(f_465_1,plain,
! [V_n_2,V_m_2] :
( ( V_m_2 != V_n_2
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| 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_465_2,plain,
! [U_2430,U_2429] :
( ( U_2429 != U_2430
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2430,U_2429)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2429,U_2430) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2430,U_2429)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2429,U_2430)
| U_2429 = U_2430 ) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
( ! [U_2434,U_2432] :
( U_2432 != U_2434
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2434,U_2432)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2432,U_2434) ) )
& ! [U_2433,U_2431] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2433,U_2431)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2431,U_2433)
| U_2431 = U_2433 ) ),
inference(miniscope,[status(thm)],[f_465_2]) ).
fof(f_465_4,plain,
( ! [U_2434,U_2432] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2434,U_2432)
| ~ sP145(U_2434,U_2432) )
& ! [U_2434,U_2432] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2432,U_2434)
| ~ sP145(U_2434,U_2432) )
& ! [U_2434,U_2432] :
( U_2432 != U_2434
| sP145(U_2434,U_2432) )
& ! [U_2431,U_2433] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2433,U_2431)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2431,U_2433)
| U_2431 = U_2433 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145])],[f_465_3]) ).
cnf(f_465_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2433,U_2431)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2431,U_2433)
| U_2431 = U_2433 ),
inference(clausify,[status(thm)],[f_465_4]) ).
cnf(f_465_6,plain,
( U_2432 != U_2434
| sP145(U_2434,U_2432) ),
inference(clausify,[status(thm)],[f_465_4]) ).
cnf(f_465_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2432,U_2434)
| ~ sP145(U_2434,U_2432) ),
inference(clausify,[status(thm)],[f_465_4]) ).
cnf(f_465_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2434,U_2432)
| ~ sP145(U_2434,U_2432) ),
inference(clausify,[status(thm)],[f_465_4]) ).
fof(f_466_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).
fof(f_466_2,plain,
! [U_2435] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2435,U_2435),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
! [U_2435] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2435,U_2435),
inference(definitional_conversion,[status(esa)],[f_466_2]) ).
cnf(f_466_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2435,U_2435),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).
fof(f_467_2,plain,
! [U_2437,U_2436] :
( U_2436 = U_2437
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2437,U_2436)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2436,U_2437) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
! [U_2437,U_2436] :
( U_2436 = U_2437
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2437,U_2436)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2436,U_2437) ),
inference(definitional_conversion,[status(esa)],[f_467_2]) ).
cnf(f_467_4,plain,
( U_2436 = U_2437
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2437,U_2436)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2436,U_2437) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_le__trans]) ).
fof(f_468_2,plain,
! [U_2440,U_2439,U_2438] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2439,U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2439) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
! [U_2439,U_2440,U_2438] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2439,U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2439) ),
inference(definitional_conversion,[status(esa)],[f_468_2]) ).
cnf(f_468_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2439,U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2439) ),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_1,plain,
! [V_n,V_m] :
( 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_469_2,plain,
! [U_2442,U_2441] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2441,U_2442)
| U_2441 != U_2442 ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
! [U_2442,U_2441] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2441,U_2442)
| U_2441 != U_2442 ),
inference(definitional_conversion,[status(esa)],[f_469_2]) ).
cnf(f_469_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2441,U_2442)
| U_2441 != U_2442 ),
inference(clausify,[status(thm)],[f_469_3]) ).
fof(f_470_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).
fof(f_470_2,plain,
! [U_2444,U_2443] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2444,U_2443)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2443,U_2444) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
! [U_2444,U_2443] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2444,U_2443)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2443,U_2444) ),
inference(definitional_conversion,[status(esa)],[f_470_2]) ).
cnf(f_470_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2444,U_2443)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2443,U_2444) ),
inference(clausify,[status(thm)],[f_470_3]) ).
fof(f_471_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_le__refl]) ).
fof(f_471_2,plain,
! [U_2445] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2445,U_2445),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
! [U_2445] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2445,U_2445),
inference(definitional_conversion,[status(esa)],[f_471_2]) ).
cnf(f_471_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2445,U_2445),
inference(clausify,[status(thm)],[f_471_3]) ).
fof(f_472_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ( V_m != V_n
& ~ 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_472_2,plain,
! [U_2447,U_2446] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2446,U_2447)
| ( U_2446 != U_2447
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2446,U_2447) ) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
( ! [U_2446,U_2447] :
( U_2446 != U_2447
| ~ sP146(U_2446,U_2447) )
& ! [U_2446,U_2447] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2446,U_2447)
| ~ sP146(U_2446,U_2447) )
& ! [U_2446,U_2447] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2446,U_2447)
| sP146(U_2446,U_2447) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146])],[f_472_2]) ).
cnf(f_472_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2446,U_2447)
| sP146(U_2446,U_2447) ),
inference(clausify,[status(thm)],[f_472_3]) ).
cnf(f_472_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2446,U_2447)
| ~ sP146(U_2446,U_2447) ),
inference(clausify,[status(thm)],[f_472_3]) ).
cnf(f_472_6,plain,
( U_2446 != U_2447
| ~ sP146(U_2446,U_2447) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| V_m = V_n
| ~ 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_473_2,plain,
! [U_2449,U_2448] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2448,U_2449)
| U_2448 = U_2449
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2448,U_2449) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_2448,U_2449] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2448,U_2449)
| U_2448 = U_2449
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2448,U_2449) ),
inference(definitional_conversion,[status(esa)],[f_473_2]) ).
cnf(f_473_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2448,U_2449)
| U_2448 = U_2449
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2448,U_2449) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).
fof(f_474_2,plain,
! [U_2451,U_2450] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2450,U_2451)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2450,U_2451) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
! [U_2451,U_2450] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2450,U_2451)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2450,U_2451) ),
inference(definitional_conversion,[status(esa)],[f_474_2]) ).
cnf(f_474_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2450,U_2451)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2450,U_2451) ),
inference(clausify,[status(thm)],[f_474_3]) ).
fof(f_475_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]) ).
fof(f_475_2,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(definitional_conversion,[status(esa)],[f_475_1]) ).
cnf(f_475_3,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_475_2]) ).
fof(f_476_1,plain,
! [V_f_2,T_b,V_Pa_2,T_a] :
( c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_Pa_2),V_f_2))
| ~ c_FunDef_Oreduction__pair(T_a,V_Pa_2) ),
inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).
fof(f_476_2,plain,
! [U_2455,U_2454,U_2453,U_2452] :
( c_FunDef_Oreduction__pair(U_2454,hAPP(hAPP(c_FunDef_Orp__inv__image(U_2452,U_2454),U_2453),U_2455))
| ~ c_FunDef_Oreduction__pair(U_2452,U_2453) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_2452,U_2453,U_2454,U_2455] :
( c_FunDef_Oreduction__pair(U_2454,hAPP(hAPP(c_FunDef_Orp__inv__image(U_2452,U_2454),U_2453),U_2455))
| ~ c_FunDef_Oreduction__pair(U_2452,U_2453) ),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
( c_FunDef_Oreduction__pair(U_2454,hAPP(hAPP(c_FunDef_Orp__inv__image(U_2452,U_2454),U_2453),U_2455))
| ~ c_FunDef_Oreduction__pair(U_2452,U_2453) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [V_r_2,T_a] :
( c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2))
| ~ c_Wellfounded_Owf(T_a,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_min__ext__wf]) ).
fof(f_477_2,plain,
! [U_2457,U_2456] :
( c_Wellfounded_Owf(tc_fun(U_2456,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_2456,U_2457))
| ~ c_Wellfounded_Owf(U_2456,U_2457) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
! [U_2457,U_2456] :
( c_Wellfounded_Owf(tc_fun(U_2456,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_2456,U_2457))
| ~ c_Wellfounded_Owf(U_2456,U_2457) ),
inference(definitional_conversion,[status(esa)],[f_477_2]) ).
cnf(f_477_4,plain,
( c_Wellfounded_Owf(tc_fun(U_2456,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_2456,U_2457))
| ~ c_Wellfounded_Owf(U_2456,U_2457) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [V_S_2,V_R_2,T_a] :
( c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)
| ~ c_Wellfounded_Owf(T_a,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_reduction__pairI]) ).
fof(f_478_2,plain,
! [U_2460,U_2459,U_2458] :
( c_FunDef_Oreduction__pair(U_2458,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool),tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool)),U_2459),U_2460))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool),c_Relation_Orel__comp(U_2458,U_2458,U_2458,U_2459,U_2460),U_2459)
| ~ c_Wellfounded_Owf(U_2458,U_2459) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_2459,U_2458,U_2460] :
( c_FunDef_Oreduction__pair(U_2458,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool),tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool)),U_2459),U_2460))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool),c_Relation_Orel__comp(U_2458,U_2458,U_2458,U_2459,U_2460),U_2459)
| ~ c_Wellfounded_Owf(U_2458,U_2459) ),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
( c_FunDef_Oreduction__pair(U_2458,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool),tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool)),U_2459),U_2460))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2458,U_2458),tc_HOL_Obool),c_Relation_Orel__comp(U_2458,U_2458,U_2458,U_2459,U_2460),U_2459)
| ~ c_Wellfounded_Owf(U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(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_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),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)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))),
inference(fof_nnf,[status(thm)],[fact_rp__inv__image__def]) ).
fof(f_479_2,plain,
! [U_2462,U_2461] : c_FunDef_Orp__inv__image(U_2461,U_2462) = c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),c_COMBS(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(U_2462,U_2461)),c_Product__Type_OPair(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),c_Relation_Oinv__image(U_2461,U_2462))))),c_Relation_Oinv__image(U_2461,U_2462))),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
! [U_2462,U_2461] : c_FunDef_Orp__inv__image(U_2461,U_2462) = c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),c_COMBS(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(U_2462,U_2461)),c_Product__Type_OPair(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),c_Relation_Oinv__image(U_2461,U_2462))))),c_Relation_Oinv__image(U_2461,U_2462))),
inference(definitional_conversion,[status(esa)],[f_479_2]) ).
cnf(f_479_4,plain,
c_FunDef_Orp__inv__image(U_2461,U_2462) = c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),c_COMBS(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)),tc_fun(tc_fun(U_2462,U_2461),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),tc_fun(tc_prod(U_2461,U_2461),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool))),tc_fun(U_2462,U_2461)),c_Product__Type_OPair(tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool),tc_fun(tc_prod(U_2462,U_2462),tc_HOL_Obool)))),c_Relation_Oinv__image(U_2461,U_2462))))),c_Relation_Oinv__image(U_2461,U_2462))),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [V_s_2,V_ca_2,T_c,V_r_2,V_ba_2,V_aa_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_aa_2),V_ca_2)),c_Relation_Orel__comp(T_a,T_b,T_c,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_ba_2),V_ca_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_rel__compI]) ).
fof(f_480_2,plain,
! [U_2470,U_2469,U_2468,U_2467,U_2466,U_2465,U_2464,U_2463] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2463,U_2468)),hAPP(hAPP(c_Product__Type_OPair(U_2463,U_2468),U_2465),U_2469)),c_Relation_Orel__comp(U_2463,U_2464,U_2468,U_2467,U_2470)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2464,U_2468)),hAPP(hAPP(c_Product__Type_OPair(U_2464,U_2468),U_2466),U_2469)),U_2470))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2463,U_2464)),hAPP(hAPP(c_Product__Type_OPair(U_2463,U_2464),U_2465),U_2466)),U_2467)) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
! [U_2463,U_2464,U_2465,U_2466,U_2467,U_2468,U_2469,U_2470] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2463,U_2468)),hAPP(hAPP(c_Product__Type_OPair(U_2463,U_2468),U_2465),U_2469)),c_Relation_Orel__comp(U_2463,U_2464,U_2468,U_2467,U_2470)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2464,U_2468)),hAPP(hAPP(c_Product__Type_OPair(U_2464,U_2468),U_2466),U_2469)),U_2470))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2463,U_2464)),hAPP(hAPP(c_Product__Type_OPair(U_2463,U_2464),U_2465),U_2466)),U_2467)) ),
inference(definitional_conversion,[status(esa)],[f_480_2]) ).
cnf(f_480_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2463,U_2468)),hAPP(hAPP(c_Product__Type_OPair(U_2463,U_2468),U_2465),U_2469)),c_Relation_Orel__comp(U_2463,U_2464,U_2468,U_2467,U_2470)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2464,U_2468)),hAPP(hAPP(c_Product__Type_OPair(U_2464,U_2468),U_2466),U_2469)),U_2470))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2463,U_2464)),hAPP(hAPP(c_Product__Type_OPair(U_2463,U_2464),U_2465),U_2466)),U_2467)) ),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_1,plain,
! [V_f_2,T_c,T_b,T_a] : c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_split__eta]) ).
fof(f_481_2,plain,
! [U_2474,U_2473,U_2472,U_2471] : c_Product__Type_Oprod_Oprod__case(U_2471,U_2472,U_2473,hAPP(hAPP(c_COMBB(tc_fun(U_2472,tc_prod(U_2471,U_2472)),tc_fun(U_2472,U_2473),U_2471),hAPP(c_COMBB(tc_prod(U_2471,U_2472),U_2473,U_2472),U_2474)),c_Product__Type_OPair(U_2471,U_2472))) = U_2474,
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
! [U_2473,U_2471,U_2472,U_2474] : c_Product__Type_Oprod_Oprod__case(U_2471,U_2472,U_2473,hAPP(hAPP(c_COMBB(tc_fun(U_2472,tc_prod(U_2471,U_2472)),tc_fun(U_2472,U_2473),U_2471),hAPP(c_COMBB(tc_prod(U_2471,U_2472),U_2473,U_2472),U_2474)),c_Product__Type_OPair(U_2471,U_2472))) = U_2474,
inference(definitional_conversion,[status(esa)],[f_481_2]) ).
cnf(f_481_4,plain,
c_Product__Type_Oprod_Oprod__case(U_2471,U_2472,U_2473,hAPP(hAPP(c_COMBB(tc_fun(U_2472,tc_prod(U_2471,U_2472)),tc_fun(U_2472,U_2473),U_2471),hAPP(c_COMBB(tc_prod(U_2471,U_2472),U_2473,U_2472),U_2474)),c_Product__Type_OPair(U_2471,U_2472))) = U_2474,
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [V_ba_2,V_aa_2,V_f1_2,T_a,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2),
inference(fof_nnf,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(f_482_2,plain,
! [U_2480,U_2479,U_2478,U_2477,U_2476,U_2475] : hAPP(c_Product__Type_Oprod_Oprod__case(U_2475,U_2476,U_2477,U_2478),hAPP(hAPP(c_Product__Type_OPair(U_2475,U_2476),U_2479),U_2480)) = hAPP(hAPP(U_2478,U_2479),U_2480),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
! [U_2475,U_2476,U_2477,U_2478,U_2479,U_2480] : hAPP(c_Product__Type_Oprod_Oprod__case(U_2475,U_2476,U_2477,U_2478),hAPP(hAPP(c_Product__Type_OPair(U_2475,U_2476),U_2479),U_2480)) = hAPP(hAPP(U_2478,U_2479),U_2480),
inference(definitional_conversion,[status(esa)],[f_482_2]) ).
cnf(f_482_4,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_2475,U_2476,U_2477,U_2478),hAPP(hAPP(c_Product__Type_OPair(U_2475,U_2476),U_2479),U_2480)) = hAPP(hAPP(U_2478,U_2479),U_2480),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_1,plain,
! [V_ba_2,V_aa_2,V_f_2,T_a,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f_2,V_aa_2),V_ba_2),
inference(fof_nnf,[status(thm)],[fact_split__conv]) ).
fof(f_483_2,plain,
! [U_2486,U_2485,U_2484,U_2483,U_2482,U_2481] : hAPP(c_Product__Type_Oprod_Oprod__case(U_2481,U_2482,U_2483,U_2484),hAPP(hAPP(c_Product__Type_OPair(U_2481,U_2482),U_2485),U_2486)) = hAPP(hAPP(U_2484,U_2485),U_2486),
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
! [U_2481,U_2482,U_2483,U_2484,U_2485,U_2486] : hAPP(c_Product__Type_Oprod_Oprod__case(U_2481,U_2482,U_2483,U_2484),hAPP(hAPP(c_Product__Type_OPair(U_2481,U_2482),U_2485),U_2486)) = hAPP(hAPP(U_2484,U_2485),U_2486),
inference(definitional_conversion,[status(esa)],[f_483_2]) ).
cnf(f_483_4,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_2481,U_2482,U_2483,U_2484),hAPP(hAPP(c_Product__Type_OPair(U_2481,U_2482),U_2485),U_2486)) = hAPP(hAPP(U_2484,U_2485),U_2486),
inference(clausify,[status(thm)],[f_483_3]) ).
fof(f_484_1,plain,
! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2),
inference(fof_nnf,[status(thm)],[fact_trancl__unfold__right]) ).
fof(f_484_2,plain,
! [U_2488,U_2487] : c_Transitive__Closure_Otrancl(U_2487,U_2488) = c_Relation_Orel__comp(U_2487,U_2487,U_2487,c_Transitive__Closure_Ortrancl(U_2487,U_2488),U_2488),
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
! [U_2488,U_2487] : c_Transitive__Closure_Otrancl(U_2487,U_2488) = c_Relation_Orel__comp(U_2487,U_2487,U_2487,c_Transitive__Closure_Ortrancl(U_2487,U_2488),U_2488),
inference(definitional_conversion,[status(esa)],[f_484_2]) ).
cnf(f_484_4,plain,
c_Transitive__Closure_Otrancl(U_2487,U_2488) = c_Relation_Orel__comp(U_2487,U_2487,U_2487,c_Transitive__Closure_Ortrancl(U_2487,U_2488),U_2488),
inference(clausify,[status(thm)],[f_484_3]) ).
fof(f_485_1,plain,
! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_trancl__unfold__left]) ).
fof(f_485_2,plain,
! [U_2490,U_2489] : c_Transitive__Closure_Otrancl(U_2489,U_2490) = c_Relation_Orel__comp(U_2489,U_2489,U_2489,U_2490,c_Transitive__Closure_Ortrancl(U_2489,U_2490)),
inference(variable_rename,[status(thm)],[f_485_1]) ).
fof(f_485_3,plain,
! [U_2490,U_2489] : c_Transitive__Closure_Otrancl(U_2489,U_2490) = c_Relation_Orel__comp(U_2489,U_2489,U_2489,U_2490,c_Transitive__Closure_Ortrancl(U_2489,U_2490)),
inference(definitional_conversion,[status(esa)],[f_485_2]) ).
cnf(f_485_4,plain,
c_Transitive__Closure_Otrancl(U_2489,U_2490) = c_Relation_Orel__comp(U_2489,U_2489,U_2489,U_2490,c_Transitive__Closure_Ortrancl(U_2489,U_2490)),
inference(clausify,[status(thm)],[f_485_3]) ).
fof(f_486_1,plain,
! [V_r_2,T_a] : c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2),
inference(fof_nnf,[status(thm)],[fact_r__comp__rtrancl__eq]) ).
fof(f_486_2,plain,
! [U_2492,U_2491] : c_Relation_Orel__comp(U_2491,U_2491,U_2491,U_2492,c_Transitive__Closure_Ortrancl(U_2491,U_2492)) = c_Relation_Orel__comp(U_2491,U_2491,U_2491,c_Transitive__Closure_Ortrancl(U_2491,U_2492),U_2492),
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
! [U_2491,U_2492] : c_Relation_Orel__comp(U_2491,U_2491,U_2491,U_2492,c_Transitive__Closure_Ortrancl(U_2491,U_2492)) = c_Relation_Orel__comp(U_2491,U_2491,U_2491,c_Transitive__Closure_Ortrancl(U_2491,U_2492),U_2492),
inference(definitional_conversion,[status(esa)],[f_486_2]) ).
cnf(f_486_4,plain,
c_Relation_Orel__comp(U_2491,U_2491,U_2491,U_2492,c_Transitive__Closure_Ortrancl(U_2491,U_2492)) = c_Relation_Orel__comp(U_2491,U_2491,U_2491,c_Transitive__Closure_Ortrancl(U_2491,U_2492),U_2492),
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_1,plain,
! [V_R_2,T_a] : c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).
fof(f_487_2,plain,
! [U_2494,U_2493] : c_Relation_Orel__comp(U_2493,U_2493,U_2493,c_Transitive__Closure_Ortrancl(U_2493,U_2494),c_Transitive__Closure_Ortrancl(U_2493,U_2494)) = c_Transitive__Closure_Ortrancl(U_2493,U_2494),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
! [U_2493,U_2494] : c_Relation_Orel__comp(U_2493,U_2493,U_2493,c_Transitive__Closure_Ortrancl(U_2493,U_2494),c_Transitive__Closure_Ortrancl(U_2493,U_2494)) = c_Transitive__Closure_Ortrancl(U_2493,U_2494),
inference(definitional_conversion,[status(esa)],[f_487_2]) ).
cnf(f_487_4,plain,
c_Relation_Orel__comp(U_2493,U_2493,U_2493,c_Transitive__Closure_Ortrancl(U_2493,U_2494),c_Transitive__Closure_Ortrancl(U_2493,U_2494)) = c_Transitive__Closure_Ortrancl(U_2493,U_2494),
inference(clausify,[status(thm)],[f_487_3]) ).
fof(f_488_1,plain,
! [V_s_2,T_c,V_r_2,T_b,T_a] :
( c_Relation_Osingle__valued(T_a,T_c,c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2))
| ~ c_Relation_Osingle__valued(T_b,T_c,V_s_2)
| ~ c_Relation_Osingle__valued(T_a,T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp]) ).
fof(f_488_2,plain,
! [U_2499,U_2498,U_2497,U_2496,U_2495] :
( c_Relation_Osingle__valued(U_2495,U_2498,c_Relation_Orel__comp(U_2495,U_2496,U_2498,U_2497,U_2499))
| ~ c_Relation_Osingle__valued(U_2496,U_2498,U_2499)
| ~ c_Relation_Osingle__valued(U_2495,U_2496,U_2497) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
! [U_2495,U_2496,U_2497,U_2498,U_2499] :
( c_Relation_Osingle__valued(U_2495,U_2498,c_Relation_Orel__comp(U_2495,U_2496,U_2498,U_2497,U_2499))
| ~ c_Relation_Osingle__valued(U_2496,U_2498,U_2499)
| ~ c_Relation_Osingle__valued(U_2495,U_2496,U_2497) ),
inference(definitional_conversion,[status(esa)],[f_488_2]) ).
cnf(f_488_4,plain,
( c_Relation_Osingle__valued(U_2495,U_2498,c_Relation_Orel__comp(U_2495,U_2496,U_2498,U_2497,U_2499))
| ~ c_Relation_Osingle__valued(U_2496,U_2498,U_2499)
| ~ c_Relation_Osingle__valued(U_2495,U_2496,U_2497) ),
inference(clausify,[status(thm)],[f_488_3]) ).
fof(f_489_1,plain,
! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] :
( hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,V_ca_2),V_p_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,V_ca_2),V_q_2)
| V_p_2 != V_q_2 ),
inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).
fof(f_489_2,plain,
! [U_2505,U_2504,U_2503,U_2502,U_2501,U_2500] :
( hAPP(c_Product__Type_Oprod_Oprod__case(U_2502,U_2503,U_2504,U_2505),U_2500) = hAPP(c_Product__Type_Oprod_Oprod__case(U_2502,U_2503,U_2504,U_2505),U_2501)
| U_2500 != U_2501 ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
! [U_2502,U_2501,U_2500,U_2503,U_2504,U_2505] :
( hAPP(c_Product__Type_Oprod_Oprod__case(U_2502,U_2503,U_2504,U_2505),U_2500) = hAPP(c_Product__Type_Oprod_Oprod__case(U_2502,U_2503,U_2504,U_2505),U_2501)
| U_2500 != U_2501 ),
inference(definitional_conversion,[status(esa)],[f_489_2]) ).
cnf(f_489_4,plain,
( hAPP(c_Product__Type_Oprod_Oprod__case(U_2502,U_2503,U_2504,U_2505),U_2500) = hAPP(c_Product__Type_Oprod_Oprod__case(U_2502,U_2503,U_2504,U_2505),U_2501)
| U_2500 != U_2501 ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_1,plain,
! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c),V_g_2),V_p_2)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a,V_f_2))),V_g_2)),V_p_2),
inference(fof_nnf,[status(thm)],[fact_split__twice]) ).
fof(f_490_2,plain,
! [U_2513,U_2512,U_2511,U_2510,U_2509,U_2508,U_2507,U_2506] : hAPP(c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508,U_2509),hAPP(c_Product__Type_Oprod_Oprod__case(U_2510,U_2511,tc_prod(U_2506,U_2507),U_2512),U_2513)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_2510,U_2511,U_2508,hAPP(hAPP(c_COMBB(tc_fun(U_2511,tc_prod(U_2506,U_2507)),tc_fun(U_2511,U_2508),U_2510),hAPP(c_COMBB(tc_prod(U_2506,U_2507),U_2508,U_2511),c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508,U_2509))),U_2512)),U_2513),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
! [U_2506,U_2507,U_2508,U_2509,U_2510,U_2511,U_2512,U_2513] : hAPP(c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508,U_2509),hAPP(c_Product__Type_Oprod_Oprod__case(U_2510,U_2511,tc_prod(U_2506,U_2507),U_2512),U_2513)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_2510,U_2511,U_2508,hAPP(hAPP(c_COMBB(tc_fun(U_2511,tc_prod(U_2506,U_2507)),tc_fun(U_2511,U_2508),U_2510),hAPP(c_COMBB(tc_prod(U_2506,U_2507),U_2508,U_2511),c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508,U_2509))),U_2512)),U_2513),
inference(definitional_conversion,[status(esa)],[f_490_2]) ).
cnf(f_490_4,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508,U_2509),hAPP(c_Product__Type_Oprod_Oprod__case(U_2510,U_2511,tc_prod(U_2506,U_2507),U_2512),U_2513)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_2510,U_2511,U_2508,hAPP(hAPP(c_COMBB(tc_fun(U_2511,tc_prod(U_2506,U_2507)),tc_fun(U_2511,U_2508),U_2510),hAPP(c_COMBB(tc_prod(U_2506,U_2507),U_2508,U_2511),c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508,U_2509))),U_2512)),U_2513),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_1,plain,
! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : c_Relation_Orel__comp(T_a,T_c,T_b,c_Relation_Orel__comp(T_a,T_d,T_c,V_R_2,V_S_2),V_T_2) = c_Relation_Orel__comp(T_a,T_d,T_b,V_R_2,c_Relation_Orel__comp(T_d,T_c,T_b,V_S_2,V_T_2)),
inference(fof_nnf,[status(thm)],[fact_O__assoc]) ).
fof(f_491_2,plain,
! [U_2520,U_2519,U_2518,U_2517,U_2516,U_2515,U_2514] : c_Relation_Orel__comp(U_2514,U_2515,U_2516,c_Relation_Orel__comp(U_2514,U_2517,U_2515,U_2518,U_2519),U_2520) = c_Relation_Orel__comp(U_2514,U_2517,U_2516,U_2518,c_Relation_Orel__comp(U_2517,U_2515,U_2516,U_2519,U_2520)),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
! [U_2516,U_2515,U_2514,U_2517,U_2518,U_2519,U_2520] : c_Relation_Orel__comp(U_2514,U_2515,U_2516,c_Relation_Orel__comp(U_2514,U_2517,U_2515,U_2518,U_2519),U_2520) = c_Relation_Orel__comp(U_2514,U_2517,U_2516,U_2518,c_Relation_Orel__comp(U_2517,U_2515,U_2516,U_2519,U_2520)),
inference(definitional_conversion,[status(esa)],[f_491_2]) ).
cnf(f_491_4,plain,
c_Relation_Orel__comp(U_2514,U_2515,U_2516,c_Relation_Orel__comp(U_2514,U_2517,U_2515,U_2518,U_2519),U_2520) = c_Relation_Orel__comp(U_2514,U_2517,U_2516,U_2518,c_Relation_Orel__comp(U_2517,U_2515,U_2516,U_2519,U_2520)),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_1,plain,
! [V_f_2,T_c,T_b,T_a] : c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,c_Product__Type_Ocurry(T_a,T_b,T_c,V_f_2)) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_split__curry]) ).
fof(f_492_2,plain,
! [U_2524,U_2523,U_2522,U_2521] : c_Product__Type_Oprod_Oprod__case(U_2521,U_2522,U_2523,c_Product__Type_Ocurry(U_2521,U_2522,U_2523,U_2524)) = U_2524,
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
! [U_2521,U_2523,U_2522,U_2524] : c_Product__Type_Oprod_Oprod__case(U_2521,U_2522,U_2523,c_Product__Type_Ocurry(U_2521,U_2522,U_2523,U_2524)) = U_2524,
inference(definitional_conversion,[status(esa)],[f_492_2]) ).
cnf(f_492_4,plain,
c_Product__Type_Oprod_Oprod__case(U_2521,U_2522,U_2523,c_Product__Type_Ocurry(U_2521,U_2522,U_2523,U_2524)) = U_2524,
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [V_f_2,T_c,T_b,T_a] : c_Product__Type_Ocurry(T_a,T_b,T_c,c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c,V_f_2)) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_curry__split]) ).
fof(f_493_2,plain,
! [U_2528,U_2527,U_2526,U_2525] : c_Product__Type_Ocurry(U_2525,U_2526,U_2527,c_Product__Type_Oprod_Oprod__case(U_2525,U_2526,U_2527,U_2528)) = U_2528,
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
! [U_2525,U_2527,U_2526,U_2528] : c_Product__Type_Ocurry(U_2525,U_2526,U_2527,c_Product__Type_Oprod_Oprod__case(U_2525,U_2526,U_2527,U_2528)) = U_2528,
inference(definitional_conversion,[status(esa)],[f_493_2]) ).
cnf(f_493_4,plain,
c_Product__Type_Ocurry(U_2525,U_2526,U_2527,c_Product__Type_Oprod_Oprod__case(U_2525,U_2526,U_2527,U_2528)) = U_2528,
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_1,plain,
! [V_R_2,T_a] :
( ( c_Wellfounded_Owf(T_a,V_R_2)
| ~ c_Wellfounded_Owf(T_a,c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2)) )
& ( c_Wellfounded_Owf(T_a,c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2))
| ~ c_Wellfounded_Owf(T_a,V_R_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__comp__self]) ).
fof(f_494_2,plain,
! [U_2530,U_2529] :
( ( c_Wellfounded_Owf(U_2529,U_2530)
| ~ c_Wellfounded_Owf(U_2529,c_Relation_Orel__comp(U_2529,U_2529,U_2529,U_2530,U_2530)) )
& ( c_Wellfounded_Owf(U_2529,c_Relation_Orel__comp(U_2529,U_2529,U_2529,U_2530,U_2530))
| ~ c_Wellfounded_Owf(U_2529,U_2530) ) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
( ! [U_2534,U_2532] :
( c_Wellfounded_Owf(U_2532,U_2534)
| ~ c_Wellfounded_Owf(U_2532,c_Relation_Orel__comp(U_2532,U_2532,U_2532,U_2534,U_2534)) )
& ! [U_2533,U_2531] :
( c_Wellfounded_Owf(U_2531,c_Relation_Orel__comp(U_2531,U_2531,U_2531,U_2533,U_2533))
| ~ c_Wellfounded_Owf(U_2531,U_2533) ) ),
inference(miniscope,[status(thm)],[f_494_2]) ).
fof(f_494_4,plain,
( ! [U_2532,U_2534] :
( c_Wellfounded_Owf(U_2532,U_2534)
| ~ c_Wellfounded_Owf(U_2532,c_Relation_Orel__comp(U_2532,U_2532,U_2532,U_2534,U_2534)) )
& ! [U_2531,U_2533] :
( c_Wellfounded_Owf(U_2531,c_Relation_Orel__comp(U_2531,U_2531,U_2531,U_2533,U_2533))
| ~ c_Wellfounded_Owf(U_2531,U_2533) ) ),
inference(definitional_conversion,[status(esa)],[f_494_3]) ).
cnf(f_494_5,plain,
( c_Wellfounded_Owf(U_2531,c_Relation_Orel__comp(U_2531,U_2531,U_2531,U_2533,U_2533))
| ~ c_Wellfounded_Owf(U_2531,U_2533) ),
inference(clausify,[status(thm)],[f_494_4]) ).
cnf(f_494_6,plain,
( c_Wellfounded_Owf(U_2532,U_2534)
| ~ c_Wellfounded_Owf(U_2532,c_Relation_Orel__comp(U_2532,U_2532,U_2532,U_2534,U_2534)) ),
inference(clausify,[status(thm)],[f_494_4]) ).
fof(f_495_1,plain,
! [T_2,T_1] :
( class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf]) ).
fof(f_495_2,plain,
! [U_2536,U_2535] :
( class_Lattices_Osemilattice__inf(tc_fun(U_2536,U_2535))
| ~ class_Lattices_Olattice(U_2535) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
! [U_2535,U_2536] :
( class_Lattices_Osemilattice__inf(tc_fun(U_2536,U_2535))
| ~ class_Lattices_Olattice(U_2535) ),
inference(definitional_conversion,[status(esa)],[f_495_2]) ).
cnf(f_495_4,plain,
( class_Lattices_Osemilattice__inf(tc_fun(U_2536,U_2535))
| ~ class_Lattices_Olattice(U_2535) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_1,plain,
! [T_2,T_1] :
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder]) ).
fof(f_496_2,plain,
! [U_2538,U_2537] :
( class_Orderings_Opreorder(tc_fun(U_2538,U_2537))
| ~ class_Orderings_Opreorder(U_2537) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
! [U_2538,U_2537] :
( class_Orderings_Opreorder(tc_fun(U_2538,U_2537))
| ~ class_Orderings_Opreorder(U_2537) ),
inference(definitional_conversion,[status(esa)],[f_496_2]) ).
cnf(f_496_4,plain,
( class_Orderings_Opreorder(tc_fun(U_2538,U_2537))
| ~ class_Orderings_Opreorder(U_2537) ),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_1,plain,
! [T_2,T_1] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice]) ).
fof(f_497_2,plain,
! [U_2540,U_2539] :
( class_Lattices_Olattice(tc_fun(U_2540,U_2539))
| ~ class_Lattices_Olattice(U_2539) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
! [U_2540,U_2539] :
( class_Lattices_Olattice(tc_fun(U_2540,U_2539))
| ~ class_Lattices_Olattice(U_2539) ),
inference(definitional_conversion,[status(esa)],[f_497_2]) ).
cnf(f_497_4,plain,
( class_Lattices_Olattice(tc_fun(U_2540,U_2539))
| ~ class_Lattices_Olattice(U_2539) ),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_1,plain,
! [T_2,T_1] :
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder]) ).
fof(f_498_2,plain,
! [U_2542,U_2541] :
( class_Orderings_Oorder(tc_fun(U_2542,U_2541))
| ~ class_Orderings_Oorder(U_2541) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
! [U_2542,U_2541] :
( class_Orderings_Oorder(tc_fun(U_2542,U_2541))
| ~ class_Orderings_Oorder(U_2541) ),
inference(definitional_conversion,[status(esa)],[f_498_2]) ).
cnf(f_498_4,plain,
( class_Orderings_Oorder(tc_fun(U_2542,U_2541))
| ~ class_Orderings_Oorder(U_2541) ),
inference(clausify,[status(thm)],[f_498_3]) ).
fof(f_499_1,plain,
! [T_2,T_1] :
( class_Orderings_Oord(tc_fun(T_2,T_1))
| ~ class_Orderings_Oord(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord]) ).
fof(f_499_2,plain,
! [U_2544,U_2543] :
( class_Orderings_Oord(tc_fun(U_2544,U_2543))
| ~ class_Orderings_Oord(U_2543) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
! [U_2543,U_2544] :
( class_Orderings_Oord(tc_fun(U_2544,U_2543))
| ~ class_Orderings_Oord(U_2543) ),
inference(definitional_conversion,[status(esa)],[f_499_2]) ).
cnf(f_499_4,plain,
( class_Orderings_Oord(tc_fun(U_2544,U_2543))
| ~ class_Orderings_Oord(U_2543) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]) ).
fof(f_500_2,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_500_1]) ).
cnf(f_500_3,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_500_2]) ).
fof(f_501_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(f_501_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_501_1]) ).
cnf(f_501_3,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_501_2]) ).
fof(f_502_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(f_502_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_502_1]) ).
cnf(f_502_3,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_502_2]) ).
fof(f_503_1,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]) ).
fof(f_503_2,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_503_1]) ).
cnf(f_503_3,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_503_2]) ).
fof(f_504_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
fof(f_504_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_504_1]) ).
cnf(f_504_3,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
fof(f_505_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_505_1]) ).
cnf(f_505_3,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_1,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]) ).
fof(f_506_2,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_506_1]) ).
cnf(f_506_3,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
fof(f_507_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_507_1]) ).
cnf(f_507_3,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_1,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]) ).
fof(f_508_2,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_508_1]) ).
cnf(f_508_3,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
fof(f_509_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_509_1]) ).
cnf(f_509_3,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
fof(f_510_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_510_1]) ).
cnf(f_510_3,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_510_2]) ).
fof(f_511_1,plain,
! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
inference(fof_nnf,[status(thm)],[help_c__COMBI__1]) ).
fof(f_511_2,plain,
! [U_2546,U_2545] : hAPP(c_COMBI(U_2545),U_2546) = U_2546,
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_2545,U_2546] : hAPP(c_COMBI(U_2545),U_2546) = U_2546,
inference(definitional_conversion,[status(esa)],[f_511_2]) ).
cnf(f_511_4,plain,
hAPP(c_COMBI(U_2545),U_2546) = U_2546,
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_1,plain,
! [V_Q,V_P,T_b,T_a] : hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P,
inference(fof_nnf,[status(thm)],[help_c__COMBK__1]) ).
fof(f_512_2,plain,
! [U_2550,U_2549,U_2548,U_2547] : hAPP(c_COMBK(U_2547,U_2548,U_2549),U_2550) = U_2549,
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_2547,U_2548,U_2549,U_2550] : hAPP(c_COMBK(U_2547,U_2548,U_2549),U_2550) = U_2549,
inference(definitional_conversion,[status(esa)],[f_512_2]) ).
cnf(f_512_4,plain,
hAPP(c_COMBK(U_2547,U_2548,U_2549),U_2550) = U_2549,
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_1,plain,
! [V_R_2,V_Q_2,V_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)),
inference(fof_nnf,[status(thm)],[help_c__COMBB__1]) ).
fof(f_513_2,plain,
! [U_2556,U_2555,U_2554,U_2553,U_2552,U_2551] : hAPP(hAPP(hAPP(c_COMBB(U_2551,U_2552,U_2553),U_2554),U_2555),U_2556) = hAPP(U_2554,hAPP(U_2555,U_2556)),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
! [U_2551,U_2552,U_2553,U_2554,U_2555,U_2556] : hAPP(hAPP(hAPP(c_COMBB(U_2551,U_2552,U_2553),U_2554),U_2555),U_2556) = hAPP(U_2554,hAPP(U_2555,U_2556)),
inference(definitional_conversion,[status(esa)],[f_513_2]) ).
cnf(f_513_4,plain,
hAPP(hAPP(hAPP(c_COMBB(U_2551,U_2552,U_2553),U_2554),U_2555),U_2556) = hAPP(U_2554,hAPP(U_2555,U_2556)),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_1,plain,
! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2),
inference(fof_nnf,[status(thm)],[help_c__COMBC__1]) ).
fof(f_514_2,plain,
! [U_2562,U_2561,U_2560,U_2559,U_2558,U_2557] : hAPP(hAPP(hAPP(c_COMBC(U_2557,U_2558,U_2559),U_2560),U_2561),U_2562) = hAPP(hAPP(U_2560,U_2562),U_2561),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_2558,U_2559,U_2560,U_2561,U_2562,U_2557] : hAPP(hAPP(hAPP(c_COMBC(U_2557,U_2558,U_2559),U_2560),U_2561),U_2562) = hAPP(hAPP(U_2560,U_2562),U_2561),
inference(definitional_conversion,[status(esa)],[f_514_2]) ).
cnf(f_514_4,plain,
hAPP(hAPP(hAPP(c_COMBC(U_2557,U_2558,U_2559),U_2560),U_2561),U_2562) = hAPP(hAPP(U_2560,U_2562),U_2561),
inference(clausify,[status(thm)],[f_514_3]) ).
fof(f_515_1,plain,
! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)),
inference(fof_nnf,[status(thm)],[help_c__COMBS__1]) ).
fof(f_515_2,plain,
! [U_2568,U_2567,U_2566,U_2565,U_2564,U_2563] : hAPP(hAPP(hAPP(c_COMBS(U_2563,U_2564,U_2565),U_2566),U_2567),U_2568) = hAPP(hAPP(U_2566,U_2568),hAPP(U_2567,U_2568)),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_2563,U_2564,U_2565,U_2566,U_2567,U_2568] : hAPP(hAPP(hAPP(c_COMBS(U_2563,U_2564,U_2565),U_2566),U_2567),U_2568) = hAPP(hAPP(U_2566,U_2568),hAPP(U_2567,U_2568)),
inference(definitional_conversion,[status(esa)],[f_515_2]) ).
cnf(f_515_4,plain,
hAPP(hAPP(hAPP(c_COMBS(U_2563,U_2564,U_2565),U_2566),U_2567),U_2568) = hAPP(hAPP(U_2566,U_2568),hAPP(U_2567,U_2568)),
inference(clausify,[status(thm)],[f_515_3]) ).
fof(f_516_1,plain,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[help_c__fequal__1]) ).
fof(f_516_2,plain,
! [U_2570,U_2569] :
( U_2569 = U_2570
| ~ hBOOL(hAPP(hAPP(c_fequal,U_2569),U_2570)) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_2569,U_2570] :
( U_2569 = U_2570
| ~ hBOOL(hAPP(hAPP(c_fequal,U_2569),U_2570)) ),
inference(definitional_conversion,[status(esa)],[f_516_2]) ).
cnf(f_516_4,plain,
( U_2569 = U_2570
| ~ hBOOL(hAPP(hAPP(c_fequal,U_2569),U_2570)) ),
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_1,plain,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
| V_x_2 != V_y_2 ),
inference(fof_nnf,[status(thm)],[help_c__fequal__2]) ).
fof(f_517_2,plain,
! [U_2572,U_2571] :
( hBOOL(hAPP(hAPP(c_fequal,U_2571),U_2572))
| U_2571 != U_2572 ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
! [U_2571,U_2572] :
( hBOOL(hAPP(hAPP(c_fequal,U_2571),U_2572))
| U_2571 != U_2572 ),
inference(definitional_conversion,[status(esa)],[f_517_2]) ).
cnf(f_517_4,plain,
( hBOOL(hAPP(hAPP(c_fequal,U_2571),U_2572))
| U_2571 != U_2572 ),
inference(clausify,[status(thm)],[f_517_3]) ).
fof(f_518_1,plain,
~ hBOOL(c_fFalse),
inference(fof_nnf,[status(thm)],[help_c__fFalse__1]) ).
fof(f_518_2,plain,
~ hBOOL(c_fFalse),
inference(definitional_conversion,[status(esa)],[f_518_1]) ).
cnf(f_518_3,plain,
~ hBOOL(c_fFalse),
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_1,plain,
! [V_Pa_2] :
( ~ hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(c_fNot,V_Pa_2)) ),
inference(fof_nnf,[status(thm)],[help_c__fNot__1]) ).
fof(f_519_2,plain,
! [U_2573] :
( ~ hBOOL(U_2573)
| ~ hBOOL(hAPP(c_fNot,U_2573)) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
! [U_2573] :
( ~ hBOOL(U_2573)
| ~ hBOOL(hAPP(c_fNot,U_2573)) ),
inference(definitional_conversion,[status(esa)],[f_519_2]) ).
cnf(f_519_4,plain,
( ~ hBOOL(U_2573)
| ~ hBOOL(hAPP(c_fNot,U_2573)) ),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_1,plain,
! [V_Pa_2] :
( hBOOL(hAPP(c_fNot,V_Pa_2))
| hBOOL(V_Pa_2) ),
inference(fof_nnf,[status(thm)],[help_c__fNot__2]) ).
fof(f_520_2,plain,
! [U_2574] :
( hBOOL(hAPP(c_fNot,U_2574))
| hBOOL(U_2574) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
! [U_2574] :
( hBOOL(hAPP(c_fNot,U_2574))
| hBOOL(U_2574) ),
inference(definitional_conversion,[status(esa)],[f_520_2]) ).
cnf(f_520_4,plain,
( hBOOL(hAPP(c_fNot,U_2574))
| hBOOL(U_2574) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_1,plain,
! [V_Q_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
| ~ hBOOL(V_Q_2)
| ~ hBOOL(V_Pa_2) ),
inference(fof_nnf,[status(thm)],[help_c__fconj__1]) ).
fof(f_521_2,plain,
! [U_2576,U_2575] :
( hBOOL(hAPP(hAPP(c_fconj,U_2575),U_2576))
| ~ hBOOL(U_2576)
| ~ hBOOL(U_2575) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
! [U_2576] :
( ! [U_2575] :
( hBOOL(hAPP(hAPP(c_fconj,U_2575),U_2576))
| ~ hBOOL(U_2575) )
| ~ hBOOL(U_2576) ),
inference(miniscope,[status(thm)],[f_521_2]) ).
fof(f_521_4,plain,
! [U_2575,U_2576] :
( hBOOL(hAPP(hAPP(c_fconj,U_2575),U_2576))
| ~ hBOOL(U_2575)
| ~ hBOOL(U_2576) ),
inference(definitional_conversion,[status(esa)],[f_521_3]) ).
cnf(f_521_5,plain,
( hBOOL(hAPP(hAPP(c_fconj,U_2575),U_2576))
| ~ hBOOL(U_2575)
| ~ hBOOL(U_2576) ),
inference(clausify,[status(thm)],[f_521_4]) ).
fof(f_522_1,plain,
! [V_Q_2,V_Pa_2] :
( hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ),
inference(fof_nnf,[status(thm)],[help_c__fconj__2]) ).
fof(f_522_2,plain,
! [U_2578,U_2577] :
( hBOOL(U_2577)
| ~ hBOOL(hAPP(hAPP(c_fconj,U_2577),U_2578)) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
! [U_2577,U_2578] :
( hBOOL(U_2577)
| ~ hBOOL(hAPP(hAPP(c_fconj,U_2577),U_2578)) ),
inference(definitional_conversion,[status(esa)],[f_522_2]) ).
cnf(f_522_4,plain,
( hBOOL(U_2577)
| ~ hBOOL(hAPP(hAPP(c_fconj,U_2577),U_2578)) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_1,plain,
! [V_Q_2,V_Pa_2] :
( hBOOL(V_Q_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ),
inference(fof_nnf,[status(thm)],[help_c__fconj__3]) ).
fof(f_523_2,plain,
! [U_2580,U_2579] :
( hBOOL(U_2580)
| ~ hBOOL(hAPP(hAPP(c_fconj,U_2579),U_2580)) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
! [U_2580] :
( ! [U_2579] : ~ hBOOL(hAPP(hAPP(c_fconj,U_2579),U_2580))
| hBOOL(U_2580) ),
inference(miniscope,[status(thm)],[f_523_2]) ).
fof(f_523_4,plain,
! [U_2579,U_2580] :
( ~ hBOOL(hAPP(hAPP(c_fconj,U_2579),U_2580))
| hBOOL(U_2580) ),
inference(definitional_conversion,[status(esa)],[f_523_3]) ).
cnf(f_523_5,plain,
( ~ hBOOL(hAPP(hAPP(c_fconj,U_2579),U_2580))
| hBOOL(U_2580) ),
inference(clausify,[status(thm)],[f_523_4]) ).
fof(f_524_1,negated_conjecture,
~ ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i))) ),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_524_2,negated_conjecture,
? [B_i] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(fof_nnf,[status(thm)],[f_524_1]) ).
fof(f_524_3,negated_conjecture,
? [U_2581] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_2581)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_2581))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_2581)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_2581)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(variable_rename,[status(thm)],[f_524_2]) ).
fof(f_524_4,negated_conjecture,
( ? [U_2583] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_2583)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_2583))) )
| ? [U_2582] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_2582)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_2582)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(miniscope,[status(thm)],[f_524_3]) ).
fof(f_524_5,negated_conjecture,
( ? [U_2583] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_2583)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,U_2583))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,sK102)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,sK102)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_2582,sK102)],[f_524_4]) ).
fof(f_524_6,negated_conjecture,
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,sK103)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,sK103))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,sK102)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,sK102)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_2583,sK103)],[f_524_5]) ).
fof(f_524_7,negated_conjecture,
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,sK103)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ sP148 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,sK103)))
| ~ sP148 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,sK102)))
| ~ sP147 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,sK102)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ sP147 )
& ( sP148
| sP147 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147,sP148])],[f_524_6]) ).
cnf(f_524_8,negated_conjecture,
( sP148
| sP147 ),
inference(clausify,[status(thm)],[f_524_7]) ).
cnf(f_524_9,negated_conjecture,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,sK102)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ sP147 ),
inference(clausify,[status(thm)],[f_524_7]) ).
cnf(f_524_10,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,sK102)))
| ~ sP147 ),
inference(clausify,[status(thm)],[f_524_7]) ).
cnf(f_524_11,negated_conjecture,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,sK103)))
| ~ sP148 ),
inference(clausify,[status(thm)],[f_524_7]) ).
cnf(f_524_12,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,sK103)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____)))
| ~ sP148 ),
inference(clausify,[status(thm)],[f_524_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( tc_prod(Eq_x_0,Eq_x_1) = tc_prod(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c_member(Eq_x_0) = c_member(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_Product__Type_OPair(Eq_x_0,Eq_x_1) = c_Product__Type_OPair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_Arrow__Order__Mirabelle_Omkbot(Eq_x_0,Eq_x_1) = c_Arrow__Order__Mirabelle_Omkbot(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_Arrow__Order__Mirabelle_Omktop(Eq_x_0,Eq_x_1) = c_Arrow__Order__Mirabelle_Omktop(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_FunDef_Oin__rel(Eq_x_0,Eq_x_1,Eq_x_2) = c_FunDef_Oin__rel(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_Recdef_Osame__fst(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Recdef_Osame__fst(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_COMBC(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBC(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_COMBB(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBB(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_Product__Type_Oprod_Oprod__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Product__Type_Oprod_Oprod__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_COMBK(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBK(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_FuncSet_OPi(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_FuncSet_OPi(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Wellfounded_Olex__prod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Wellfounded_Olex__prod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( c_Product__Type_Ointernal__split(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Product__Type_Ointernal__split(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_Arrow__Order__Mirabelle_Oabove(Eq_x_0,Eq_x_1,Eq_x_2) = c_Arrow__Order__Mirabelle_Oabove(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_Product__Type_Ocurry(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Ocurry(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_FuncSet_Ocompose(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_FuncSet_Ocompose(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_Wellfounded_Oacc(Eq_x_0,Eq_x_1) = c_Wellfounded_Oacc(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_Wellfounded_Oaccp(Eq_x_0,Eq_x_1) = c_Wellfounded_Oaccp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_FuncSet_Oextensional(Eq_x_0,Eq_x_1,Eq_x_2) = c_FuncSet_Oextensional(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( c_Transitive__Closure_Ortrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortrancl(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_Recdef_Owfrec__rel(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Recdef_Owfrec__rel(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_Recdef_Ocut(Eq_x_0,Eq_x_1) = c_Recdef_Ocut(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( c_FuncSet_Orestrict(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_FuncSet_Orestrict(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( c_COMBS(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBS(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( c_HOL_Oundefined(Eq_x_0) = c_HOL_Oundefined(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_Relation_ODomain(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_ODomain(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( c_FuncSet_Oextensional__funcset(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_FuncSet_Oextensional__funcset(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( c_Relation_ORange(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_ORange(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( c_Relation_OId__on(Eq_x_0,Eq_x_1) = c_Relation_OId__on(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( c_Lattices_Osemilattice__inf__class_Oinf(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lattices_Osemilattice__inf__class_Oinf(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( c_Relation_Oinv__image(Eq_x_0,Eq_x_1) = c_Relation_Oinv__image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( c_Transitive__Closure_Otrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Otrancl(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( c_Transitive__Closure_Ortranclp(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortranclp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( c_Set_Oinsert(Eq_x_0,Eq_x_1,Eq_x_2) = c_Set_Oinsert(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( c_Transitive__Closure_Otranclp(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Otranclp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( c_Fun_Ofun__upd(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Fun_Ofun__upd(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( c_Wellfounded_Omeasure(Eq_x_0) = c_Wellfounded_Omeasure(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( c_Recdef_Owfrec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Recdef_Owfrec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( c_HOL_OThe(Eq_x_0,Eq_x_1) = c_HOL_OThe(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( c_Nitpick_Owfrec_H(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Owfrec_H(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( c_Nitpick_Owf__wfrec_H(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Owf__wfrec_H(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( c_Nitpick_Owf__wfrec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nitpick_Owf__wfrec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( c_Fun_Othe__inv__into(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Fun_Othe__inv__into(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( c_Fun_Ooverride__on(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Fun_Ooverride__on(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( c_Wellfounded_Omlex__prod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Wellfounded_Omlex__prod(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( c_Wellfounded_Omin__ext(Eq_x_0,Eq_x_1) = c_Wellfounded_Omin__ext(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( c_FunDef_Orp__inv__image(Eq_x_0,Eq_x_1) = c_FunDef_Orp__inv__image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( c_Relation_Orel__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Relation_Orel__comp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( c_Product__Type_Oprod_Oprod__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Oprod_Oprod__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK29(Eq_x_0,Eq_x_1,Eq_x_2) = sK29(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( sK44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( sK45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( sK48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK57(Eq_x_0,Eq_x_1) = sK57(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK60(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( sK61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK61(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( sK70(Eq_x_0,Eq_x_1) = sK70(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( sK71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK72(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK72(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( sK73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( sK74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,axiom,
( sK75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_133,axiom,
( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_134,axiom,
( sK78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( sK80(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK86(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK86(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( sK87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK87(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( sK88(Eq_x_0,Eq_x_1) = sK88(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK90(Eq_x_0,Eq_x_1) = sK90(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK91(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK91(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK92(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK92(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_149,axiom,
( sK93(Eq_x_0,Eq_x_1,Eq_x_2) = sK93(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,axiom,
( sK94(Eq_x_0,Eq_x_1) = sK94(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_151,axiom,
( sK95(Eq_x_0,Eq_x_1) = sK95(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_152,axiom,
( sK96(Eq_x_0,Eq_x_1,Eq_x_2) = sK96(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_153,axiom,
( sK97(Eq_x_0,Eq_x_1) = sK97(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_154,axiom,
( sK98(Eq_x_0,Eq_x_1) = sK98(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_155,axiom,
( sK99(Eq_x_0,Eq_x_1) = sK99(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,axiom,
( sK100(Eq_x_0,Eq_x_1) = sK100(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_157,axiom,
( sK101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_159,axiom,
( c_Nitpick_Orefl_H(Eq_y_0,Eq_y_1)
| ~ c_Nitpick_Orefl_H(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_160,axiom,
( c_Arrow__Order__Mirabelle_Ounanimity(Eq_y_0)
| ~ c_Arrow__Order__Mirabelle_Ounanimity(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_161,axiom,
( c_Arrow__Order__Mirabelle_OIIA(Eq_y_0)
| ~ c_Arrow__Order__Mirabelle_OIIA(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_162,axiom,
( c_Arrow__Order__Mirabelle_Odictator(Eq_y_0,Eq_y_1)
| ~ c_Arrow__Order__Mirabelle_Odictator(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_163,axiom,
( c_Recdef_Oadm__wf(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Recdef_Oadm__wf(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,axiom,
( c_Relation_Osingle__valued(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Relation_Osingle__valued(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_165,axiom,
( c_Predicate_ODomainP(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Predicate_ODomainP(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_166,axiom,
( c_Relation_Oirrefl(Eq_y_0,Eq_y_1)
| ~ c_Relation_Oirrefl(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( c_Predicate_ORangeP(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Predicate_ORangeP(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_168,axiom,
( class_Lattices_Olattice(Eq_y_0)
| ~ class_Lattices_Olattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_169,axiom,
( c_Relation_Ototal__on(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Relation_Ototal__on(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( class_Lattices_Osemilattice__inf(Eq_y_0)
| ~ class_Lattices_Osemilattice__inf(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_171,axiom,
( c_Relation_Orefl__on(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Relation_Orefl__on(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_172,axiom,
( c_Wellfounded_Oacyclic(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded_Oacyclic(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_173,axiom,
( c_Wellfounded_Owf(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded_Owf(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_174,axiom,
( c_Relation_Oantisym(Eq_y_0,Eq_y_1)
| ~ c_Relation_Oantisym(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,axiom,
( c_Wellfounded_OwfP(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded_OwfP(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_176,axiom,
( c_Orderings_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_177,axiom,
( c_Orderings_Oord__class_Oless__eq(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_178,axiom,
( class_Orderings_Opreorder(Eq_y_0)
| ~ class_Orderings_Opreorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_179,axiom,
( c_FunDef_Oreduction__pair(Eq_y_0,Eq_y_1)
| ~ c_FunDef_Oreduction__pair(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_180,axiom,
( class_Orderings_Oord(Eq_y_0)
| ~ class_Orderings_Oord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_181,axiom,
( class_Orderings_Olinorder(Eq_y_0)
| ~ class_Orderings_Olinorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_182,axiom,
( class_Orderings_Oorder(Eq_y_0)
| ~ class_Orderings_Oorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_184,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_187,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_197,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_198,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( sP19(Eq_y_0,Eq_y_1)
| ~ sP19(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_205,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_206,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_207,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_208,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_209,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_210,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_212,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_214,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_217,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_218,axiom,
( sP35(Eq_y_0,Eq_y_1)
| ~ sP35(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,axiom,
( sP36(Eq_y_0,Eq_y_1)
| ~ sP36(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_220,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_221,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,axiom,
( sP40(Eq_y_0)
| ~ sP40(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_224,axiom,
( sP41(Eq_y_0)
| ~ sP41(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_225,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_226,axiom,
( sP43(Eq_y_0,Eq_y_1)
| ~ sP43(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_227,axiom,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_228,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_229,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_230,axiom,
( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_231,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_232,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_233,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_234,axiom,
( sP51(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_235,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_236,axiom,
( sP53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_237,axiom,
( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_238,axiom,
( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_239,axiom,
( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_240,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_241,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_242,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_243,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_244,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_245,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_246,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_247,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_248,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_249,axiom,
( sP66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_250,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_251,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_252,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_253,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_254,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_255,axiom,
( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_256,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_257,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_258,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_259,axiom,
( sP76(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_260,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_261,axiom,
( sP78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_262,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_263,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_264,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_265,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_266,axiom,
( sP83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_267,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_268,axiom,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_269,axiom,
( sP86(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP86(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_270,axiom,
( sP87(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_271,axiom,
( sP88(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_272,axiom,
( sP89(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_273,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_274,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_275,axiom,
( sP92(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP92(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_276,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_277,axiom,
( sP94(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_278,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_279,axiom,
( sP96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_280,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_281,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_282,axiom,
( sP99(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_283,axiom,
( sP100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_284,axiom,
( sP101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_285,axiom,
( sP102(Eq_y_0,Eq_y_1)
| ~ sP102(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_286,axiom,
( sP103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_287,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_288,axiom,
( sP105(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_289,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_290,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP107(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_291,axiom,
( sP108(Eq_y_0,Eq_y_1)
| ~ sP108(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_292,axiom,
( sP109(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP109(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_293,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_294,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_295,axiom,
( sP112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP112(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_296,axiom,
( sP113(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP113(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_297,axiom,
( sP114(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_298,axiom,
( sP115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_299,axiom,
( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_300,axiom,
( sP117(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_301,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_302,axiom,
( sP119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_303,axiom,
( sP120(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_304,axiom,
( sP121(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP121(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_305,axiom,
( sP122(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP122(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_306,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_307,axiom,
( sP124(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP124(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_308,axiom,
( sP125(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_309,axiom,
( sP126(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP126(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_310,axiom,
( sP127(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_311,axiom,
( sP128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_312,axiom,
( sP129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_313,axiom,
( sP130(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP130(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_314,axiom,
( sP131(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_315,axiom,
( sP132(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_316,axiom,
( sP133(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_317,axiom,
( sP134(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_318,axiom,
( sP135(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_319,axiom,
( sP136(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP136(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_320,axiom,
( sP137(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP137(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_321,axiom,
( sP138(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_322,axiom,
( sP139(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP139(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_323,axiom,
( sP140(Eq_y_0,Eq_y_1)
| ~ sP140(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_324,axiom,
( sP141(Eq_y_0,Eq_y_1)
| ~ sP141(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_325,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_326,axiom,
( sP143(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_327,axiom,
( sP144(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_328,axiom,
( sP145(Eq_y_0,Eq_y_1)
| ~ sP145(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_329,axiom,
( sP146(Eq_y_0,Eq_y_1)
| ~ sP146(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT147+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 21:14:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 33.54/33.89 % SZS status Theorem for theBenchmark
% 33.54/33.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------