%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SCT149+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:55:33 AM UTC 2026
% Result : Theorem 1.96s 7.21s
% Output : Proof 1.96s
% 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_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('theBenchmark.p',fact_assms_I3_J) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('theBenchmark.p',fact_u) ).
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_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_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__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_Ib_A_060_092_060_094bsub_062P_H_Ai_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_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',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_Ib_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Aa_J_096) ).
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__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_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__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_ba,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_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,v_P_H____))) ),
file('theBenchmark.p',fact_ba) ).
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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_linear__alt,axiom,
? [B_L] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_L),c_Arrow__Order__Mirabelle_OLin)),
file('theBenchmark.p',fact_linear__alt) ).
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_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_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_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_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_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_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_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_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_internal__split__conv,axiom,
! [V_ba_2,V_aa_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(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_curry__def,axiom,
! [V_y_2,V_x_2,V_ca_2,T_a,T_c,T_b] : 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_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(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_curryE,axiom,
! [V_ba_2,V_aa_2,V_f_2,T_b,T_a] :
( hBOOL(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_curryD,axiom,
! [V_ba_2,V_aa_2,V_f_2,T_b,T_a] :
( hBOOL(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_curry__conv,axiom,
! [V_ba_2,V_aa_2,V_f_2,T_a,T_c,T_b] : 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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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_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_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_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_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_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_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__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_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_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_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_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_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__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__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_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__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__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_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__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__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_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__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_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_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_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_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_Inf__fin_Oidem,axiom,
! [V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x) = V_x ),
file('theBenchmark.p',fact_Inf__fin_Oidem) ).
fof(fact_IdI,axiom,
! [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_Relation_OId(T_a))),
file('theBenchmark.p',fact_IdI) ).
fof(fact_restrict__ext,axiom,
! [T_b,V_g_2,V_f_2,V_A_2,T_a] :
( ! [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) )
=> c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2) = c_FuncSet_Orestrict(T_a,T_b,V_g_2,V_A_2) ),
file('theBenchmark.p',fact_restrict__ext) ).
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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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__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__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_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_single__valued__Id,axiom,
! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)),
file('theBenchmark.p',fact_single__valued__Id) ).
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_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__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_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_pair__in__Id__conv,axiom,
! [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_Relation_OId(T_a)))
<=> V_aa_2 = V_ba_2 ),
file('theBenchmark.p',fact_pair__in__Id__conv) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_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_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__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_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__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_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_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_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_IdE,axiom,
! [V_p_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
=> ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ),
file('theBenchmark.p',fact_IdE) ).
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_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_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_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_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_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_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_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_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__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__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_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_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_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_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__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_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_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__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__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__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__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_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_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_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__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_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_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_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_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__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__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__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__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__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_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_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_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_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__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__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__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__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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_wf__pred__nat,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('theBenchmark.p',fact_wf__pred__nat) ).
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_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_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_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_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__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_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_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_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__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__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_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_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__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_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_antisym__Id,axiom,
! [T_a] : c_Relation_Oantisym(T_a,c_Relation_OId(T_a)),
file('theBenchmark.p',fact_antisym__Id) ).
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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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__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__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__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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_min__rpair__set,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
file('theBenchmark.p',fact_min__rpair__set) ).
fof(fact_max__rpair__set,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
file('theBenchmark.p',fact_max__rpair__set) ).
fof(fact_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) = hAPP(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_rel__comp__mono,axiom,
! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_H_2,V_r_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_s_H_2,V_s_2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_H_2,V_s_H_2),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)) ) ),
file('theBenchmark.p',fact_rel__comp__mono) ).
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_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_internal__split__def,axiom,
! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),
file('theBenchmark.p',fact_internal__split__def) ).
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(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,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_b____),v_a____)),hAPP(v_F,v_P_H____))) ),
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]) ).
cnf(f_1_4,plain,
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(fof_nnf,[status(thm)],[fact_assms_I3_J]) ).
cnf(f_2_2,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(fof_nnf,[status(thm)],[fact_u]) ).
cnf(f_3_2,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
v_a____ != v_b____,
inference(fof_nnf,[status(thm)],[fact__096a_A_126_061_Ab_096]) ).
cnf(f_4_2,plain,
v_a____ != v_b____,
inference(clausify,[status(thm)],[f_4_1]) ).
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_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_5_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_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(v_P_H____,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(v_P_H____,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))) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_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_a____),v_b____)),hAPP(v_P____,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(v_P_H____,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_b____),v_a____)),hAPP(v_P_H____,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))) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_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_a____)),hAPP(v_P_H____,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))) ),
inference(clausify,[status(thm)],[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_b____)),hAPP(v_P____,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(v_P_H____,U_5))) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_9,U_8,U_7,U_6] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_7))
& ~ hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_6)) )
| ( hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_7))
& hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_6)) )
| U_6 != U_7 ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_6))
| hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_6))
| U_6 != U_7 ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_7))
| hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_6))
| U_6 != U_7 ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_6))
| hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_7))
| U_6 != U_7 ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_7))
| hBOOL(hAPP(hAPP(c_member(U_8),U_9),U_7))
| U_6 != U_7 ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_13,U_12,U_11,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),U_10),U_11)),c_Arrow__Order__Mirabelle_Omkbot(U_12,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),U_10),U_11)),U_12))
& U_10 != U_13 )
| ( U_10 = U_11
& U_10 = U_13 )
| U_11 = 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),U_10),U_11)),U_12))
| U_10 = U_13 )
& ( U_10 != U_11
| U_10 != U_13 )
& U_11 != 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),U_10),U_11)),c_Arrow__Order__Mirabelle_Omkbot(U_12,U_13))) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_21,U_19,U_17,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),U_15),U_17)),c_Arrow__Order__Mirabelle_Omkbot(U_19,U_21)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_15),U_17)),U_19))
& U_15 != U_21 )
| ( U_15 = U_17
& U_15 = U_21 )
| U_17 = U_21 )
& ! [U_20,U_18,U_16,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),U_14),U_16)),U_18))
| U_14 = U_20 )
& ( U_14 != U_16
| U_14 != U_20 )
& U_16 != U_20 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_14),U_16)),c_Arrow__Order__Mirabelle_Omkbot(U_18,U_20))) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( U_16 != U_20
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_14),U_16)),c_Arrow__Order__Mirabelle_Omkbot(U_18,U_20))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( U_14 != U_16
| U_14 != U_20
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_14),U_16)),c_Arrow__Order__Mirabelle_Omkbot(U_18,U_20))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
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),U_14),U_16)),U_18))
| U_14 = U_20
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_14),U_16)),c_Arrow__Order__Mirabelle_Omkbot(U_18,U_20))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( U_15 != U_21
| U_15 = U_21
| U_17 = U_21
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_15),U_17)),c_Arrow__Order__Mirabelle_Omkbot(U_19,U_21))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_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_15),U_17)),U_19))
| U_15 = U_21
| U_17 = U_21
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_15),U_17)),c_Arrow__Order__Mirabelle_Omkbot(U_19,U_21))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_9,plain,
( U_15 != U_21
| U_15 = U_17
| U_17 = U_21
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_15),U_17)),c_Arrow__Order__Mirabelle_Omkbot(U_19,U_21))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_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_15),U_17)),U_19))
| U_15 = U_17
| U_17 = U_21
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_15),U_17)),c_Arrow__Order__Mirabelle_Omkbot(U_19,U_21))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_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_Omktop(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_23 != U_25 )
| ( U_22 = U_23
& U_23 = U_25 )
| U_22 = 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_23 = U_25 )
& ( U_22 != U_23
| U_23 != U_25 )
& U_22 != 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_Omktop(U_24,U_25))) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_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_Omktop(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_29 != U_33 )
| ( U_27 = U_29
& U_29 = U_33 )
| U_27 = 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_28 = U_32 )
& ( U_26 != U_28
| U_28 != U_32 )
& U_26 != 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_Omktop(U_30,U_32))) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_26 != 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_Omktop(U_30,U_32))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( U_26 != U_28
| 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_Omktop(U_30,U_32))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_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_26),U_28)),U_30))
| 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_Omktop(U_30,U_32))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( U_29 != U_33
| U_29 = U_33
| U_27 = 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)),c_Arrow__Order__Mirabelle_Omktop(U_31,U_33))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_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_27),U_29)),U_31))
| U_29 = U_33
| U_27 = 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)),c_Arrow__Order__Mirabelle_Omktop(U_31,U_33))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_9,plain,
( U_29 != U_33
| U_27 = U_29
| U_27 = 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)),c_Arrow__Order__Mirabelle_Omktop(U_31,U_33))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_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_27),U_29)),U_31))
| U_27 = U_29
| U_27 = 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)),c_Arrow__Order__Mirabelle_Omktop(U_31,U_33))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_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)],[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_Ib_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Aa_J_096]) ).
fof(f_9_2,plain,
! [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),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_34)),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_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),v_b____),v_a____)),hAPP(v_P_H____,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),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_34)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_36] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_36)),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_36))) )
& ! [U_35] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_35)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_35)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_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_a____)),hAPP(v_P_H____,U_35)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_35)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_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_36)),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_36))) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [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),v_a____),v_b____)),hAPP(v_P____,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),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_37)),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_37)),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_37))) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [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),v_a____),v_b____)),hAPP(v_P____,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),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_39)),v_c____),v_b____))) )
& ! [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),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_38)),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_38))) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_38)),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_38))) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_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_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),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_39)),v_c____),v_b____))) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_40] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_40)),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_40)),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_40)),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_40)),v_c____),v_b____))) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_42] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_42)),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_42)),v_c____),v_b____)),v_b____),v_a____))) )
& ! [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),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_41)),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_41)),v_c____),v_b____))) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_41)),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_41)),v_c____),v_b____))) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_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_42)),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_42)),v_c____),v_b____)),v_b____),v_a____))) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_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_12_2,plain,
! [U_43] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_43)),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_43)),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_43)),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_43)),v_c____),v_b____)),v_b____),v_a____))) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [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),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,U_45)),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_45)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) )
& ! [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),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_44)),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_44)),v_c____),v_b____)),v_b____),v_a____))) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_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_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_44)),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_44)),v_c____),v_b____)),v_b____),v_a____))) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_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_45)),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_45)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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_13_2,plain,
! [U_46] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_46)),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_46))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_46)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_46)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_48] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_48)),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_48))) )
& ! [U_47] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_47)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_47)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_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_P____,U_47)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_47)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_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_48)),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_48))) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_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_14_2,plain,
! [U_53,U_52,U_51,U_50,U_49] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_49,U_50,U_51),U_52),U_53))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_49,U_50)),hAPP(hAPP(c_Product__Type_OPair(U_49,U_50),U_52),U_53)),U_51)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_49,U_50)),hAPP(hAPP(c_Product__Type_OPair(U_49,U_50),U_52),U_53)),U_51))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_49,U_50,U_51),U_52),U_53)) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_63,U_61,U_59,U_57,U_55] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_55,U_57,U_59),U_61),U_63))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_55,U_57)),hAPP(hAPP(c_Product__Type_OPair(U_55,U_57),U_61),U_63)),U_59)) )
& ! [U_62,U_60,U_58,U_56,U_54] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_54,U_56)),hAPP(hAPP(c_Product__Type_OPair(U_54,U_56),U_60),U_62)),U_58))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_54,U_56,U_58),U_60),U_62)) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_54,U_56)),hAPP(hAPP(c_Product__Type_OPair(U_54,U_56),U_60),U_62)),U_58))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_54,U_56,U_58),U_60),U_62)) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_55,U_57,U_59),U_61),U_63))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_55,U_57)),hAPP(hAPP(c_Product__Type_OPair(U_55,U_57),U_61),U_63)),U_59)) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_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_15_2,plain,
! [U_70,U_69,U_68,U_67,U_66,U_65,U_64] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_70,U_66),tc_prod(U_70,U_66))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_70,U_66),tc_prod(U_70,U_66)),hAPP(hAPP(c_Product__Type_OPair(U_70,U_66),U_65),U_67)),hAPP(hAPP(c_Product__Type_OPair(U_70,U_66),U_65),U_68))),c_Recdef_Osame__fst(U_70,U_66,U_64,U_69)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_66,U_66)),hAPP(hAPP(c_Product__Type_OPair(U_66,U_66),U_67),U_68)),hAPP(U_69,U_65)))
| ~ hBOOL(hAPP(U_64,U_65)) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_70,U_66),tc_prod(U_70,U_66))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_70,U_66),tc_prod(U_70,U_66)),hAPP(hAPP(c_Product__Type_OPair(U_70,U_66),U_65),U_67)),hAPP(hAPP(c_Product__Type_OPair(U_70,U_66),U_65),U_68))),c_Recdef_Osame__fst(U_70,U_66,U_64,U_69)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_66,U_66)),hAPP(hAPP(c_Product__Type_OPair(U_66,U_66),U_67),U_68)),hAPP(U_69,U_65)))
| ~ hBOOL(hAPP(U_64,U_65)) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_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]) ).
cnf(f_16_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(clausify,[status(thm)],[f_16_1]) ).
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_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,v_P_H____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,v_P_H____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(fof_nnf,[status(thm)],[fact_ba]) ).
cnf(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_a____)),hAPP(v_F,v_P_H____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_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_a____)),hAPP(v_F,v_P_H____))) ),
inference(clausify,[status(thm)],[f_17_1]) ).
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]) ).
cnf(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(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_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]) ).
cnf(f_19_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_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_19_1]) ).
cnf(f_19_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_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_19_1]) ).
fof(f_20_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]) ).
cnf(f_20_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_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_20_1]) ).
cnf(f_20_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_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_20_1]) ).
fof(f_21_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]) ).
cnf(f_21_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_a____),v_b____)),hAPP(v_F,v_P____))) ),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_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_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_21_1]) ).
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]) ).
cnf(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(clausify,[status(thm)],[f_22_1]) ).
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]) ).
cnf(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(clausify,[status(thm)],[f_23_1]) ).
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]) ).
cnf(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(clausify,[status(thm)],[f_24_1]) ).
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_74,U_73,U_72,U_71] :
( hBOOL(hAPP(hAPP(c_member(U_73),U_71),U_74))
| ~ hBOOL(hAPP(hAPP(c_member(U_73),U_72),U_74))
| U_71 != U_72 ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_73),U_71),U_74))
| ~ hBOOL(hAPP(hAPP(c_member(U_73),U_72),U_74))
| U_71 != U_72 ),
inference(clausify,[status(thm)],[f_25_2]) ).
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_78,U_77,U_76,U_75] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_77),U_75),U_78))
| ~ hBOOL(hAPP(hAPP(c_member(U_77),U_76),U_78)) )
& ( hBOOL(hAPP(hAPP(c_member(U_77),U_76),U_78))
| ~ hBOOL(hAPP(hAPP(c_member(U_77),U_75),U_78)) ) )
| U_75 != U_76 ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_77),U_76),U_78))
| ~ hBOOL(hAPP(hAPP(c_member(U_77),U_75),U_78))
| U_75 != U_76 ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_77),U_75),U_78))
| ~ hBOOL(hAPP(hAPP(c_member(U_77),U_76),U_78))
| U_75 != U_76 ),
inference(clausify,[status(thm)],[f_26_2]) ).
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_82,U_81,U_80,U_79] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_79))
| ~ hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_80)) )
& ( hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_80))
| ~ hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_79)) ) )
| U_79 != U_80 ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_80))
| ~ hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_79))
| U_79 != U_80 ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_79))
| ~ hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_80))
| U_79 != U_80 ),
inference(clausify,[status(thm)],[f_27_2]) ).
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_85,U_84,U_83] :
( ( hBOOL(hAPP(hAPP(c_member(U_83),U_84),U_85))
| ~ hBOOL(hAPP(U_85,U_84)) )
& ( hBOOL(hAPP(U_85,U_84))
| ~ hBOOL(hAPP(hAPP(c_member(U_83),U_84),U_85)) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_91,U_89] :
( ! [U_87] : hBOOL(hAPP(hAPP(c_member(U_87),U_89),U_91))
| ~ hBOOL(hAPP(U_91,U_89)) )
& ! [U_90,U_88] :
( ! [U_86] : ~ hBOOL(hAPP(hAPP(c_member(U_86),U_88),U_90))
| hBOOL(hAPP(U_90,U_88)) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_86),U_88),U_90))
| hBOOL(hAPP(U_90,U_88)) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_87),U_89),U_91))
| ~ hBOOL(hAPP(U_91,U_89)) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_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_29_2,plain,
! [U_98,U_97,U_96,U_95,U_94,U_93] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ? [U_92] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,U_92)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,U_92))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,U_92)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,U_92))) ) )
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_98,U_97,U_96,U_95,U_94,U_93] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ? [U_100] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,U_100)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,U_100))) )
| ? [U_99] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,U_99)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,U_99))) )
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_98,U_97,U_96,U_95,U_94,U_93] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ? [U_100] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,U_100)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,U_100))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,sK2(U_98,U_97,U_96,U_95,U_94,U_93))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,sK2(U_98,U_97,U_96,U_95,U_94,U_93)))) )
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_99,sK2(U_98,U_97,U_96,U_95,U_94,U_93))],[f_29_3]) ).
fof(f_29_5,plain,
! [U_98,U_97,U_96,U_95,U_94,U_93] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,sK3(U_98,U_97,U_96,U_95,U_94,U_93))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,sK3(U_98,U_97,U_96,U_95,U_94,U_93)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,sK2(U_98,U_97,U_96,U_95,U_94,U_93))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,sK2(U_98,U_97,U_96,U_95,U_94,U_93)))) )
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_100,sK3(U_98,U_97,U_96,U_95,U_94,U_93))],[f_29_4]) ).
cnf(f_29_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_95),U_96)),hAPP(U_98,sK3(U_98,U_97,U_96,U_95,U_94,U_93))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,sK2(U_98,U_97,U_96,U_95,U_94,U_93))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_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_93),U_94)),hAPP(U_97,sK3(U_98,U_97,U_96,U_95,U_94,U_93))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(U_97,sK2(U_98,U_97,U_96,U_95,U_94,U_93))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_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_95),U_96)),hAPP(U_98,sK3(U_98,U_97,U_96,U_95,U_94,U_93))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,sK2(U_98,U_97,U_96,U_95,U_94,U_93))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_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_93),U_94)),hAPP(U_97,sK3(U_98,U_97,U_96,U_95,U_94,U_93))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(U_98,sK2(U_98,U_97,U_96,U_95,U_94,U_93))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_95),U_96)),hAPP(v_F,U_98)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_93),U_94)),hAPP(v_F,U_97)))
| ~ 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_98),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_97),c_Arrow__Order__Mirabelle_OProf))
| U_94 = U_95
| U_93 = U_96
| U_95 = U_96
| U_93 = U_94 ),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_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_30_2,plain,
! [U_107,U_106,U_105,U_104,U_103,U_102] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106))) ) )
| ? [U_101] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,U_101)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,U_101))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,U_101)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,U_101))) ) )
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_107,U_106,U_105,U_104,U_103,U_102] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106))) ) )
| ? [U_109] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,U_109)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,U_109))) )
| ? [U_108] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,U_108)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,U_108))) )
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_107,U_106,U_105,U_104,U_103,U_102] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106))) ) )
| ? [U_109] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,U_109)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,U_109))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,sK4(U_107,U_106,U_105,U_104,U_103,U_102)))) )
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_108,sK4(U_107,U_106,U_105,U_104,U_103,U_102))],[f_30_3]) ).
fof(f_30_5,plain,
! [U_107,U_106,U_105,U_104,U_103,U_102] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,sK5(U_107,U_106,U_105,U_104,U_103,U_102)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,sK4(U_107,U_106,U_105,U_104,U_103,U_102)))) )
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_109,sK5(U_107,U_106,U_105,U_104,U_103,U_102))],[f_30_4]) ).
cnf(f_30_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_104),U_105)),hAPP(U_107,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_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_102),U_103)),hAPP(U_106,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_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_104),U_105)),hAPP(U_107,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_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_102),U_103)),hAPP(U_106,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_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_104),U_105)),hAPP(U_107,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_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_102),U_103)),hAPP(U_106,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(U_106,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_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_104),U_105)),hAPP(U_107,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_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_102),U_103)),hAPP(U_106,sK5(U_107,U_106,U_105,U_104,U_103,U_102))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(U_107,sK4(U_107,U_106,U_105,U_104,U_103,U_102))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_102),U_103)),hAPP(v_F,U_106)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_104),U_105)),hAPP(v_F,U_107)))
| ~ 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_107),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_106),c_Arrow__Order__Mirabelle_OProf))
| U_103 = U_104
| U_102 = U_105
| U_104 = U_105
| U_102 = U_103 ),
inference(clausify,[status(thm)],[f_30_5]) ).
fof(f_31_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_31_2,plain,
! [U_113,U_112,U_111,U_110] :
( ( hAPP(hAPP(c_COMBC(U_110,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),U_110),c_COMBC(U_111,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_prod(U_110,U_111)),tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),U_110),hAPP(c_COMBB(tc_prod(U_110,U_111),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool),U_111),c_member(tc_prod(U_110,U_111)))),c_Product__Type_OPair(U_110,U_111)))),U_112) = hAPP(hAPP(c_COMBC(U_110,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),U_110),c_COMBC(U_111,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_prod(U_110,U_111)),tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),U_110),hAPP(c_COMBB(tc_prod(U_110,U_111),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool),U_111),c_member(tc_prod(U_110,U_111)))),c_Product__Type_OPair(U_110,U_111)))),U_113)
| U_112 != U_113 )
& ( U_112 = U_113
| hAPP(hAPP(c_COMBC(U_110,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),U_110),c_COMBC(U_111,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_prod(U_110,U_111)),tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),U_110),hAPP(c_COMBB(tc_prod(U_110,U_111),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool),U_111),c_member(tc_prod(U_110,U_111)))),c_Product__Type_OPair(U_110,U_111)))),U_112) != hAPP(hAPP(c_COMBC(U_110,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_fun(U_111,tc_HOL_Obool)),U_110),c_COMBC(U_111,tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_111,tc_prod(U_110,U_111)),tc_fun(U_111,tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool)),U_110),hAPP(c_COMBB(tc_prod(U_110,U_111),tc_fun(tc_fun(tc_prod(U_110,U_111),tc_HOL_Obool),tc_HOL_Obool),U_111),c_member(tc_prod(U_110,U_111)))),c_Product__Type_OPair(U_110,U_111)))),U_113) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_121,U_119] :
( ! [U_117,U_115] : hAPP(hAPP(c_COMBC(U_115,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),U_115),c_COMBC(U_117,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_prod(U_115,U_117)),tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),U_115),hAPP(c_COMBB(tc_prod(U_115,U_117),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool),U_117),c_member(tc_prod(U_115,U_117)))),c_Product__Type_OPair(U_115,U_117)))),U_119) = hAPP(hAPP(c_COMBC(U_115,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),U_115),c_COMBC(U_117,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_prod(U_115,U_117)),tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),U_115),hAPP(c_COMBB(tc_prod(U_115,U_117),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool),U_117),c_member(tc_prod(U_115,U_117)))),c_Product__Type_OPair(U_115,U_117)))),U_121)
| U_119 != U_121 )
& ! [U_120,U_118] :
( ! [U_116,U_114] : hAPP(hAPP(c_COMBC(U_114,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),U_114),c_COMBC(U_116,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_prod(U_114,U_116)),tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),U_114),hAPP(c_COMBB(tc_prod(U_114,U_116),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool),U_116),c_member(tc_prod(U_114,U_116)))),c_Product__Type_OPair(U_114,U_116)))),U_118) != hAPP(hAPP(c_COMBC(U_114,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),U_114),c_COMBC(U_116,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_prod(U_114,U_116)),tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),U_114),hAPP(c_COMBB(tc_prod(U_114,U_116),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool),U_116),c_member(tc_prod(U_114,U_116)))),c_Product__Type_OPair(U_114,U_116)))),U_120)
| U_118 = U_120 ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( hAPP(hAPP(c_COMBC(U_114,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),U_114),c_COMBC(U_116,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_prod(U_114,U_116)),tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),U_114),hAPP(c_COMBB(tc_prod(U_114,U_116),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool),U_116),c_member(tc_prod(U_114,U_116)))),c_Product__Type_OPair(U_114,U_116)))),U_118) != hAPP(hAPP(c_COMBC(U_114,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_fun(U_116,tc_HOL_Obool)),U_114),c_COMBC(U_116,tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_116,tc_prod(U_114,U_116)),tc_fun(U_116,tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool)),U_114),hAPP(c_COMBB(tc_prod(U_114,U_116),tc_fun(tc_fun(tc_prod(U_114,U_116),tc_HOL_Obool),tc_HOL_Obool),U_116),c_member(tc_prod(U_114,U_116)))),c_Product__Type_OPair(U_114,U_116)))),U_120)
| U_118 = U_120 ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( hAPP(hAPP(c_COMBC(U_115,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),U_115),c_COMBC(U_117,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_prod(U_115,U_117)),tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),U_115),hAPP(c_COMBB(tc_prod(U_115,U_117),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool),U_117),c_member(tc_prod(U_115,U_117)))),c_Product__Type_OPair(U_115,U_117)))),U_119) = hAPP(hAPP(c_COMBC(U_115,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_fun(U_117,tc_HOL_Obool)),U_115),c_COMBC(U_117,tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_117,tc_prod(U_115,U_117)),tc_fun(U_117,tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool)),U_115),hAPP(c_COMBB(tc_prod(U_115,U_117),tc_fun(tc_fun(tc_prod(U_115,U_117),tc_HOL_Obool),tc_HOL_Obool),U_117),c_member(tc_prod(U_115,U_117)))),c_Product__Type_OPair(U_115,U_117)))),U_121)
| U_119 != U_121 ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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]) ).
cnf(f_32_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(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_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_33_2,plain,
! [U_132] :
( ( c_Arrow__Order__Mirabelle_OIIA(U_132)
| ? [U_131] :
( ? [U_130] :
( ? [U_129,U_128] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_132,U_131)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_132,U_130))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_132,U_130)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_132,U_131))) ) )
& ! [U_127] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_131,U_127)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_130,U_127))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_130,U_127)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_131,U_127))) ) ) )
& 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_130),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_131),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_132,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_132,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_132,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_132,U_126))) ) )
| ? [U_122] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,U_122)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,U_122))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,U_122)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,U_122))) ) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_132) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_138] :
( c_Arrow__Order__Mirabelle_OIIA(U_138)
| ? [U_131] :
( ? [U_130] :
( ? [U_129,U_128] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_131)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_131))) ) )
& ! [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_129),U_128)),hAPP(U_131,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_129),U_128)),hAPP(U_130,U_136))) )
& ! [U_135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_130,U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_131,U_135))) ) )
& 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_130),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_131),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_137] :
( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126))) ) )
| ? [U_134] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,U_134)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,U_134))) )
| ? [U_133] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,U_133)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,U_133))) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_138] :
( c_Arrow__Order__Mirabelle_OIIA(U_138)
| ? [U_131] :
( ? [U_130] :
( ? [U_129,U_128] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_131)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_131))) ) )
& ! [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_129),U_128)),hAPP(U_131,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_129),U_128)),hAPP(U_130,U_136))) )
& ! [U_135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_130,U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_131,U_135))) ) )
& 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_130),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_131),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_137] :
( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126))) ) )
| ? [U_134] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,U_134)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,U_134))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123)))) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_133,sK6(U_137,U_126,U_125,U_124,U_123))],[f_33_3]) ).
fof(f_33_5,plain,
( ! [U_138] :
( c_Arrow__Order__Mirabelle_OIIA(U_138)
| ? [U_131] :
( ? [U_130] :
( ? [U_129,U_128] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_131)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_131))) ) )
& ! [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_129),U_128)),hAPP(U_131,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_129),U_128)),hAPP(U_130,U_136))) )
& ! [U_135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_130,U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_131,U_135))) ) )
& 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_130),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_131),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_137] :
( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123)))) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_134,sK7(U_137,U_126,U_125,U_124,U_123))],[f_33_4]) ).
fof(f_33_6,plain,
( ! [U_138] :
( c_Arrow__Order__Mirabelle_OIIA(U_138)
| ( ? [U_130] :
( ? [U_129,U_128] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,sK8(U_138))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,U_130)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,sK8(U_138)))) ) )
& ! [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_129),U_128)),hAPP(sK8(U_138),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_129),U_128)),hAPP(U_130,U_136))) )
& ! [U_135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_130,U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(sK8(U_138),U_135))) ) )
& 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_130),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))),sK8(U_138)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_137] :
( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123)))) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_131,sK8(U_138))],[f_33_5]) ).
fof(f_33_7,plain,
( ! [U_138] :
( c_Arrow__Order__Mirabelle_OIIA(U_138)
| ( ? [U_129,U_128] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,sK8(U_138))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,sK9(U_138)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,sK9(U_138))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(U_138,sK8(U_138)))) ) )
& ! [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_129),U_128)),hAPP(sK8(U_138),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_129),U_128)),hAPP(sK9(U_138),U_136))) )
& ! [U_135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(sK9(U_138),U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_129),U_128)),hAPP(sK8(U_138),U_135))) ) )
& 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))),sK9(U_138)),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))),sK8(U_138)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_137] :
( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123)))) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_130,sK9(U_138))],[f_33_6]) ).
fof(f_33_8,plain,
( ! [U_138] :
( c_Arrow__Order__Mirabelle_OIIA(U_138)
| ( ? [U_128] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),U_128)),hAPP(U_138,sK8(U_138))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),U_128)),hAPP(U_138,sK9(U_138)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),U_128)),hAPP(U_138,sK9(U_138))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),U_128)),hAPP(U_138,sK8(U_138)))) ) )
& ! [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),sK10(U_138)),U_128)),hAPP(sK8(U_138),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),sK10(U_138)),U_128)),hAPP(sK9(U_138),U_136))) )
& ! [U_135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),U_128)),hAPP(sK9(U_138),U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),U_128)),hAPP(sK8(U_138),U_135))) ) )
& 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))),sK9(U_138)),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))),sK8(U_138)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_137] :
( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123)))) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_129,sK10(U_138))],[f_33_7]) ).
fof(f_33_9,plain,
( ! [U_138] :
( c_Arrow__Order__Mirabelle_OIIA(U_138)
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK8(U_138))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK9(U_138)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK9(U_138))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK8(U_138)))) ) )
& ! [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),sK10(U_138)),sK11(U_138))),hAPP(sK8(U_138),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),sK10(U_138)),sK11(U_138))),hAPP(sK9(U_138),U_136))) )
& ! [U_135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(sK9(U_138),U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(sK8(U_138),U_135))) )
& 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))),sK9(U_138)),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))),sK8(U_138)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_137] :
( ! [U_126] :
( ! [U_125] :
( ! [U_124,U_123] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123)))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123)))) ) )
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_128,sK11(U_138))],[f_33_8]) ).
cnf(f_33_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_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_126,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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_124),U_123)),hAPP(U_125,sK7(U_137,U_126,U_125,U_124,U_123))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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_124),U_123)),hAPP(U_126,sK7(U_137,U_126,U_125,U_124,U_123))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_125,sK6(U_137,U_126,U_125,U_124,U_123))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_126)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_124),U_123)),hAPP(U_137,U_125)))
| ~ 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_125),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_126),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(U_137) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_18,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))),sK8(U_138)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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))),sK9(U_138)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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),sK10(U_138)),sK11(U_138))),hAPP(sK9(U_138),U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(sK8(U_138),U_135)))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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),sK10(U_138)),sK11(U_138))),hAPP(sK8(U_138),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),sK10(U_138)),sK11(U_138))),hAPP(sK9(U_138),U_136)))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK9(U_138))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK8(U_138))))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_23,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),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK8(U_138))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK8(U_138))))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK9(U_138))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK9(U_138))))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
cnf(f_33_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),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK8(U_138))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK10(U_138)),sK11(U_138))),hAPP(U_138,sK9(U_138))))
| c_Arrow__Order__Mirabelle_OIIA(U_138) ),
inference(clausify,[status(thm)],[f_33_9]) ).
fof(f_34_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_34_2,plain,
! [U_147] :
( ( c_Arrow__Order__Mirabelle_Ounanimity(U_147)
| ? [U_146] :
( ? [U_145,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_145),U_144)),hAPP(U_147,U_146)))
& ! [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_145),U_144)),hAPP(U_146,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_146),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [U_142] :
( ! [U_141,U_140] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_147,U_142)))
| ? [U_139] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_142,U_139))) )
| ~ 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)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_147) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_149] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_149)
| ? [U_146] :
( ? [U_145,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_145),U_144)),hAPP(U_149,U_146)))
& ! [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_145),U_144)),hAPP(U_146,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_146),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_148] :
( ! [U_142] :
( ! [U_141,U_140] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_148,U_142)))
| ? [U_139] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_142,U_139))) )
| ~ 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)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_148) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_149] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_149)
| ? [U_146] :
( ? [U_145,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_145),U_144)),hAPP(U_149,U_146)))
& ! [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_145),U_144)),hAPP(U_146,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_146),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_148] :
( ! [U_142] :
( ! [U_141,U_140] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_148,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_141),U_140)),hAPP(U_142,sK12(U_148,U_142,U_141,U_140)))) )
| ~ 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)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_148) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_139,sK12(U_148,U_142,U_141,U_140))],[f_34_3]) ).
fof(f_34_5,plain,
( ! [U_149] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_149)
| ( ? [U_145,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_145),U_144)),hAPP(U_149,sK13(U_149))))
& ! [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_145),U_144)),hAPP(sK13(U_149),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))),sK13(U_149)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_148] :
( ! [U_142] :
( ! [U_141,U_140] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_148,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_141),U_140)),hAPP(U_142,sK12(U_148,U_142,U_141,U_140)))) )
| ~ 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)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_148) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_146,sK13(U_149))],[f_34_4]) ).
fof(f_34_6,plain,
( ! [U_149] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_149)
| ( ? [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),sK14(U_149)),U_144)),hAPP(U_149,sK13(U_149))))
& ! [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),sK14(U_149)),U_144)),hAPP(sK13(U_149),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))),sK13(U_149)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_148] :
( ! [U_142] :
( ! [U_141,U_140] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_148,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_141),U_140)),hAPP(U_142,sK12(U_148,U_142,U_141,U_140)))) )
| ~ 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)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_148) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_145,sK14(U_149))],[f_34_5]) ).
fof(f_34_7,plain,
( ! [U_149] :
( c_Arrow__Order__Mirabelle_Ounanimity(U_149)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK14(U_149)),sK15(U_149))),hAPP(U_149,sK13(U_149))))
& ! [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),sK14(U_149)),sK15(U_149))),hAPP(sK13(U_149),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))),sK13(U_149)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_148] :
( ! [U_142] :
( ! [U_141,U_140] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_141),U_140)),hAPP(U_148,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_141),U_140)),hAPP(U_142,sK12(U_148,U_142,U_141,U_140)))) )
| ~ 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)) )
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_148) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_144,sK15(U_149))],[f_34_6]) ).
cnf(f_34_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_141),U_140)),hAPP(U_148,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_141),U_140)),hAPP(U_142,sK12(U_148,U_142,U_141,U_140))))
| ~ 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))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(U_148) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_9,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))),sK13(U_149)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(U_149) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_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),sK14(U_149)),sK15(U_149))),hAPP(sK13(U_149),U_143)))
| c_Arrow__Order__Mirabelle_Ounanimity(U_149) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_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),sK14(U_149)),sK15(U_149))),hAPP(U_149,sK13(U_149))))
| c_Arrow__Order__Mirabelle_Ounanimity(U_149) ),
inference(clausify,[status(thm)],[f_34_7]) ).
fof(f_35_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_35_2,plain,
! [U_157,U_156,U_155,U_154,U_153,U_152,U_151,U_150] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_150,U_151),tc_prod(U_150,U_151))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_150,U_151),tc_prod(U_150,U_151)),hAPP(hAPP(c_Product__Type_OPair(U_150,U_151),U_152),U_153)),hAPP(hAPP(c_Product__Type_OPair(U_150,U_151),U_154),U_155))),c_Wellfounded_Olex__prod(U_150,U_151,U_156,U_157)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_151,U_151)),hAPP(hAPP(c_Product__Type_OPair(U_151,U_151),U_153),U_155)),U_157))
| U_152 != U_154 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_150,U_150)),hAPP(hAPP(c_Product__Type_OPair(U_150,U_150),U_152),U_154)),U_156)) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_151,U_151)),hAPP(hAPP(c_Product__Type_OPair(U_151,U_151),U_153),U_155)),U_157))
& U_152 = U_154 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_150,U_150)),hAPP(hAPP(c_Product__Type_OPair(U_150,U_150),U_152),U_154)),U_156))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_150,U_151),tc_prod(U_150,U_151))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_150,U_151),tc_prod(U_150,U_151)),hAPP(hAPP(c_Product__Type_OPair(U_150,U_151),U_152),U_153)),hAPP(hAPP(c_Product__Type_OPair(U_150,U_151),U_154),U_155))),c_Wellfounded_Olex__prod(U_150,U_151,U_156,U_157))) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_173,U_171,U_169,U_167,U_165,U_163,U_161,U_159] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_159,U_161),tc_prod(U_159,U_161))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_159,U_161),tc_prod(U_159,U_161)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_161),U_163),U_165)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_161),U_167),U_169))),c_Wellfounded_Olex__prod(U_159,U_161,U_171,U_173)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_161,U_161)),hAPP(hAPP(c_Product__Type_OPair(U_161,U_161),U_165),U_169)),U_173))
| U_163 != U_167 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_159,U_159)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_159),U_163),U_167)),U_171)) ) )
& ! [U_172,U_170,U_168,U_166,U_164,U_162,U_160,U_158] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_160,U_160)),hAPP(hAPP(c_Product__Type_OPair(U_160,U_160),U_164),U_168)),U_172))
& U_162 = U_166 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_158,U_158)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_158),U_162),U_166)),U_170))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_158,U_160),tc_prod(U_158,U_160))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_158,U_160),tc_prod(U_158,U_160)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_160),U_162),U_164)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_160),U_166),U_168))),c_Wellfounded_Olex__prod(U_158,U_160,U_170,U_172))) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( U_162 = U_166
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_158,U_158)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_158),U_162),U_166)),U_170))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_158,U_160),tc_prod(U_158,U_160))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_158,U_160),tc_prod(U_158,U_160)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_160),U_162),U_164)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_160),U_166),U_168))),c_Wellfounded_Olex__prod(U_158,U_160,U_170,U_172))) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_160,U_160)),hAPP(hAPP(c_Product__Type_OPair(U_160,U_160),U_164),U_168)),U_172))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_158,U_158)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_158),U_162),U_166)),U_170))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_158,U_160),tc_prod(U_158,U_160))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_158,U_160),tc_prod(U_158,U_160)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_160),U_162),U_164)),hAPP(hAPP(c_Product__Type_OPair(U_158,U_160),U_166),U_168))),c_Wellfounded_Olex__prod(U_158,U_160,U_170,U_172))) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_159,U_159)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_159),U_163),U_167)),U_171))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_159,U_161),tc_prod(U_159,U_161))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_159,U_161),tc_prod(U_159,U_161)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_161),U_163),U_165)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_161),U_167),U_169))),c_Wellfounded_Olex__prod(U_159,U_161,U_171,U_173))) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_161,U_161)),hAPP(hAPP(c_Product__Type_OPair(U_161,U_161),U_165),U_169)),U_173))
| U_163 != U_167
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_159,U_161),tc_prod(U_159,U_161))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_159,U_161),tc_prod(U_159,U_161)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_161),U_163),U_165)),hAPP(hAPP(c_Product__Type_OPair(U_159,U_161),U_167),U_169))),c_Wellfounded_Olex__prod(U_159,U_161,U_171,U_173))) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_177,U_176] :
( ( c_Arrow__Order__Mirabelle_Odictator(U_176,U_177)
| ? [U_175] :
( hAPP(U_176,U_175) != hAPP(U_175,U_177)
& 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_175),c_Arrow__Order__Mirabelle_OProf)) ) )
& ( ! [U_174] :
( hAPP(U_176,U_174) = hAPP(U_174,U_177)
| ~ 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_174),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Odictator(U_176,U_177) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_181,U_179] :
( c_Arrow__Order__Mirabelle_Odictator(U_179,U_181)
| ? [U_175] :
( hAPP(U_179,U_175) != hAPP(U_175,U_181)
& 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_175),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_180,U_178] :
( ! [U_174] :
( hAPP(U_178,U_174) = hAPP(U_174,U_180)
| ~ 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_174),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Odictator(U_178,U_180) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_181,U_179] :
( c_Arrow__Order__Mirabelle_Odictator(U_179,U_181)
| ( hAPP(U_179,sK16(U_181,U_179)) != hAPP(sK16(U_181,U_179),U_181)
& 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))),sK16(U_181,U_179)),c_Arrow__Order__Mirabelle_OProf)) ) )
& ! [U_180,U_178] :
( ! [U_174] :
( hAPP(U_178,U_174) = hAPP(U_174,U_180)
| ~ 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_174),c_Arrow__Order__Mirabelle_OProf)) )
| ~ c_Arrow__Order__Mirabelle_Odictator(U_178,U_180) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_175,sK16(U_181,U_179))],[f_36_3]) ).
cnf(f_36_5,plain,
( hAPP(U_178,U_174) = hAPP(U_174,U_180)
| ~ 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_174),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_Odictator(U_178,U_180) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,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))),sK16(U_181,U_179)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(U_179,U_181) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
( hAPP(U_179,sK16(U_181,U_179)) != hAPP(sK16(U_181,U_179),U_181)
| c_Arrow__Order__Mirabelle_Odictator(U_179,U_181) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_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_37_2,plain,
! [U_186,U_185,U_184,U_183,U_182] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),U_184))
& U_185 != U_182 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_183),U_186)),U_184))
& U_186 != U_183
& U_185 = U_182 ) )
& U_186 != U_182 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
& U_186 = U_182 )
| U_185 = U_186 )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),U_184))
| U_185 = U_182 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_183),U_186)),U_184))
| U_186 = U_183
| U_185 != U_182 ) )
| U_186 = U_182 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_186 != U_182 )
& U_185 != U_186 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_185 != U_186
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_185),U_183)),U_184))
| U_186 != U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_183),U_186)),U_184))
| U_186 = U_183
| U_185 != U_182
| U_186 = U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_185),U_186)),U_184))
| U_185 = U_182
| U_186 = U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_7,plain,
( U_186 != U_182
| U_186 = U_182
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_8,plain,
( U_185 != U_182
| U_185 = U_182
| U_186 = U_182
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_185),U_186)),U_184))
| U_185 = U_182
| U_186 = U_182
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_10,plain,
( U_186 != U_183
| U_185 != U_182
| U_186 = U_182
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_183),U_186)),U_184))
| U_185 != U_182
| U_186 = U_182
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_12,plain,
( U_186 != U_183
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),U_184))
| U_186 = U_182
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_183),U_186)),U_184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),U_184))
| U_186 = U_182
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_14,plain,
( U_186 != U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_15,plain,
( U_185 != U_182
| U_185 = U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_185),U_186)),U_184))
| U_185 = U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_17,plain,
( U_186 != U_183
| U_185 != U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_183),U_186)),U_184))
| U_185 != U_182
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_19,plain,
( U_186 != U_183
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),U_184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_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_183),U_186)),U_184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),U_184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_183)),U_184))
| U_185 = U_186
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_185),U_186)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,U_184),U_182),U_183)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_184),c_Arrow__Order__Mirabelle_OLin))
| U_182 = U_183 ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_187] :
( 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_187)),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_187),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_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))),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_187)),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_187),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_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_39_2,plain,
! [U_190,U_189,U_188] :
( ( hAPP(hAPP(c_COMBC(U_188,tc_fun(U_188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_188)),U_189) = hAPP(hAPP(c_COMBC(U_188,tc_fun(U_188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_188)),U_190)
| U_189 != U_190 )
& ( U_189 = U_190
| hAPP(hAPP(c_COMBC(U_188,tc_fun(U_188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_188)),U_189) != hAPP(hAPP(c_COMBC(U_188,tc_fun(U_188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_188)),U_190) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_196,U_194] :
( ! [U_192] : hAPP(hAPP(c_COMBC(U_192,tc_fun(U_192,tc_HOL_Obool),tc_HOL_Obool),c_member(U_192)),U_194) = hAPP(hAPP(c_COMBC(U_192,tc_fun(U_192,tc_HOL_Obool),tc_HOL_Obool),c_member(U_192)),U_196)
| U_194 != U_196 )
& ! [U_195,U_193] :
( ! [U_191] : hAPP(hAPP(c_COMBC(U_191,tc_fun(U_191,tc_HOL_Obool),tc_HOL_Obool),c_member(U_191)),U_193) != hAPP(hAPP(c_COMBC(U_191,tc_fun(U_191,tc_HOL_Obool),tc_HOL_Obool),c_member(U_191)),U_195)
| U_193 = U_195 ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( hAPP(hAPP(c_COMBC(U_191,tc_fun(U_191,tc_HOL_Obool),tc_HOL_Obool),c_member(U_191)),U_193) != hAPP(hAPP(c_COMBC(U_191,tc_fun(U_191,tc_HOL_Obool),tc_HOL_Obool),c_member(U_191)),U_195)
| U_193 = U_195 ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( hAPP(hAPP(c_COMBC(U_192,tc_fun(U_192,tc_HOL_Obool),tc_HOL_Obool),c_member(U_192)),U_194) = hAPP(hAPP(c_COMBC(U_192,tc_fun(U_192,tc_HOL_Obool),tc_HOL_Obool),c_member(U_192)),U_196)
| U_194 != U_196 ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_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_40_2,plain,
! [U_199,U_198,U_197] :
( 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_199),U_197),U_198)),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_199),c_Arrow__Order__Mirabelle_OLin))
| U_197 = U_198 ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,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_199),U_197),U_198)),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_199),c_Arrow__Order__Mirabelle_OLin))
| U_197 = U_198 ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_201,U_200] :
( 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_200,U_201)),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_200),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,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_200,U_201)),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_200),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_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_42_2,plain,
! [U_203,U_202] :
( 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_202,U_203)),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_202),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,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_202,U_203)),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_202),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_206,U_205,U_204] :
( ( hBOOL(hAPP(hAPP(c_member(U_204),U_205),hAPP(c_fequal,U_206)))
| U_205 != U_206 )
& ( U_205 = U_206
| ~ hBOOL(hAPP(hAPP(c_member(U_204),U_205),hAPP(c_fequal,U_206))) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_212,U_210] :
( ! [U_208] : hBOOL(hAPP(hAPP(c_member(U_208),U_210),hAPP(c_fequal,U_212)))
| U_210 != U_212 )
& ! [U_211,U_209] :
( ! [U_207] : ~ hBOOL(hAPP(hAPP(c_member(U_207),U_209),hAPP(c_fequal,U_211)))
| U_209 = U_211 ) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_207),U_209),hAPP(c_fequal,U_211)))
| U_209 = U_211 ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_208),U_210),hAPP(c_fequal,U_212)))
| U_210 != U_212 ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_215,U_214,U_213] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_214),U_215)),U_213))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_215),U_214)),U_213)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_215),U_214)),U_213))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_214),U_215)),U_213)) ) )
| U_214 = U_215
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_213),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_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),U_215),U_214)),U_213))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_214),U_215)),U_213))
| U_214 = U_215
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_213),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_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_214),U_215)),U_213))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_215),U_214)),U_213))
| U_214 = U_215
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_213),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_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_45_2,plain,
! [U_218,U_217,U_216] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_218),U_217)),U_216))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_217),U_218)),U_216))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_216),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_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),U_218),U_217)),U_216))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_217),U_218)),U_216))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_216),c_Arrow__Order__Mirabelle_OLin)) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_224,U_223,U_222,U_221,U_220,U_219] :
( ~ hBOOL(hAPP(hAPP(c_member(U_219),U_224),U_222))
| hBOOL(hAPP(hAPP(c_member(U_220),hAPP(U_221,U_224)),hAPP(U_223,U_224)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_219,U_220)),U_221),c_FuncSet_OPi(U_219,U_220,U_222,U_223))) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_219),U_224),U_222))
| hBOOL(hAPP(hAPP(c_member(U_220),hAPP(U_221,U_224)),hAPP(U_223,U_224)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_219,U_220)),U_221),c_FuncSet_OPi(U_219,U_220,U_222,U_223))) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_229,U_228,U_227,U_226,U_225] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),U_227))
& U_229 != U_226 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_225)),U_227))
& U_228 != U_225
& U_229 = U_226 ) )
& U_228 != U_226 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
& U_228 = U_226 )
| U_228 = U_229 )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),U_227))
| U_229 = U_226 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_225)),U_227))
| U_228 = U_225
| U_229 != U_226 ) )
| U_228 = U_226 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 != U_226 )
& U_228 != U_229 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226))) ) )
| ~ 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_47_1]) ).
cnf(f_47_3,plain,
( U_228 != U_229
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_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_225),U_229)),U_227))
| U_228 != U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_225)),U_227))
| U_228 = U_225
| U_229 != U_226
| U_228 = U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_229)),U_227))
| U_229 = U_226
| U_228 = U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_7,plain,
( U_228 != U_226
| U_228 = U_226
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_8,plain,
( U_229 != U_226
| U_229 = U_226
| U_228 = U_226
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_229)),U_227))
| U_229 = U_226
| U_228 = U_226
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_10,plain,
( U_228 != U_225
| U_229 != U_226
| U_228 = U_226
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_225)),U_227))
| U_229 != U_226
| U_228 = U_226
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_12,plain,
( U_228 != U_225
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),U_227))
| U_228 = U_226
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_225)),U_227))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),U_227))
| U_228 = U_226
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_14,plain,
( U_228 != U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_15,plain,
( U_229 != U_226
| U_229 = U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_229)),U_227))
| U_229 = U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_17,plain,
( U_228 != U_225
| U_229 != U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_225)),U_227))
| U_229 != U_226
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_19,plain,
( U_228 != U_225
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),U_227))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
cnf(f_47_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_228),U_225)),U_227))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),U_227))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_225),U_229)),U_227))
| U_228 = U_229
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_228),U_229)),c_Arrow__Order__Mirabelle_Oabove(U_227,U_225,U_226)))
| ~ 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_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_234,U_233] :
( c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ? [U_232] :
( ? [U_231,U_230] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_231),U_230)),hAPP(U_233,U_232)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_231),U_230)),hAPP(U_232,U_234)))
& U_231 != U_230 )
& 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_232),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_233),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_48_1]) ).
fof(f_48_3,plain,
! [U_234,U_233] :
( c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ( ? [U_231,U_230] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_231),U_230)),hAPP(U_233,sK17(U_234,U_233))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),U_231),U_230)),hAPP(sK17(U_234,U_233),U_234)))
& U_231 != U_230 )
& 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))),sK17(U_234,U_233)),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_233),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,[sK17]),skolemize(U_232,sK17(U_234,U_233))],[f_48_2]) ).
fof(f_48_4,plain,
! [U_234,U_233] :
( c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ( ? [U_230] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK18(U_234,U_233)),U_230)),hAPP(U_233,sK17(U_234,U_233))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK18(U_234,U_233)),U_230)),hAPP(sK17(U_234,U_233),U_234)))
& sK18(U_234,U_233) != U_230 )
& 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))),sK17(U_234,U_233)),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_233),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,[sK18]),skolemize(U_231,sK18(U_234,U_233))],[f_48_3]) ).
fof(f_48_5,plain,
! [U_234,U_233] :
( c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK18(U_234,U_233)),sK19(U_234,U_233))),hAPP(U_233,sK17(U_234,U_233))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK18(U_234,U_233)),sK19(U_234,U_233))),hAPP(sK17(U_234,U_233),U_234)))
& sK18(U_234,U_233) != sK19(U_234,U_233)
& 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))),sK17(U_234,U_233)),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_233),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,[sK19]),skolemize(U_230,sK19(U_234,U_233))],[f_48_4]) ).
cnf(f_48_6,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))),sK17(U_234,U_233)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ~ 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_233),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_48_5]) ).
cnf(f_48_7,plain,
( sK18(U_234,U_233) != sK19(U_234,U_233)
| c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ~ 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_233),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_48_5]) ).
cnf(f_48_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),sK18(U_234,U_233)),sK19(U_234,U_233))),hAPP(sK17(U_234,U_233),U_234)))
| c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ~ 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_233),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_48_5]) ).
cnf(f_48_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),sK18(U_234,U_233)),sK19(U_234,U_233))),hAPP(U_233,sK17(U_234,U_233))))
| c_Arrow__Order__Mirabelle_Odictator(U_233,U_234)
| ~ 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_233),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_48_5]) ).
fof(f_49_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_49_2,plain,
! [U_240,U_239,U_238,U_237,U_236,U_235] :
( hBOOL(hAPP(hAPP(c_member(U_236),hAPP(U_237,U_240)),U_239))
| ~ hBOOL(hAPP(hAPP(c_member(U_235),U_240),U_238))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_235,U_236)),U_237),c_FuncSet_OPi(U_235,U_236,U_238,c_COMBK(tc_fun(U_236,tc_HOL_Obool),U_235,U_239)))) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_236),hAPP(U_237,U_240)),U_239))
| ~ hBOOL(hAPP(hAPP(c_member(U_235),U_240),U_238))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_235,U_236)),U_237),c_FuncSet_OPi(U_235,U_236,U_238,c_COMBK(tc_fun(U_236,tc_HOL_Obool),U_235,U_239)))) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_246,U_245,U_244,U_243,U_242,U_241] :
( hBOOL(hAPP(hAPP(c_member(U_242),hAPP(U_243,U_246)),hAPP(U_245,U_246)))
| ~ hBOOL(hAPP(hAPP(c_member(U_241),U_246),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_241,U_242)),U_243),c_FuncSet_OPi(U_241,U_242,U_244,U_245))) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_242),hAPP(U_243,U_246)),hAPP(U_245,U_246)))
| ~ hBOOL(hAPP(hAPP(c_member(U_241),U_246),U_244))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_241,U_242)),U_243),c_FuncSet_OPi(U_241,U_242,U_244,U_245))) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_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_51_2,plain,
! [U_248,U_247] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_247,U_247)),c_COMBI(U_247)),c_FuncSet_OPi(U_247,U_247,U_248,c_COMBK(tc_fun(U_247,tc_HOL_Obool),U_247,U_248)))),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_247,U_247)),c_COMBI(U_247)),c_FuncSet_OPi(U_247,U_247,U_248,c_COMBK(tc_fun(U_247,tc_HOL_Obool),U_247,U_248)))),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_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_52_2,plain,
! [U_251,U_250,U_249] :
( 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_251,U_249,U_250)),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_251),c_Arrow__Order__Mirabelle_OLin))
| U_249 = U_250 ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,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_251,U_249,U_250)),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_251),c_Arrow__Order__Mirabelle_OLin))
| U_249 = U_250 ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_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_53_2,plain,
! [U_254,U_253] :
( ? [U_252] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_254)),U_252))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_252),c_Arrow__Order__Mirabelle_OLin)) )
| U_253 = U_254 ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [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_253),U_254)),sK20(U_254,U_253)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK20(U_254,U_253)),c_Arrow__Order__Mirabelle_OLin)) )
| U_253 = U_254 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_252,sK20(U_254,U_253))],[f_53_2]) ).
cnf(f_53_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK20(U_254,U_253)),c_Arrow__Order__Mirabelle_OLin))
| U_253 = U_254 ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_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_253),U_254)),sK20(U_254,U_253)))
| U_253 = U_254 ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_2,plain,
! [U_258,U_257] :
( ( c_Nitpick_Orefl_H(U_257,U_258)
| ? [U_256] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_257,U_257)),hAPP(hAPP(c_Product__Type_OPair(U_257,U_257),U_256),U_256)),U_258)) )
& ( ! [U_255] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_257,U_257)),hAPP(hAPP(c_Product__Type_OPair(U_257,U_257),U_255),U_255)),U_258))
| ~ c_Nitpick_Orefl_H(U_257,U_258) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_262,U_260] :
( c_Nitpick_Orefl_H(U_260,U_262)
| ? [U_256] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_260,U_260)),hAPP(hAPP(c_Product__Type_OPair(U_260,U_260),U_256),U_256)),U_262)) )
& ! [U_261,U_259] :
( ! [U_255] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_259,U_259)),hAPP(hAPP(c_Product__Type_OPair(U_259,U_259),U_255),U_255)),U_261))
| ~ c_Nitpick_Orefl_H(U_259,U_261) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
( ! [U_262,U_260] :
( c_Nitpick_Orefl_H(U_260,U_262)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_260,U_260)),hAPP(hAPP(c_Product__Type_OPair(U_260,U_260),sK21(U_262,U_260)),sK21(U_262,U_260))),U_262)) )
& ! [U_261,U_259] :
( ! [U_255] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_259,U_259)),hAPP(hAPP(c_Product__Type_OPair(U_259,U_259),U_255),U_255)),U_261))
| ~ c_Nitpick_Orefl_H(U_259,U_261) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_256,sK21(U_262,U_260))],[f_54_3]) ).
cnf(f_54_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_259,U_259)),hAPP(hAPP(c_Product__Type_OPair(U_259,U_259),U_255),U_255)),U_261))
| ~ c_Nitpick_Orefl_H(U_259,U_261) ),
inference(clausify,[status(thm)],[f_54_4]) ).
cnf(f_54_6,plain,
( c_Nitpick_Orefl_H(U_260,U_262)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_260,U_260)),hAPP(hAPP(c_Product__Type_OPair(U_260,U_260),sK21(U_262,U_260)),sK21(U_262,U_260))),U_262)) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_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_55_2,plain,
! [U_267,U_266,U_265] :
( ( hBOOL(hAPP(hAPP(c_member(U_265),U_266),c_Wellfounded_Oacc(U_265,U_267)))
| ? [U_264] :
( ~ hBOOL(hAPP(hAPP(c_member(U_265),U_264),c_Wellfounded_Oacc(U_265,U_267)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_265,U_265)),hAPP(hAPP(c_Product__Type_OPair(U_265,U_265),U_264),U_266)),U_267)) ) )
& ( ! [U_263] :
( hBOOL(hAPP(hAPP(c_member(U_265),U_263),c_Wellfounded_Oacc(U_265,U_267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_265,U_265)),hAPP(hAPP(c_Product__Type_OPair(U_265,U_265),U_263),U_266)),U_267)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_265),U_266),c_Wellfounded_Oacc(U_265,U_267))) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_273,U_271,U_269] :
( hBOOL(hAPP(hAPP(c_member(U_269),U_271),c_Wellfounded_Oacc(U_269,U_273)))
| ? [U_264] :
( ~ hBOOL(hAPP(hAPP(c_member(U_269),U_264),c_Wellfounded_Oacc(U_269,U_273)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_269,U_269)),hAPP(hAPP(c_Product__Type_OPair(U_269,U_269),U_264),U_271)),U_273)) ) )
& ! [U_272,U_270,U_268] :
( ! [U_263] :
( hBOOL(hAPP(hAPP(c_member(U_268),U_263),c_Wellfounded_Oacc(U_268,U_272)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_268,U_268)),hAPP(hAPP(c_Product__Type_OPair(U_268,U_268),U_263),U_270)),U_272)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_268),U_270),c_Wellfounded_Oacc(U_268,U_272))) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
( ! [U_273,U_271,U_269] :
( hBOOL(hAPP(hAPP(c_member(U_269),U_271),c_Wellfounded_Oacc(U_269,U_273)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_269),sK22(U_273,U_271,U_269)),c_Wellfounded_Oacc(U_269,U_273)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_269,U_269)),hAPP(hAPP(c_Product__Type_OPair(U_269,U_269),sK22(U_273,U_271,U_269)),U_271)),U_273)) ) )
& ! [U_272,U_270,U_268] :
( ! [U_263] :
( hBOOL(hAPP(hAPP(c_member(U_268),U_263),c_Wellfounded_Oacc(U_268,U_272)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_268,U_268)),hAPP(hAPP(c_Product__Type_OPair(U_268,U_268),U_263),U_270)),U_272)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_268),U_270),c_Wellfounded_Oacc(U_268,U_272))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_264,sK22(U_273,U_271,U_269))],[f_55_3]) ).
cnf(f_55_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_268),U_263),c_Wellfounded_Oacc(U_268,U_272)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_268,U_268)),hAPP(hAPP(c_Product__Type_OPair(U_268,U_268),U_263),U_270)),U_272))
| ~ hBOOL(hAPP(hAPP(c_member(U_268),U_270),c_Wellfounded_Oacc(U_268,U_272))) ),
inference(clausify,[status(thm)],[f_55_4]) ).
cnf(f_55_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_269,U_269)),hAPP(hAPP(c_Product__Type_OPair(U_269,U_269),sK22(U_273,U_271,U_269)),U_271)),U_273))
| hBOOL(hAPP(hAPP(c_member(U_269),U_271),c_Wellfounded_Oacc(U_269,U_273))) ),
inference(clausify,[status(thm)],[f_55_4]) ).
cnf(f_55_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_269),sK22(U_273,U_271,U_269)),c_Wellfounded_Oacc(U_269,U_273)))
| hBOOL(hAPP(hAPP(c_member(U_269),U_271),c_Wellfounded_Oacc(U_269,U_273))) ),
inference(clausify,[status(thm)],[f_55_4]) ).
fof(f_56_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_56_2,plain,
! [U_277,U_276,U_275,U_274] :
( hBOOL(hAPP(hAPP(c_member(U_274),U_277),c_Wellfounded_Oacc(U_274,U_276)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_274,U_274)),hAPP(hAPP(c_Product__Type_OPair(U_274,U_274),U_277),U_275)),U_276))
| ~ hBOOL(hAPP(hAPP(c_member(U_274),U_275),c_Wellfounded_Oacc(U_274,U_276))) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_274),U_277),c_Wellfounded_Oacc(U_274,U_276)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_274,U_274)),hAPP(hAPP(c_Product__Type_OPair(U_274,U_274),U_277),U_275)),U_276))
| ~ hBOOL(hAPP(hAPP(c_member(U_274),U_275),c_Wellfounded_Oacc(U_274,U_276))) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_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_57_2,plain,
! [U_280,U_279,U_278] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_278,hAPP(hAPP(c_COMBC(U_278,tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_fun(U_278,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_278,tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_fun(U_278,tc_HOL_Obool)),U_278),c_COMBC(U_278,tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_278,tc_prod(U_278,U_278)),tc_fun(U_278,tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool)),U_278),hAPP(c_COMBB(tc_prod(U_278,U_278),tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool),U_278),c_member(tc_prod(U_278,U_278)))),c_Product__Type_OPair(U_278,U_278)))),U_279)),U_280))
| ~ hBOOL(hAPP(hAPP(c_member(U_278),U_280),c_Wellfounded_Oacc(U_278,U_279))) )
& ( hBOOL(hAPP(hAPP(c_member(U_278),U_280),c_Wellfounded_Oacc(U_278,U_279)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_278,hAPP(hAPP(c_COMBC(U_278,tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_fun(U_278,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_278,tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_fun(U_278,tc_HOL_Obool)),U_278),c_COMBC(U_278,tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_278,tc_prod(U_278,U_278)),tc_fun(U_278,tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool)),U_278),hAPP(c_COMBB(tc_prod(U_278,U_278),tc_fun(tc_fun(tc_prod(U_278,U_278),tc_HOL_Obool),tc_HOL_Obool),U_278),c_member(tc_prod(U_278,U_278)))),c_Product__Type_OPair(U_278,U_278)))),U_279)),U_280)) ) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_286,U_284,U_282] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_282,hAPP(hAPP(c_COMBC(U_282,tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_fun(U_282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_282,tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_fun(U_282,tc_HOL_Obool)),U_282),c_COMBC(U_282,tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_282,tc_prod(U_282,U_282)),tc_fun(U_282,tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool)),U_282),hAPP(c_COMBB(tc_prod(U_282,U_282),tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool),U_282),c_member(tc_prod(U_282,U_282)))),c_Product__Type_OPair(U_282,U_282)))),U_284)),U_286))
| ~ hBOOL(hAPP(hAPP(c_member(U_282),U_286),c_Wellfounded_Oacc(U_282,U_284))) )
& ! [U_285,U_283,U_281] :
( hBOOL(hAPP(hAPP(c_member(U_281),U_285),c_Wellfounded_Oacc(U_281,U_283)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_281,hAPP(hAPP(c_COMBC(U_281,tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_fun(U_281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_281,tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_fun(U_281,tc_HOL_Obool)),U_281),c_COMBC(U_281,tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_281,tc_prod(U_281,U_281)),tc_fun(U_281,tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool)),U_281),hAPP(c_COMBB(tc_prod(U_281,U_281),tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool),U_281),c_member(tc_prod(U_281,U_281)))),c_Product__Type_OPair(U_281,U_281)))),U_283)),U_285)) ) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_281),U_285),c_Wellfounded_Oacc(U_281,U_283)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_281,hAPP(hAPP(c_COMBC(U_281,tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_fun(U_281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_281,tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_fun(U_281,tc_HOL_Obool)),U_281),c_COMBC(U_281,tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_281,tc_prod(U_281,U_281)),tc_fun(U_281,tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool)),U_281),hAPP(c_COMBB(tc_prod(U_281,U_281),tc_fun(tc_fun(tc_prod(U_281,U_281),tc_HOL_Obool),tc_HOL_Obool),U_281),c_member(tc_prod(U_281,U_281)))),c_Product__Type_OPair(U_281,U_281)))),U_283)),U_285)) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_282,hAPP(hAPP(c_COMBC(U_282,tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_fun(U_282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_282,tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_fun(U_282,tc_HOL_Obool)),U_282),c_COMBC(U_282,tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_282,tc_prod(U_282,U_282)),tc_fun(U_282,tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool)),U_282),hAPP(c_COMBB(tc_prod(U_282,U_282),tc_fun(tc_fun(tc_prod(U_282,U_282),tc_HOL_Obool),tc_HOL_Obool),U_282),c_member(tc_prod(U_282,U_282)))),c_Product__Type_OPair(U_282,U_282)))),U_284)),U_286))
| ~ hBOOL(hAPP(hAPP(c_member(U_282),U_286),c_Wellfounded_Oacc(U_282,U_284))) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_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_58_2,plain,
! [U_290,U_289,U_288] :
( ? [U_287] :
( ~ hBOOL(hAPP(hAPP(c_member(U_288),U_287),c_Wellfounded_Oacc(U_288,U_290)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_288,U_288)),hAPP(hAPP(c_Product__Type_OPair(U_288,U_288),U_287),U_289)),U_290)) )
| hBOOL(hAPP(hAPP(c_member(U_288),U_289),c_Wellfounded_Oacc(U_288,U_290))) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_290,U_289,U_288] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_288),sK23(U_290,U_289,U_288)),c_Wellfounded_Oacc(U_288,U_290)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_288,U_288)),hAPP(hAPP(c_Product__Type_OPair(U_288,U_288),sK23(U_290,U_289,U_288)),U_289)),U_290)) )
| hBOOL(hAPP(hAPP(c_member(U_288),U_289),c_Wellfounded_Oacc(U_288,U_290))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_287,sK23(U_290,U_289,U_288))],[f_58_2]) ).
cnf(f_58_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_288,U_288)),hAPP(hAPP(c_Product__Type_OPair(U_288,U_288),sK23(U_290,U_289,U_288)),U_289)),U_290))
| hBOOL(hAPP(hAPP(c_member(U_288),U_289),c_Wellfounded_Oacc(U_288,U_290))) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_288),sK23(U_290,U_289,U_288)),c_Wellfounded_Oacc(U_288,U_290)))
| hBOOL(hAPP(hAPP(c_member(U_288),U_289),c_Wellfounded_Oacc(U_288,U_290))) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
! [U_294,U_293,U_292] :
( hBOOL(hAPP(hAPP(c_member(U_292),U_293),c_Wellfounded_Oacc(U_292,U_294)))
| ? [U_291] :
( ~ hBOOL(hAPP(hAPP(c_member(U_292),U_291),c_Wellfounded_Oacc(U_292,U_294)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_292,U_292)),hAPP(hAPP(c_Product__Type_OPair(U_292,U_292),U_291),U_293)),U_294)) ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_294,U_293,U_292] :
( hBOOL(hAPP(hAPP(c_member(U_292),U_293),c_Wellfounded_Oacc(U_292,U_294)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_292),sK24(U_294,U_293,U_292)),c_Wellfounded_Oacc(U_292,U_294)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_292,U_292)),hAPP(hAPP(c_Product__Type_OPair(U_292,U_292),sK24(U_294,U_293,U_292)),U_293)),U_294)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_291,sK24(U_294,U_293,U_292))],[f_59_2]) ).
cnf(f_59_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_292,U_292)),hAPP(hAPP(c_Product__Type_OPair(U_292,U_292),sK24(U_294,U_293,U_292)),U_293)),U_294))
| hBOOL(hAPP(hAPP(c_member(U_292),U_293),c_Wellfounded_Oacc(U_292,U_294))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_292),sK24(U_294,U_293,U_292)),c_Wellfounded_Oacc(U_292,U_294)))
| hBOOL(hAPP(hAPP(c_member(U_292),U_293),c_Wellfounded_Oacc(U_292,U_294))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_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_60_2,plain,
! [U_300,U_299,U_298,U_297,U_296] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_296,U_298)),U_299),c_FuncSet_OPi(U_296,U_298,U_297,U_300)))
| ? [U_295] :
( ~ hBOOL(hAPP(hAPP(c_member(U_298),hAPP(U_299,U_295)),hAPP(U_300,U_295)))
& hBOOL(hAPP(hAPP(c_member(U_296),U_295),U_297)) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_300,U_299,U_298,U_297,U_296] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_296,U_298)),U_299),c_FuncSet_OPi(U_296,U_298,U_297,U_300)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_298),hAPP(U_299,sK25(U_300,U_299,U_298,U_297,U_296))),hAPP(U_300,sK25(U_300,U_299,U_298,U_297,U_296))))
& hBOOL(hAPP(hAPP(c_member(U_296),sK25(U_300,U_299,U_298,U_297,U_296)),U_297)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_295,sK25(U_300,U_299,U_298,U_297,U_296))],[f_60_2]) ).
cnf(f_60_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_296),sK25(U_300,U_299,U_298,U_297,U_296)),U_297))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_296,U_298)),U_299),c_FuncSet_OPi(U_296,U_298,U_297,U_300))) ),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_298),hAPP(U_299,sK25(U_300,U_299,U_298,U_297,U_296))),hAPP(U_300,sK25(U_300,U_299,U_298,U_297,U_296))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_296,U_298)),U_299),c_FuncSet_OPi(U_296,U_298,U_297,U_300))) ),
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,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_61_2,plain,
! [U_306,U_305,U_304,U_303,U_302] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_302,U_304)),U_305),c_FuncSet_OPi(U_302,U_304,U_303,c_COMBK(tc_fun(U_304,tc_HOL_Obool),U_302,U_306))))
| ? [U_301] :
( ~ hBOOL(hAPP(hAPP(c_member(U_304),hAPP(U_305,U_301)),U_306))
& hBOOL(hAPP(hAPP(c_member(U_302),U_301),U_303)) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_306,U_305,U_304,U_303,U_302] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_302,U_304)),U_305),c_FuncSet_OPi(U_302,U_304,U_303,c_COMBK(tc_fun(U_304,tc_HOL_Obool),U_302,U_306))))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_304),hAPP(U_305,sK26(U_306,U_305,U_304,U_303,U_302))),U_306))
& hBOOL(hAPP(hAPP(c_member(U_302),sK26(U_306,U_305,U_304,U_303,U_302)),U_303)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_301,sK26(U_306,U_305,U_304,U_303,U_302))],[f_61_2]) ).
cnf(f_61_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_302),sK26(U_306,U_305,U_304,U_303,U_302)),U_303))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_302,U_304)),U_305),c_FuncSet_OPi(U_302,U_304,U_303,c_COMBK(tc_fun(U_304,tc_HOL_Obool),U_302,U_306)))) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_304),hAPP(U_305,sK26(U_306,U_305,U_304,U_303,U_302))),U_306))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_302,U_304)),U_305),c_FuncSet_OPi(U_302,U_304,U_303,c_COMBK(tc_fun(U_304,tc_HOL_Obool),U_302,U_306)))) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_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_62_2,plain,
! [U_312,U_311,U_310,U_309,U_308] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_308,U_310)),U_311),c_FuncSet_OPi(U_308,U_310,U_309,U_312)))
| ? [U_307] :
( ~ hBOOL(hAPP(hAPP(c_member(U_310),hAPP(U_311,U_307)),hAPP(U_312,U_307)))
& hBOOL(hAPP(hAPP(c_member(U_308),U_307),U_309)) ) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_312,U_311,U_310,U_309,U_308] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_308,U_310)),U_311),c_FuncSet_OPi(U_308,U_310,U_309,U_312)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_310),hAPP(U_311,sK27(U_312,U_311,U_310,U_309,U_308))),hAPP(U_312,sK27(U_312,U_311,U_310,U_309,U_308))))
& hBOOL(hAPP(hAPP(c_member(U_308),sK27(U_312,U_311,U_310,U_309,U_308)),U_309)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_307,sK27(U_312,U_311,U_310,U_309,U_308))],[f_62_2]) ).
cnf(f_62_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_308),sK27(U_312,U_311,U_310,U_309,U_308)),U_309))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_308,U_310)),U_311),c_FuncSet_OPi(U_308,U_310,U_309,U_312))) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_310),hAPP(U_311,sK27(U_312,U_311,U_310,U_309,U_308))),hAPP(U_312,sK27(U_312,U_311,U_310,U_309,U_308))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_308,U_310)),U_311),c_FuncSet_OPi(U_308,U_310,U_309,U_312))) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_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_63_2,plain,
! [U_319,U_318,U_317,U_316,U_315,U_314] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319))) ) )
| ? [U_313] :
( hAPP(U_316,U_313) != hAPP(U_317,U_313)
& hBOOL(hAPP(hAPP(c_member(U_314),U_313),U_315)) ) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_319,U_318,U_317,U_316,U_315,U_314] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319))) ) )
| ( hAPP(U_316,sK28(U_319,U_318,U_317,U_316,U_315,U_314)) != hAPP(U_317,sK28(U_319,U_318,U_317,U_316,U_315,U_314))
& hBOOL(hAPP(hAPP(c_member(U_314),sK28(U_319,U_318,U_317,U_316,U_315,U_314)),U_315)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_313,sK28(U_319,U_318,U_317,U_316,U_315,U_314))],[f_63_2]) ).
cnf(f_63_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| hBOOL(hAPP(hAPP(c_member(U_314),sK28(U_319,U_318,U_317,U_316,U_315,U_314)),U_315)) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| hBOOL(hAPP(hAPP(c_member(U_314),sK28(U_319,U_318,U_317,U_316,U_315,U_314)),U_315)) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| hAPP(U_316,sK28(U_319,U_318,U_317,U_316,U_315,U_314)) != hAPP(U_317,sK28(U_319,U_318,U_317,U_316,U_315,U_314)) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_316),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_314,U_318)),U_317),c_FuncSet_OPi(U_314,U_318,U_315,U_319)))
| hAPP(U_316,sK28(U_319,U_318,U_317,U_316,U_315,U_314)) != hAPP(U_317,sK28(U_319,U_318,U_317,U_316,U_315,U_314)) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_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_64_2,plain,
! [U_327,U_326,U_325,U_324,U_323,U_322,U_321,U_320] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_320,U_325)),c_FuncSet_Ocompose(U_320,U_321,U_325,U_323,U_326,U_322)),c_FuncSet_OPi(U_320,U_325,U_323,c_COMBK(tc_fun(U_325,tc_HOL_Obool),U_320,U_327))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_321,U_325)),U_326),c_FuncSet_OPi(U_321,U_325,U_324,c_COMBK(tc_fun(U_325,tc_HOL_Obool),U_321,U_327))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_320,U_321)),U_322),c_FuncSet_OPi(U_320,U_321,U_323,c_COMBK(tc_fun(U_321,tc_HOL_Obool),U_320,U_324)))) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_320,U_325)),c_FuncSet_Ocompose(U_320,U_321,U_325,U_323,U_326,U_322)),c_FuncSet_OPi(U_320,U_325,U_323,c_COMBK(tc_fun(U_325,tc_HOL_Obool),U_320,U_327))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_321,U_325)),U_326),c_FuncSet_OPi(U_321,U_325,U_324,c_COMBK(tc_fun(U_325,tc_HOL_Obool),U_321,U_327))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_320,U_321)),U_322),c_FuncSet_OPi(U_320,U_321,U_323,c_COMBK(tc_fun(U_321,tc_HOL_Obool),U_320,U_324)))) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_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_65_2,plain,
! [U_338,U_337,U_336,U_335,U_334,U_333,U_332,U_331,U_330,U_329,U_328] :
( c_FuncSet_Ocompose(U_328,U_333,U_336,U_331,U_337,c_FuncSet_Ocompose(U_328,U_329,U_333,U_331,U_334,U_330)) = c_FuncSet_Ocompose(U_328,U_329,U_336,U_331,c_FuncSet_Ocompose(U_329,U_333,U_336,U_332,U_337,U_334),U_330)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_333,U_336)),U_337),c_FuncSet_OPi(U_333,U_336,U_335,c_COMBK(tc_fun(U_336,tc_HOL_Obool),U_333,U_338))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_329,U_333)),U_334),c_FuncSet_OPi(U_329,U_333,U_332,c_COMBK(tc_fun(U_333,tc_HOL_Obool),U_329,U_335))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_328,U_329)),U_330),c_FuncSet_OPi(U_328,U_329,U_331,c_COMBK(tc_fun(U_329,tc_HOL_Obool),U_328,U_332)))) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( c_FuncSet_Ocompose(U_328,U_333,U_336,U_331,U_337,c_FuncSet_Ocompose(U_328,U_329,U_333,U_331,U_334,U_330)) = c_FuncSet_Ocompose(U_328,U_329,U_336,U_331,c_FuncSet_Ocompose(U_329,U_333,U_336,U_332,U_337,U_334),U_330)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_333,U_336)),U_337),c_FuncSet_OPi(U_333,U_336,U_335,c_COMBK(tc_fun(U_336,tc_HOL_Obool),U_333,U_338))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_329,U_333)),U_334),c_FuncSet_OPi(U_329,U_333,U_332,c_COMBK(tc_fun(U_333,tc_HOL_Obool),U_329,U_335))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_328,U_329)),U_330),c_FuncSet_OPi(U_328,U_329,U_331,c_COMBK(tc_fun(U_329,tc_HOL_Obool),U_328,U_332)))) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_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_66_2,plain,
! [U_343,U_342,U_341] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_341,U_342),U_343))
| ? [U_340] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_341,U_342),U_340))
& hBOOL(hAPP(hAPP(U_342,U_340),U_343)) ) )
& ( ! [U_339] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_341,U_342),U_339))
| ~ hBOOL(hAPP(hAPP(U_342,U_339),U_343)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_341,U_342),U_343)) ) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_349,U_347,U_345] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_345,U_347),U_349))
| ? [U_340] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_345,U_347),U_340))
& hBOOL(hAPP(hAPP(U_347,U_340),U_349)) ) )
& ! [U_348,U_346,U_344] :
( ! [U_339] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_344,U_346),U_339))
| ~ hBOOL(hAPP(hAPP(U_346,U_339),U_348)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_344,U_346),U_348)) ) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
( ! [U_349,U_347,U_345] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_345,U_347),U_349))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_345,U_347),sK29(U_349,U_347,U_345)))
& hBOOL(hAPP(hAPP(U_347,sK29(U_349,U_347,U_345)),U_349)) ) )
& ! [U_348,U_346,U_344] :
( ! [U_339] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_344,U_346),U_339))
| ~ hBOOL(hAPP(hAPP(U_346,U_339),U_348)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_344,U_346),U_348)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_340,sK29(U_349,U_347,U_345))],[f_66_3]) ).
cnf(f_66_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_344,U_346),U_339))
| ~ hBOOL(hAPP(hAPP(U_346,U_339),U_348))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_344,U_346),U_348)) ),
inference(clausify,[status(thm)],[f_66_4]) ).
cnf(f_66_6,plain,
( hBOOL(hAPP(hAPP(U_347,sK29(U_349,U_347,U_345)),U_349))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_345,U_347),U_349)) ),
inference(clausify,[status(thm)],[f_66_4]) ).
cnf(f_66_7,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_345,U_347),sK29(U_349,U_347,U_345)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_345,U_347),U_349)) ),
inference(clausify,[status(thm)],[f_66_4]) ).
fof(f_67_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_67_2,plain,
! [U_354,U_353,U_352] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_352,U_353),U_354))
| ? [U_351] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_352,U_353),U_351))
& hBOOL(hAPP(hAPP(U_353,U_351),U_354)) ) )
& ( ! [U_350] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_352,U_353),U_350))
| ~ hBOOL(hAPP(hAPP(U_353,U_350),U_354)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_352,U_353),U_354)) ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_360,U_358,U_356] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_356,U_358),U_360))
| ? [U_351] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_356,U_358),U_351))
& hBOOL(hAPP(hAPP(U_358,U_351),U_360)) ) )
& ! [U_359,U_357,U_355] :
( ! [U_350] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_355,U_357),U_350))
| ~ hBOOL(hAPP(hAPP(U_357,U_350),U_359)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_355,U_357),U_359)) ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
( ! [U_360,U_358,U_356] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_356,U_358),U_360))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_356,U_358),sK30(U_360,U_358,U_356)))
& hBOOL(hAPP(hAPP(U_358,sK30(U_360,U_358,U_356)),U_360)) ) )
& ! [U_359,U_357,U_355] :
( ! [U_350] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_355,U_357),U_350))
| ~ hBOOL(hAPP(hAPP(U_357,U_350),U_359)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_355,U_357),U_359)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_351,sK30(U_360,U_358,U_356))],[f_67_3]) ).
cnf(f_67_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_355,U_357),U_350))
| ~ hBOOL(hAPP(hAPP(U_357,U_350),U_359))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_355,U_357),U_359)) ),
inference(clausify,[status(thm)],[f_67_4]) ).
cnf(f_67_6,plain,
( hBOOL(hAPP(hAPP(U_358,sK30(U_360,U_358,U_356)),U_360))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_356,U_358),U_360)) ),
inference(clausify,[status(thm)],[f_67_4]) ).
cnf(f_67_7,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_356,U_358),sK30(U_360,U_358,U_356)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_356,U_358),U_360)) ),
inference(clausify,[status(thm)],[f_67_4]) ).
fof(f_68_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_68_2,plain,
! [U_364,U_363,U_362,U_361] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_361,U_362),U_364))
| ~ hBOOL(hAPP(hAPP(U_362,U_364),U_363))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_361,U_362),U_363)) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_361,U_362),U_364))
| ~ hBOOL(hAPP(hAPP(U_362,U_364),U_363))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_361,U_362),U_363)) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_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_69_2,plain,
! [U_371,U_370,U_369,U_368,U_367,U_366,U_365] :
( hAPP(c_FuncSet_Ocompose(U_365,U_368,U_369,U_367,U_370,U_371),U_366) = hAPP(U_370,hAPP(U_371,U_366))
| ~ hBOOL(hAPP(hAPP(c_member(U_365),U_366),U_367)) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( hAPP(c_FuncSet_Ocompose(U_365,U_368,U_369,U_367,U_370,U_371),U_366) = hAPP(U_370,hAPP(U_371,U_366))
| ~ hBOOL(hAPP(hAPP(c_member(U_365),U_366),U_367)) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_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_70_2,plain,
! [U_377,U_376,U_375,U_374,U_373,U_372] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_372,U_373)),c_FuncSet_Ocompose(U_372,U_374,U_373,U_375,U_376,U_377)),c_FuncSet_Oextensional(U_372,U_373,U_375))),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_372,U_373)),c_FuncSet_Ocompose(U_372,U_374,U_373,U_375,U_376,U_377)),c_FuncSet_Oextensional(U_372,U_373,U_375))),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_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_71_2,plain,
! [U_381,U_380,U_379,U_378] :
( hBOOL(hAPP(hAPP(c_member(U_378),U_381),c_Wellfounded_Oacc(U_378,U_380)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_378,U_378)),hAPP(hAPP(c_Product__Type_OPair(U_378,U_378),U_381),U_379)),c_Transitive__Closure_Ortrancl(U_378,U_380)))
| ~ hBOOL(hAPP(hAPP(c_member(U_378),U_379),c_Wellfounded_Oacc(U_378,U_380))) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_378),U_381),c_Wellfounded_Oacc(U_378,U_380)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_378,U_378)),hAPP(hAPP(c_Product__Type_OPair(U_378,U_378),U_381),U_379)),c_Transitive__Closure_Ortrancl(U_378,U_380)))
| ~ hBOOL(hAPP(hAPP(c_member(U_378),U_379),c_Wellfounded_Oacc(U_378,U_380))) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_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_72_2,plain,
! [U_385,U_384,U_383,U_382] :
( hBOOL(hAPP(hAPP(c_member(U_382),U_383),c_Wellfounded_Oacc(U_382,U_385)))
| ~ hBOOL(hAPP(hAPP(c_member(U_382),U_384),c_Wellfounded_Oacc(U_382,U_385)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_382,U_382)),hAPP(hAPP(c_Product__Type_OPair(U_382,U_382),U_383),U_384)),c_Transitive__Closure_Ortrancl(U_382,U_385))) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_382),U_383),c_Wellfounded_Oacc(U_382,U_385)))
| ~ hBOOL(hAPP(hAPP(c_member(U_382),U_384),c_Wellfounded_Oacc(U_382,U_385)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_382,U_382)),hAPP(hAPP(c_Product__Type_OPair(U_382,U_382),U_383),U_384)),c_Transitive__Closure_Ortrancl(U_382,U_385))) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_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_73_2,plain,
! [U_395,U_394,U_393,U_392,U_391,U_390] :
( ( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_390,U_391,U_392,U_393,U_394),hAPP(hAPP(U_393,U_395),U_394)))
| ! [U_389] :
( ? [U_388] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_390,U_391,U_392,U_393,U_388),hAPP(U_389,U_388)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_390,U_390)),hAPP(hAPP(c_Product__Type_OPair(U_390,U_390),U_388),U_394)),U_392)) )
| hAPP(hAPP(U_393,U_395),U_394) != hAPP(hAPP(U_393,U_389),U_394) ) )
& ( ? [U_387] :
( ! [U_386] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_390,U_391,U_392,U_393,U_386),hAPP(U_387,U_386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_390,U_390)),hAPP(hAPP(c_Product__Type_OPair(U_390,U_390),U_386),U_394)),U_392)) )
& hAPP(hAPP(U_393,U_395),U_394) = hAPP(hAPP(U_393,U_387),U_394) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_390,U_391,U_392,U_393,U_394),hAPP(hAPP(U_393,U_395),U_394))) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_407,U_405,U_403,U_401,U_399,U_397] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,U_405),hAPP(hAPP(U_403,U_407),U_405)))
| ! [U_389] :
( ? [U_388] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,U_388),hAPP(U_389,U_388)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_397,U_397)),hAPP(hAPP(c_Product__Type_OPair(U_397,U_397),U_388),U_405)),U_401)) )
| hAPP(hAPP(U_403,U_407),U_405) != hAPP(hAPP(U_403,U_389),U_405) ) )
& ! [U_406,U_404,U_402,U_400,U_398,U_396] :
( ? [U_387] :
( ! [U_386] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_386),hAPP(U_387,U_386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_396,U_396)),hAPP(hAPP(c_Product__Type_OPair(U_396,U_396),U_386),U_404)),U_400)) )
& hAPP(hAPP(U_402,U_406),U_404) = hAPP(hAPP(U_402,U_387),U_404) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_404),hAPP(hAPP(U_402,U_406),U_404))) ) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_407,U_405,U_403,U_401,U_399,U_397] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,U_405),hAPP(hAPP(U_403,U_407),U_405)))
| ! [U_389] :
( ? [U_388] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,U_388),hAPP(U_389,U_388)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_397,U_397)),hAPP(hAPP(c_Product__Type_OPair(U_397,U_397),U_388),U_405)),U_401)) )
| hAPP(hAPP(U_403,U_407),U_405) != hAPP(hAPP(U_403,U_389),U_405) ) )
& ! [U_406,U_404,U_402,U_400,U_398,U_396] :
( ( ! [U_386] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_386),hAPP(sK31(U_406,U_404,U_402,U_400,U_398,U_396),U_386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_396,U_396)),hAPP(hAPP(c_Product__Type_OPair(U_396,U_396),U_386),U_404)),U_400)) )
& hAPP(hAPP(U_402,U_406),U_404) = hAPP(hAPP(U_402,sK31(U_406,U_404,U_402,U_400,U_398,U_396)),U_404) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_404),hAPP(hAPP(U_402,U_406),U_404))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_387,sK31(U_406,U_404,U_402,U_400,U_398,U_396))],[f_73_3]) ).
fof(f_73_5,plain,
( ! [U_407,U_405,U_403,U_401,U_399,U_397] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,U_405),hAPP(hAPP(U_403,U_407),U_405)))
| ! [U_389] :
( ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,sK32(U_407,U_405,U_403,U_401,U_399,U_397,U_389)),hAPP(U_389,sK32(U_407,U_405,U_403,U_401,U_399,U_397,U_389))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_397,U_397)),hAPP(hAPP(c_Product__Type_OPair(U_397,U_397),sK32(U_407,U_405,U_403,U_401,U_399,U_397,U_389)),U_405)),U_401)) )
| hAPP(hAPP(U_403,U_407),U_405) != hAPP(hAPP(U_403,U_389),U_405) ) )
& ! [U_406,U_404,U_402,U_400,U_398,U_396] :
( ( ! [U_386] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_386),hAPP(sK31(U_406,U_404,U_402,U_400,U_398,U_396),U_386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_396,U_396)),hAPP(hAPP(c_Product__Type_OPair(U_396,U_396),U_386),U_404)),U_400)) )
& hAPP(hAPP(U_402,U_406),U_404) = hAPP(hAPP(U_402,sK31(U_406,U_404,U_402,U_400,U_398,U_396)),U_404) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_404),hAPP(hAPP(U_402,U_406),U_404))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_388,sK32(U_407,U_405,U_403,U_401,U_399,U_397,U_389))],[f_73_4]) ).
cnf(f_73_6,plain,
( hAPP(hAPP(U_402,U_406),U_404) = hAPP(hAPP(U_402,sK31(U_406,U_404,U_402,U_400,U_398,U_396)),U_404)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_404),hAPP(hAPP(U_402,U_406),U_404))) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_7,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_386),hAPP(sK31(U_406,U_404,U_402,U_400,U_398,U_396),U_386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_396,U_396)),hAPP(hAPP(c_Product__Type_OPair(U_396,U_396),U_386),U_404)),U_400))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_396,U_398,U_400,U_402,U_404),hAPP(hAPP(U_402,U_406),U_404))) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_397,U_397)),hAPP(hAPP(c_Product__Type_OPair(U_397,U_397),sK32(U_407,U_405,U_403,U_401,U_399,U_397,U_389)),U_405)),U_401))
| hAPP(hAPP(U_403,U_407),U_405) != hAPP(hAPP(U_403,U_389),U_405)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,U_405),hAPP(hAPP(U_403,U_407),U_405))) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_9,plain,
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,sK32(U_407,U_405,U_403,U_401,U_399,U_397,U_389)),hAPP(U_389,sK32(U_407,U_405,U_403,U_401,U_399,U_397,U_389))))
| hAPP(hAPP(U_403,U_407),U_405) != hAPP(hAPP(U_403,U_389),U_405)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(U_397,U_399,U_401,U_403,U_405),hAPP(hAPP(U_403,U_407),U_405))) ),
inference(clausify,[status(thm)],[f_73_5]) ).
fof(f_74_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_74_2,plain,
! [U_413,U_412,U_411,U_410,U_409,U_408] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_410,U_413),U_409),U_408),U_412),U_411) = hAPP(U_409,U_411)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_410,U_410)),hAPP(hAPP(c_Product__Type_OPair(U_410,U_410),U_411),U_412)),U_408)) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_410,U_413),U_409),U_408),U_412),U_411) = hAPP(U_409,U_411)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_410,U_410)),hAPP(hAPP(c_Product__Type_OPair(U_410,U_410),U_411),U_412)),U_408)) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_75_2,plain,
! [U_421,U_420,U_419,U_418,U_417,U_416] :
( ( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_416,U_417),U_418),U_419),U_420) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_416,U_417),U_421),U_419),U_420)
| ? [U_415] :
( hAPP(U_418,U_415) != hAPP(U_421,U_415)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_416,U_416)),hAPP(hAPP(c_Product__Type_OPair(U_416,U_416),U_415),U_420)),U_419)) ) )
& ( ! [U_414] :
( hAPP(U_418,U_414) = hAPP(U_421,U_414)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_416,U_416)),hAPP(hAPP(c_Product__Type_OPair(U_416,U_416),U_414),U_420)),U_419)) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_416,U_417),U_418),U_419),U_420) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_416,U_417),U_421),U_419),U_420) ) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
( ! [U_433,U_431,U_429,U_427,U_425,U_423] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_427),U_429),U_431) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_433),U_429),U_431)
| ? [U_415] :
( hAPP(U_427,U_415) != hAPP(U_433,U_415)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_423,U_423)),hAPP(hAPP(c_Product__Type_OPair(U_423,U_423),U_415),U_431)),U_429)) ) )
& ! [U_432,U_430,U_428,U_426,U_424,U_422] :
( ! [U_414] :
( hAPP(U_426,U_414) = hAPP(U_432,U_414)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_422,U_422)),hAPP(hAPP(c_Product__Type_OPair(U_422,U_422),U_414),U_430)),U_428)) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_422,U_424),U_426),U_428),U_430) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_422,U_424),U_432),U_428),U_430) ) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
fof(f_75_4,plain,
( ! [U_433,U_431,U_429,U_427,U_425,U_423] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_427),U_429),U_431) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_433),U_429),U_431)
| ( hAPP(U_427,sK33(U_433,U_431,U_429,U_427,U_425,U_423)) != hAPP(U_433,sK33(U_433,U_431,U_429,U_427,U_425,U_423))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_423,U_423)),hAPP(hAPP(c_Product__Type_OPair(U_423,U_423),sK33(U_433,U_431,U_429,U_427,U_425,U_423)),U_431)),U_429)) ) )
& ! [U_432,U_430,U_428,U_426,U_424,U_422] :
( ! [U_414] :
( hAPP(U_426,U_414) = hAPP(U_432,U_414)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_422,U_422)),hAPP(hAPP(c_Product__Type_OPair(U_422,U_422),U_414),U_430)),U_428)) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_422,U_424),U_426),U_428),U_430) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_422,U_424),U_432),U_428),U_430) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_415,sK33(U_433,U_431,U_429,U_427,U_425,U_423))],[f_75_3]) ).
cnf(f_75_5,plain,
( hAPP(U_426,U_414) = hAPP(U_432,U_414)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_422,U_422)),hAPP(hAPP(c_Product__Type_OPair(U_422,U_422),U_414),U_430)),U_428))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_422,U_424),U_426),U_428),U_430) != hAPP(hAPP(hAPP(c_Recdef_Ocut(U_422,U_424),U_432),U_428),U_430) ),
inference(clausify,[status(thm)],[f_75_4]) ).
cnf(f_75_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_423,U_423)),hAPP(hAPP(c_Product__Type_OPair(U_423,U_423),sK33(U_433,U_431,U_429,U_427,U_425,U_423)),U_431)),U_429))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_427),U_429),U_431) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_433),U_429),U_431) ),
inference(clausify,[status(thm)],[f_75_4]) ).
cnf(f_75_7,plain,
( hAPP(U_427,sK33(U_433,U_431,U_429,U_427,U_425,U_423)) != hAPP(U_433,sK33(U_433,U_431,U_429,U_427,U_425,U_423))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_427),U_429),U_431) = hAPP(hAPP(hAPP(c_Recdef_Ocut(U_423,U_425),U_433),U_429),U_431) ),
inference(clausify,[status(thm)],[f_75_4]) ).
fof(f_76_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_76_2,plain,
! [U_439,U_438,U_437,U_436,U_435,U_434] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_434,U_438),U_439),U_437),U_436),U_435) = hAPP(U_439,U_435)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_434,U_434)),hAPP(hAPP(c_Product__Type_OPair(U_434,U_434),U_435),U_436)),U_437)) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_434,U_438),U_439),U_437),U_436),U_435) = hAPP(U_439,U_435)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_434,U_434)),hAPP(hAPP(c_Product__Type_OPair(U_434,U_434),U_435),U_436)),U_437)) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
? [B_L] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_L),c_Arrow__Order__Mirabelle_OLin)),
inference(fof_nnf,[status(thm)],[fact_linear__alt]) ).
fof(f_77_2,plain,
? [U_440] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),U_440),c_Arrow__Order__Mirabelle_OLin)),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK34),c_Arrow__Order__Mirabelle_OLin)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_440,sK34)],[f_77_2]) ).
cnf(f_77_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK34),c_Arrow__Order__Mirabelle_OLin)),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_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_78_2,plain,
! [U_449,U_448,U_447] :
( ( ! [U_446] : hBOOL(hAPP(U_447,U_446))
| ? [U_445,U_444] : ~ hBOOL(hAPP(U_447,hAPP(hAPP(c_Product__Type_OPair(U_448,U_449),U_445),U_444))) )
& ( ! [U_443,U_442] : hBOOL(hAPP(U_447,hAPP(hAPP(c_Product__Type_OPair(U_448,U_449),U_443),U_442)))
| ? [U_441] : ~ hBOOL(hAPP(U_447,U_441)) ) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_455,U_453,U_451] :
( ! [U_446] : hBOOL(hAPP(U_451,U_446))
| ? [U_445,U_444] : ~ hBOOL(hAPP(U_451,hAPP(hAPP(c_Product__Type_OPair(U_453,U_455),U_445),U_444))) )
& ! [U_454,U_452,U_450] :
( ! [U_443,U_442] : hBOOL(hAPP(U_450,hAPP(hAPP(c_Product__Type_OPair(U_452,U_454),U_443),U_442)))
| ? [U_441] : ~ hBOOL(hAPP(U_450,U_441)) ) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
fof(f_78_4,plain,
( ! [U_455,U_453,U_451] :
( ! [U_446] : hBOOL(hAPP(U_451,U_446))
| ? [U_445,U_444] : ~ hBOOL(hAPP(U_451,hAPP(hAPP(c_Product__Type_OPair(U_453,U_455),U_445),U_444))) )
& ! [U_454,U_452,U_450] :
( ! [U_443,U_442] : hBOOL(hAPP(U_450,hAPP(hAPP(c_Product__Type_OPair(U_452,U_454),U_443),U_442)))
| ~ hBOOL(hAPP(U_450,sK35(U_454,U_452,U_450))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_441,sK35(U_454,U_452,U_450))],[f_78_3]) ).
fof(f_78_5,plain,
( ! [U_455,U_453,U_451] :
( ! [U_446] : hBOOL(hAPP(U_451,U_446))
| ? [U_444] : ~ hBOOL(hAPP(U_451,hAPP(hAPP(c_Product__Type_OPair(U_453,U_455),sK36(U_455,U_453,U_451)),U_444))) )
& ! [U_454,U_452,U_450] :
( ! [U_443,U_442] : hBOOL(hAPP(U_450,hAPP(hAPP(c_Product__Type_OPair(U_452,U_454),U_443),U_442)))
| ~ hBOOL(hAPP(U_450,sK35(U_454,U_452,U_450))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_445,sK36(U_455,U_453,U_451))],[f_78_4]) ).
fof(f_78_6,plain,
( ! [U_455,U_453,U_451] :
( ! [U_446] : hBOOL(hAPP(U_451,U_446))
| ~ hBOOL(hAPP(U_451,hAPP(hAPP(c_Product__Type_OPair(U_453,U_455),sK36(U_455,U_453,U_451)),sK37(U_455,U_453,U_451)))) )
& ! [U_454,U_452,U_450] :
( ! [U_443,U_442] : hBOOL(hAPP(U_450,hAPP(hAPP(c_Product__Type_OPair(U_452,U_454),U_443),U_442)))
| ~ hBOOL(hAPP(U_450,sK35(U_454,U_452,U_450))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_444,sK37(U_455,U_453,U_451))],[f_78_5]) ).
cnf(f_78_7,plain,
( hBOOL(hAPP(U_450,hAPP(hAPP(c_Product__Type_OPair(U_452,U_454),U_443),U_442)))
| ~ hBOOL(hAPP(U_450,sK35(U_454,U_452,U_450))) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_8,plain,
( hBOOL(hAPP(U_451,U_446))
| ~ hBOOL(hAPP(U_451,hAPP(hAPP(c_Product__Type_OPair(U_453,U_455),sK36(U_455,U_453,U_451)),sK37(U_455,U_453,U_451)))) ),
inference(clausify,[status(thm)],[f_78_6]) ).
fof(f_79_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_79_2,plain,
! [U_461,U_460,U_459,U_458,U_457,U_456] :
( ( U_459 = U_461
& U_458 = U_460 )
| hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_458),U_459) != hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_460),U_461) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_461,U_460,U_459,U_458] :
( ! [U_457,U_456] : hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_458),U_459) != hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_460),U_461)
| ( U_459 = U_461
& U_458 = U_460 ) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( U_458 = U_460
| hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_458),U_459) != hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_460),U_461) ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_5,plain,
( U_459 = U_461
| hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_458),U_459) != hAPP(hAPP(c_Product__Type_OPair(U_456,U_457),U_460),U_461) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_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_80_2,plain,
! [U_467,U_466,U_465,U_464,U_463,U_462] :
( ( hAPP(hAPP(c_Product__Type_OPair(U_462,U_463),U_464),U_465) = hAPP(hAPP(c_Product__Type_OPair(U_462,U_463),U_466),U_467)
| U_465 != U_467
| U_464 != U_466 )
& ( ( U_465 = U_467
& U_464 = U_466 )
| hAPP(hAPP(c_Product__Type_OPair(U_462,U_463),U_464),U_465) != hAPP(hAPP(c_Product__Type_OPair(U_462,U_463),U_466),U_467) ) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_479,U_477,U_475,U_473] :
( ! [U_471,U_469] : hAPP(hAPP(c_Product__Type_OPair(U_469,U_471),U_473),U_475) = hAPP(hAPP(c_Product__Type_OPair(U_469,U_471),U_477),U_479)
| U_475 != U_479
| U_473 != U_477 )
& ! [U_478,U_476,U_474,U_472] :
( ! [U_470,U_468] : hAPP(hAPP(c_Product__Type_OPair(U_468,U_470),U_472),U_474) != hAPP(hAPP(c_Product__Type_OPair(U_468,U_470),U_476),U_478)
| ( U_474 = U_478
& U_472 = U_476 ) ) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
cnf(f_80_4,plain,
( U_472 = U_476
| hAPP(hAPP(c_Product__Type_OPair(U_468,U_470),U_472),U_474) != hAPP(hAPP(c_Product__Type_OPair(U_468,U_470),U_476),U_478) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_5,plain,
( U_474 = U_478
| hAPP(hAPP(c_Product__Type_OPair(U_468,U_470),U_472),U_474) != hAPP(hAPP(c_Product__Type_OPair(U_468,U_470),U_476),U_478) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_6,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_469,U_471),U_473),U_475) = hAPP(hAPP(c_Product__Type_OPair(U_469,U_471),U_477),U_479)
| U_475 != U_479
| U_473 != U_477 ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_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_81_2,plain,
! [U_482,U_481,U_480] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_480,U_480)),hAPP(hAPP(c_Product__Type_OPair(U_480,U_480),U_481),U_481)),c_Transitive__Closure_Ortrancl(U_480,U_482))),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(U_480,U_480)),hAPP(hAPP(c_Product__Type_OPair(U_480,U_480),U_481),U_481)),c_Transitive__Closure_Ortrancl(U_480,U_482))),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_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_82_2,plain,
! [U_485,U_484,U_483] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_483,U_483)),U_484),c_Transitive__Closure_Ortrancl(U_483,U_485)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_483,U_483)),U_484),U_485)) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_483,U_483)),U_484),c_Transitive__Closure_Ortrancl(U_483,U_485)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_483,U_483)),U_484),U_485)) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_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_83_2,plain,
! [U_490,U_489,U_488,U_487,U_486] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_486,U_486)),hAPP(hAPP(c_Product__Type_OPair(U_486,U_486),U_487),U_490)),c_Transitive__Closure_Ortrancl(U_486,U_489)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_486,U_486)),hAPP(hAPP(c_Product__Type_OPair(U_486,U_486),U_488),U_490)),c_Transitive__Closure_Ortrancl(U_486,U_489)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_486,U_486)),hAPP(hAPP(c_Product__Type_OPair(U_486,U_486),U_487),U_488)),c_Transitive__Closure_Ortrancl(U_486,U_489))) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_486,U_486)),hAPP(hAPP(c_Product__Type_OPair(U_486,U_486),U_487),U_490)),c_Transitive__Closure_Ortrancl(U_486,U_489)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_486,U_486)),hAPP(hAPP(c_Product__Type_OPair(U_486,U_486),U_488),U_490)),c_Transitive__Closure_Ortrancl(U_486,U_489)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_486,U_486)),hAPP(hAPP(c_Product__Type_OPair(U_486,U_486),U_487),U_488)),c_Transitive__Closure_Ortrancl(U_486,U_489))) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_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_84_2,plain,
! [U_495,U_494,U_493,U_492,U_491] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_491,U_491)),hAPP(hAPP(c_Product__Type_OPair(U_491,U_491),U_492),U_495)),c_Transitive__Closure_Ortrancl(U_491,U_494)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_491,U_491)),hAPP(hAPP(c_Product__Type_OPair(U_491,U_491),U_493),U_495)),U_494))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_491,U_491)),hAPP(hAPP(c_Product__Type_OPair(U_491,U_491),U_492),U_493)),c_Transitive__Closure_Ortrancl(U_491,U_494))) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_491,U_491)),hAPP(hAPP(c_Product__Type_OPair(U_491,U_491),U_492),U_495)),c_Transitive__Closure_Ortrancl(U_491,U_494)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_491,U_491)),hAPP(hAPP(c_Product__Type_OPair(U_491,U_491),U_493),U_495)),U_494))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_491,U_491)),hAPP(hAPP(c_Product__Type_OPair(U_491,U_491),U_492),U_493)),c_Transitive__Closure_Ortrancl(U_491,U_494))) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_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_85_2,plain,
! [U_500,U_499,U_498,U_497,U_496] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_496,U_496)),hAPP(hAPP(c_Product__Type_OPair(U_496,U_496),U_497),U_500)),c_Transitive__Closure_Ortrancl(U_496,U_499)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_496,U_496)),hAPP(hAPP(c_Product__Type_OPair(U_496,U_496),U_498),U_500)),c_Transitive__Closure_Ortrancl(U_496,U_499)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_496,U_496)),hAPP(hAPP(c_Product__Type_OPair(U_496,U_496),U_497),U_498)),U_499)) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_496,U_496)),hAPP(hAPP(c_Product__Type_OPair(U_496,U_496),U_497),U_500)),c_Transitive__Closure_Ortrancl(U_496,U_499)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_496,U_496)),hAPP(hAPP(c_Product__Type_OPair(U_496,U_496),U_498),U_500)),c_Transitive__Closure_Ortrancl(U_496,U_499)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_496,U_496)),hAPP(hAPP(c_Product__Type_OPair(U_496,U_496),U_497),U_498)),U_499)) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_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_86_2,plain,
! [U_506,U_505,U_504,U_503,U_502,U_501] : c_Product__Type_Oprod_Oprod__rec(U_501,U_502,U_503,U_504,hAPP(hAPP(c_Product__Type_OPair(U_501,U_502),U_505),U_506)) = hAPP(hAPP(U_504,U_505),U_506),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
c_Product__Type_Oprod_Oprod__rec(U_501,U_502,U_503,U_504,hAPP(hAPP(c_Product__Type_OPair(U_501,U_502),U_505),U_506)) = hAPP(hAPP(U_504,U_505),U_506),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_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_87_2,plain,
! [U_511,U_510,U_509,U_508,U_507] :
( c_FuncSet_Ocompose(U_507,U_508,U_508,U_510,c_FuncSet_Orestrict(U_508,U_508,c_COMBI(U_508),U_511),U_509) = U_509
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_507,U_508)),U_509),c_FuncSet_Oextensional(U_507,U_508,U_510)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_507,U_508)),U_509),c_FuncSet_OPi(U_507,U_508,U_510,c_COMBK(tc_fun(U_508,tc_HOL_Obool),U_507,U_511)))) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( c_FuncSet_Ocompose(U_507,U_508,U_508,U_510,c_FuncSet_Orestrict(U_508,U_508,c_COMBI(U_508),U_511),U_509) = U_509
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_507,U_508)),U_509),c_FuncSet_Oextensional(U_507,U_508,U_510)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_507,U_508)),U_509),c_FuncSet_OPi(U_507,U_508,U_510,c_COMBK(tc_fun(U_508,tc_HOL_Obool),U_507,U_511)))) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_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_88_2,plain,
! [U_516,U_515,U_514,U_513,U_512] :
( c_FuncSet_Ocompose(U_512,U_512,U_513,U_515,U_514,c_FuncSet_Orestrict(U_512,U_512,c_COMBI(U_512),U_515)) = U_514
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_512,U_513)),U_514),c_FuncSet_Oextensional(U_512,U_513,U_515)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_512,U_513)),U_514),c_FuncSet_OPi(U_512,U_513,U_515,c_COMBK(tc_fun(U_513,tc_HOL_Obool),U_512,U_516)))) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( c_FuncSet_Ocompose(U_512,U_512,U_513,U_515,U_514,c_FuncSet_Orestrict(U_512,U_512,c_COMBI(U_512),U_515)) = U_514
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_512,U_513)),U_514),c_FuncSet_Oextensional(U_512,U_513,U_515)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_512,U_513)),U_514),c_FuncSet_OPi(U_512,U_513,U_515,c_COMBK(tc_fun(U_513,tc_HOL_Obool),U_512,U_516)))) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_522,U_521,U_520,U_519,U_518,U_517] : c_FuncSet_Ocompose(U_517,U_518,U_519,U_520,U_521,U_522) = c_FuncSet_Orestrict(U_517,U_519,hAPP(hAPP(c_COMBB(U_518,U_519,U_517),U_521),U_522),U_520),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
c_FuncSet_Ocompose(U_517,U_518,U_519,U_520,U_521,U_522) = c_FuncSet_Orestrict(U_517,U_519,hAPP(hAPP(c_COMBB(U_518,U_519,U_517),U_521),U_522),U_520),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_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_90_2,plain,
! [U_526,U_525,U_524,U_523] :
( c_FuncSet_Orestrict(U_523,U_524,U_525,U_526) = U_525
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_523,U_524)),U_525),c_FuncSet_Oextensional(U_523,U_524,U_526))) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( c_FuncSet_Orestrict(U_523,U_524,U_525,U_526) = U_525
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_523,U_524)),U_525),c_FuncSet_Oextensional(U_523,U_524,U_526))) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_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_91_2,plain,
! [U_530,U_529,U_528,U_527] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_527,U_528)),c_FuncSet_Orestrict(U_527,U_528,U_529,U_530)),c_FuncSet_Oextensional(U_527,U_528,U_530))),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_527,U_528)),c_FuncSet_Orestrict(U_527,U_528,U_529,U_530)),c_FuncSet_Oextensional(U_527,U_528,U_530))),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_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_92_2,plain,
! [U_532,U_531] : c_Transitive__Closure_Ortrancl(U_531,c_Transitive__Closure_Ortrancl(U_531,U_532)) = c_Transitive__Closure_Ortrancl(U_531,U_532),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
c_Transitive__Closure_Ortrancl(U_531,c_Transitive__Closure_Ortrancl(U_531,U_532)) = c_Transitive__Closure_Ortrancl(U_531,U_532),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_93_2,plain,
! [U_538,U_537,U_536,U_535,U_534] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_534,U_536)),c_FuncSet_Orestrict(U_534,U_536,U_537,U_535)),c_FuncSet_OPi(U_534,U_536,U_535,U_538)))
| ? [U_533] :
( ~ hBOOL(hAPP(hAPP(c_member(U_536),hAPP(U_537,U_533)),hAPP(U_538,U_533)))
& hBOOL(hAPP(hAPP(c_member(U_534),U_533),U_535)) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_538,U_537,U_536,U_535,U_534] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_534,U_536)),c_FuncSet_Orestrict(U_534,U_536,U_537,U_535)),c_FuncSet_OPi(U_534,U_536,U_535,U_538)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_536),hAPP(U_537,sK38(U_538,U_537,U_536,U_535,U_534))),hAPP(U_538,sK38(U_538,U_537,U_536,U_535,U_534))))
& hBOOL(hAPP(hAPP(c_member(U_534),sK38(U_538,U_537,U_536,U_535,U_534)),U_535)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_533,sK38(U_538,U_537,U_536,U_535,U_534))],[f_93_2]) ).
cnf(f_93_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_534),sK38(U_538,U_537,U_536,U_535,U_534)),U_535))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_534,U_536)),c_FuncSet_Orestrict(U_534,U_536,U_537,U_535)),c_FuncSet_OPi(U_534,U_536,U_535,U_538))) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_536),hAPP(U_537,sK38(U_538,U_537,U_536,U_535,U_534))),hAPP(U_538,sK38(U_538,U_537,U_536,U_535,U_534))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_534,U_536)),c_FuncSet_Orestrict(U_534,U_536,U_537,U_535)),c_FuncSet_OPi(U_534,U_536,U_535,U_538))) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_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_94_2,plain,
! [U_542,U_541,U_540,U_539] : c_Recdef_Oadm__wf(U_539,U_540,U_541,hAPP(hAPP(c_COMBC(tc_fun(U_539,U_540),tc_fun(U_539,U_539),tc_fun(U_539,U_540)),hAPP(hAPP(c_COMBB(tc_fun(U_539,tc_fun(U_539,U_540)),tc_fun(tc_fun(U_539,U_539),tc_fun(U_539,U_540)),tc_fun(U_539,U_540)),c_COMBS(U_539,U_539,U_540)),hAPP(hAPP(c_COMBB(tc_fun(U_539,tc_fun(U_539,U_540)),tc_fun(U_539,tc_fun(U_539,U_540)),tc_fun(U_539,U_540)),hAPP(c_COMBB(tc_fun(U_539,U_540),tc_fun(U_539,U_540),U_539),U_542)),hAPP(hAPP(c_COMBC(tc_fun(U_539,U_540),tc_fun(tc_prod(U_539,U_539),tc_HOL_Obool),tc_fun(U_539,tc_fun(U_539,U_540))),c_Recdef_Ocut(U_539,U_540)),U_541)))),c_COMBI(U_539))),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
c_Recdef_Oadm__wf(U_539,U_540,U_541,hAPP(hAPP(c_COMBC(tc_fun(U_539,U_540),tc_fun(U_539,U_539),tc_fun(U_539,U_540)),hAPP(hAPP(c_COMBB(tc_fun(U_539,tc_fun(U_539,U_540)),tc_fun(tc_fun(U_539,U_539),tc_fun(U_539,U_540)),tc_fun(U_539,U_540)),c_COMBS(U_539,U_539,U_540)),hAPP(hAPP(c_COMBB(tc_fun(U_539,tc_fun(U_539,U_540)),tc_fun(U_539,tc_fun(U_539,U_540)),tc_fun(U_539,U_540)),hAPP(c_COMBB(tc_fun(U_539,U_540),tc_fun(U_539,U_540),U_539),U_542)),hAPP(hAPP(c_COMBC(tc_fun(U_539,U_540),tc_fun(tc_prod(U_539,U_539),tc_HOL_Obool),tc_fun(U_539,tc_fun(U_539,U_540))),c_Recdef_Ocut(U_539,U_540)),U_541)))),c_COMBI(U_539))),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_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_95_2,plain,
! [U_548,U_547,U_546,U_545,U_544] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_544,U_546)),c_FuncSet_Orestrict(U_544,U_546,U_547,U_545)),c_FuncSet_OPi(U_544,U_546,U_545,c_COMBK(tc_fun(U_546,tc_HOL_Obool),U_544,U_548))))
| ? [U_543] :
( ~ hBOOL(hAPP(hAPP(c_member(U_546),hAPP(U_547,U_543)),U_548))
& hBOOL(hAPP(hAPP(c_member(U_544),U_543),U_545)) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_548,U_547,U_546,U_545,U_544] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_544,U_546)),c_FuncSet_Orestrict(U_544,U_546,U_547,U_545)),c_FuncSet_OPi(U_544,U_546,U_545,c_COMBK(tc_fun(U_546,tc_HOL_Obool),U_544,U_548))))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_546),hAPP(U_547,sK39(U_548,U_547,U_546,U_545,U_544))),U_548))
& hBOOL(hAPP(hAPP(c_member(U_544),sK39(U_548,U_547,U_546,U_545,U_544)),U_545)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_543,sK39(U_548,U_547,U_546,U_545,U_544))],[f_95_2]) ).
cnf(f_95_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_544),sK39(U_548,U_547,U_546,U_545,U_544)),U_545))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_544,U_546)),c_FuncSet_Orestrict(U_544,U_546,U_547,U_545)),c_FuncSet_OPi(U_544,U_546,U_545,c_COMBK(tc_fun(U_546,tc_HOL_Obool),U_544,U_548)))) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_546),hAPP(U_547,sK39(U_548,U_547,U_546,U_545,U_544))),U_548))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_544,U_546)),c_FuncSet_Orestrict(U_544,U_546,U_547,U_545)),c_FuncSet_OPi(U_544,U_546,U_545,c_COMBK(tc_fun(U_546,tc_HOL_Obool),U_544,U_548)))) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_553,U_552,U_551,U_550,U_549] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_553),U_552)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_552),U_553)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_551),U_553)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_551),U_552)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| ~ c_Relation_Osingle__valued(U_549,U_549,U_550) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_553),U_552)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_552),U_553)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_551),U_553)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_549,U_549)),hAPP(hAPP(c_Product__Type_OPair(U_549,U_549),U_551),U_552)),c_Transitive__Closure_Ortrancl(U_549,U_550)))
| ~ c_Relation_Osingle__valued(U_549,U_549,U_550) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_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_97_2,plain,
! [U_559,U_558,U_557,U_556,U_555,U_554] :
( ( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_554,U_558),U_559),U_557),U_556),U_555) = c_HOL_Oundefined(U_558)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_554,U_554)),hAPP(hAPP(c_Product__Type_OPair(U_554,U_554),U_555),U_556)),U_557)) )
& ( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_554,U_558),U_559),U_557),U_556),U_555) = hAPP(U_559,U_555)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_554,U_554)),hAPP(hAPP(c_Product__Type_OPair(U_554,U_554),U_555),U_556)),U_557)) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( ! [U_571,U_569,U_567,U_565,U_563,U_561] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_561,U_569),U_571),U_567),U_565),U_563) = c_HOL_Oundefined(U_569)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_561,U_561)),hAPP(hAPP(c_Product__Type_OPair(U_561,U_561),U_563),U_565)),U_567)) )
& ! [U_570,U_568,U_566,U_564,U_562,U_560] :
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_560,U_568),U_570),U_566),U_564),U_562) = hAPP(U_570,U_562)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_560,U_560)),hAPP(hAPP(c_Product__Type_OPair(U_560,U_560),U_562),U_564)),U_566)) ) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_560,U_568),U_570),U_566),U_564),U_562) = hAPP(U_570,U_562)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_560,U_560)),hAPP(hAPP(c_Product__Type_OPair(U_560,U_560),U_562),U_564)),U_566)) ),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_5,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(U_561,U_569),U_571),U_567),U_565),U_563) = c_HOL_Oundefined(U_569)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_561,U_561)),hAPP(hAPP(c_Product__Type_OPair(U_561,U_561),U_563),U_565)),U_567)) ),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_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_98_2,plain,
! [U_575,U_574,U_573,U_572] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_572,U_572)),hAPP(hAPP(c_Product__Type_OPair(U_572,U_572),U_573),U_575)),c_Transitive__Closure_Ortrancl(U_572,U_574)))
| U_573 != U_575 )
& ( U_573 = U_575
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_572,U_572)),hAPP(hAPP(c_Product__Type_OPair(U_572,U_572),U_573),U_575)),c_Transitive__Closure_Ortrancl(U_572,U_574))) ) )
| hBOOL(hAPP(hAPP(c_member(U_572),U_573),c_Relation_ODomain(U_572,U_572,U_574))) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( U_573 = U_575
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_572,U_572)),hAPP(hAPP(c_Product__Type_OPair(U_572,U_572),U_573),U_575)),c_Transitive__Closure_Ortrancl(U_572,U_574)))
| hBOOL(hAPP(hAPP(c_member(U_572),U_573),c_Relation_ODomain(U_572,U_572,U_574))) ),
inference(clausify,[status(thm)],[f_98_2]) ).
cnf(f_98_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_572,U_572)),hAPP(hAPP(c_Product__Type_OPair(U_572,U_572),U_573),U_575)),c_Transitive__Closure_Ortrancl(U_572,U_574)))
| U_573 != U_575
| hBOOL(hAPP(hAPP(c_member(U_572),U_573),c_Relation_ODomain(U_572,U_572,U_574))) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [V_ba_2,V_aa_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(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_99_2,plain,
! [U_581,U_580,U_579,U_578,U_577,U_576] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_576,U_577,U_578),U_579),hAPP(hAPP(c_Product__Type_OPair(U_576,U_577),U_580),U_581)) = hAPP(hAPP(U_579,U_580),U_581),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
hAPP(hAPP(c_Product__Type_Ointernal__split(U_576,U_577,U_578),U_579),hAPP(hAPP(c_Product__Type_OPair(U_576,U_577),U_580),U_581)) = hAPP(hAPP(U_579,U_580),U_581),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [V_y_2,V_x_2,V_ca_2,T_a,T_c,T_b] : 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_100_2,plain,
! [U_587,U_586,U_585,U_584,U_583,U_582] : c_Product__Type_Ocurry(U_582,U_583,U_584,U_585,U_586,U_587) = hAPP(U_585,hAPP(hAPP(c_Product__Type_OPair(U_582,U_583),U_586),U_587)),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
c_Product__Type_Ocurry(U_582,U_583,U_584,U_585,U_586,U_587) = hAPP(U_585,hAPP(hAPP(c_Product__Type_OPair(U_582,U_583),U_586),U_587)),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [V_ba_2,V_aa_2,T_b,T_a,V_f_2] :
( hBOOL(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_101_2,plain,
! [U_592,U_591,U_590,U_589,U_588] :
( hBOOL(c_Product__Type_Ocurry(U_589,U_590,tc_HOL_Obool,U_588,U_591,U_592))
| ~ hBOOL(hAPP(U_588,hAPP(hAPP(c_Product__Type_OPair(U_589,U_590),U_591),U_592))) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( hBOOL(c_Product__Type_Ocurry(U_589,U_590,tc_HOL_Obool,U_588,U_591,U_592))
| ~ hBOOL(hAPP(U_588,hAPP(hAPP(c_Product__Type_OPair(U_589,U_590),U_591),U_592))) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_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(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_102_2,plain,
! [U_597,U_596,U_595,U_594,U_593] :
( hBOOL(hAPP(U_595,hAPP(hAPP(c_Product__Type_OPair(U_593,U_594),U_596),U_597)))
| ~ hBOOL(c_Product__Type_Ocurry(U_593,U_594,tc_HOL_Obool,U_595,U_596,U_597)) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( hBOOL(hAPP(U_595,hAPP(hAPP(c_Product__Type_OPair(U_593,U_594),U_596),U_597)))
| ~ hBOOL(c_Product__Type_Ocurry(U_593,U_594,tc_HOL_Obool,U_595,U_596,U_597)) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_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(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_103_2,plain,
! [U_602,U_601,U_600,U_599,U_598] :
( hBOOL(hAPP(U_600,hAPP(hAPP(c_Product__Type_OPair(U_598,U_599),U_601),U_602)))
| ~ hBOOL(c_Product__Type_Ocurry(U_598,U_599,tc_HOL_Obool,U_600,U_601,U_602)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( hBOOL(hAPP(U_600,hAPP(hAPP(c_Product__Type_OPair(U_598,U_599),U_601),U_602)))
| ~ hBOOL(c_Product__Type_Ocurry(U_598,U_599,tc_HOL_Obool,U_600,U_601,U_602)) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [V_ba_2,V_aa_2,V_f_2,T_a,T_c,T_b] : 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_104_2,plain,
! [U_608,U_607,U_606,U_605,U_604,U_603] : c_Product__Type_Ocurry(U_603,U_604,U_605,U_606,U_607,U_608) = hAPP(U_606,hAPP(hAPP(c_Product__Type_OPair(U_603,U_604),U_607),U_608)),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
c_Product__Type_Ocurry(U_603,U_604,U_605,U_606,U_607,U_608) = hAPP(U_606,hAPP(hAPP(c_Product__Type_OPair(U_603,U_604),U_607),U_608)),
inference(clausify,[status(thm)],[f_104_2]) ).
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_613,U_612,U_611,U_610,U_609] :
( ( hAPP(c_FuncSet_Orestrict(U_609,U_612,U_613,U_611),U_610) = c_HOL_Oundefined(U_612)
| hBOOL(hAPP(hAPP(c_member(U_609),U_610),U_611)) )
& ( hAPP(c_FuncSet_Orestrict(U_609,U_612,U_613,U_611),U_610) = hAPP(U_613,U_610)
| ~ hBOOL(hAPP(hAPP(c_member(U_609),U_610),U_611)) ) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( ! [U_623,U_621,U_619,U_617,U_615] :
( hAPP(c_FuncSet_Orestrict(U_615,U_621,U_623,U_619),U_617) = c_HOL_Oundefined(U_621)
| hBOOL(hAPP(hAPP(c_member(U_615),U_617),U_619)) )
& ! [U_622,U_620,U_618,U_616,U_614] :
( hAPP(c_FuncSet_Orestrict(U_614,U_620,U_622,U_618),U_616) = hAPP(U_622,U_616)
| ~ hBOOL(hAPP(hAPP(c_member(U_614),U_616),U_618)) ) ),
inference(miniscope,[status(thm)],[f_105_2]) ).
cnf(f_105_4,plain,
( hAPP(c_FuncSet_Orestrict(U_614,U_620,U_622,U_618),U_616) = hAPP(U_622,U_616)
| ~ hBOOL(hAPP(hAPP(c_member(U_614),U_616),U_618)) ),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_5,plain,
( hAPP(c_FuncSet_Orestrict(U_615,U_621,U_623,U_619),U_617) = c_HOL_Oundefined(U_621)
| hBOOL(hAPP(hAPP(c_member(U_615),U_617),U_619)) ),
inference(clausify,[status(thm)],[f_105_3]) ).
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_628,U_627,U_626,U_625,U_624] :
( ( hAPP(c_FuncSet_Orestrict(U_624,U_627,U_628,U_626),U_625) = c_HOL_Oundefined(U_627)
| hBOOL(hAPP(hAPP(c_member(U_624),U_625),U_626)) )
& ( hAPP(c_FuncSet_Orestrict(U_624,U_627,U_628,U_626),U_625) = hAPP(U_628,U_625)
| ~ hBOOL(hAPP(hAPP(c_member(U_624),U_625),U_626)) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_638,U_636,U_634,U_632,U_630] :
( hAPP(c_FuncSet_Orestrict(U_630,U_636,U_638,U_634),U_632) = c_HOL_Oundefined(U_636)
| hBOOL(hAPP(hAPP(c_member(U_630),U_632),U_634)) )
& ! [U_637,U_635,U_633,U_631,U_629] :
( hAPP(c_FuncSet_Orestrict(U_629,U_635,U_637,U_633),U_631) = hAPP(U_637,U_631)
| ~ hBOOL(hAPP(hAPP(c_member(U_629),U_631),U_633)) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( hAPP(c_FuncSet_Orestrict(U_629,U_635,U_637,U_633),U_631) = hAPP(U_637,U_631)
| ~ hBOOL(hAPP(hAPP(c_member(U_629),U_631),U_633)) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
( hAPP(c_FuncSet_Orestrict(U_630,U_636,U_638,U_634),U_632) = c_HOL_Oundefined(U_636)
| hBOOL(hAPP(hAPP(c_member(U_630),U_632),U_634)) ),
inference(clausify,[status(thm)],[f_106_3]) ).
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_643,U_642,U_641,U_640,U_639] :
( hAPP(U_641,U_643) = c_HOL_Oundefined(U_640)
| hBOOL(hAPP(hAPP(c_member(U_639),U_643),U_642))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_639,U_640)),U_641),c_FuncSet_Oextensional(U_639,U_640,U_642))) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( hAPP(U_641,U_643) = c_HOL_Oundefined(U_640)
| hBOOL(hAPP(hAPP(c_member(U_639),U_643),U_642))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_639,U_640)),U_641),c_FuncSet_Oextensional(U_639,U_640,U_642))) ),
inference(clausify,[status(thm)],[f_107_2]) ).
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_648,U_647,U_646,U_645,U_644] :
( hBOOL(hAPP(hAPP(c_member(U_644),U_646),c_Relation_ODomain(U_644,U_645,U_648)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_644,U_645)),hAPP(hAPP(c_Product__Type_OPair(U_644,U_645),U_646),U_647)),U_648)) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_644),U_646),c_Relation_ODomain(U_644,U_645,U_648)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_644,U_645)),hAPP(hAPP(c_Product__Type_OPair(U_644,U_645),U_646),U_647)),U_648)) ),
inference(clausify,[status(thm)],[f_108_2]) ).
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_654,U_653,U_652,U_651] :
( ( hBOOL(hAPP(hAPP(c_member(U_651),U_652),c_Relation_ODomain(U_651,U_653,U_654)))
| ! [U_650] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_651,U_653)),hAPP(hAPP(c_Product__Type_OPair(U_651,U_653),U_652),U_650)),U_654)) )
& ( ? [U_649] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_651,U_653)),hAPP(hAPP(c_Product__Type_OPair(U_651,U_653),U_652),U_649)),U_654))
| ~ hBOOL(hAPP(hAPP(c_member(U_651),U_652),c_Relation_ODomain(U_651,U_653,U_654))) ) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_662,U_660,U_658,U_656] :
( hBOOL(hAPP(hAPP(c_member(U_656),U_658),c_Relation_ODomain(U_656,U_660,U_662)))
| ! [U_650] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_656,U_660)),hAPP(hAPP(c_Product__Type_OPair(U_656,U_660),U_658),U_650)),U_662)) )
& ! [U_661,U_659,U_657,U_655] :
( ? [U_649] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_655,U_659)),hAPP(hAPP(c_Product__Type_OPair(U_655,U_659),U_657),U_649)),U_661))
| ~ hBOOL(hAPP(hAPP(c_member(U_655),U_657),c_Relation_ODomain(U_655,U_659,U_661))) ) ),
inference(miniscope,[status(thm)],[f_109_2]) ).
fof(f_109_4,plain,
( ! [U_662,U_660,U_658,U_656] :
( hBOOL(hAPP(hAPP(c_member(U_656),U_658),c_Relation_ODomain(U_656,U_660,U_662)))
| ! [U_650] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_656,U_660)),hAPP(hAPP(c_Product__Type_OPair(U_656,U_660),U_658),U_650)),U_662)) )
& ! [U_661,U_659,U_657,U_655] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_655,U_659)),hAPP(hAPP(c_Product__Type_OPair(U_655,U_659),U_657),sK40(U_661,U_659,U_657,U_655))),U_661))
| ~ hBOOL(hAPP(hAPP(c_member(U_655),U_657),c_Relation_ODomain(U_655,U_659,U_661))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_649,sK40(U_661,U_659,U_657,U_655))],[f_109_3]) ).
cnf(f_109_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_655,U_659)),hAPP(hAPP(c_Product__Type_OPair(U_655,U_659),U_657),sK40(U_661,U_659,U_657,U_655))),U_661))
| ~ hBOOL(hAPP(hAPP(c_member(U_655),U_657),c_Relation_ODomain(U_655,U_659,U_661))) ),
inference(clausify,[status(thm)],[f_109_4]) ).
cnf(f_109_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_656),U_658),c_Relation_ODomain(U_656,U_660,U_662)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_656,U_660)),hAPP(hAPP(c_Product__Type_OPair(U_656,U_660),U_658),U_650)),U_662)) ),
inference(clausify,[status(thm)],[f_109_4]) ).
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_668,U_667,U_666,U_665,U_664,U_663] :
( U_667 = U_668
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_663,U_664)),hAPP(hAPP(c_Product__Type_OPair(U_663,U_664),U_666),U_668)),U_665))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_663,U_664)),hAPP(hAPP(c_Product__Type_OPair(U_663,U_664),U_666),U_667)),U_665))
| ~ c_Relation_Osingle__valued(U_663,U_664,U_665) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( U_667 = U_668
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_663,U_664)),hAPP(hAPP(c_Product__Type_OPair(U_663,U_664),U_666),U_668)),U_665))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_663,U_664)),hAPP(hAPP(c_Product__Type_OPair(U_663,U_664),U_666),U_667)),U_665))
| ~ c_Relation_Osingle__valued(U_663,U_664,U_665) ),
inference(clausify,[status(thm)],[f_110_2]) ).
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_677,U_676,U_675] :
( ( c_Relation_Osingle__valued(U_675,U_676,U_677)
| ? [U_674,U_673] :
( ? [U_672] :
( U_673 != U_672
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_675,U_676)),hAPP(hAPP(c_Product__Type_OPair(U_675,U_676),U_674),U_672)),U_677)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_675,U_676)),hAPP(hAPP(c_Product__Type_OPair(U_675,U_676),U_674),U_673)),U_677)) ) )
& ( ! [U_671,U_670] :
( ! [U_669] :
( U_670 = U_669
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_675,U_676)),hAPP(hAPP(c_Product__Type_OPair(U_675,U_676),U_671),U_669)),U_677)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_675,U_676)),hAPP(hAPP(c_Product__Type_OPair(U_675,U_676),U_671),U_670)),U_677)) )
| ~ c_Relation_Osingle__valued(U_675,U_676,U_677) ) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
( ! [U_683,U_681,U_679] :
( c_Relation_Osingle__valued(U_679,U_681,U_683)
| ? [U_674,U_673] :
( ? [U_672] :
( U_673 != U_672
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),U_674),U_672)),U_683)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),U_674),U_673)),U_683)) ) )
& ! [U_682,U_680,U_678] :
( ! [U_671,U_670] :
( ! [U_669] :
( U_670 = U_669
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_669)),U_682)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_670)),U_682)) )
| ~ c_Relation_Osingle__valued(U_678,U_680,U_682) ) ),
inference(miniscope,[status(thm)],[f_111_2]) ).
fof(f_111_4,plain,
( ! [U_683,U_681,U_679] :
( c_Relation_Osingle__valued(U_679,U_681,U_683)
| ? [U_673] :
( ? [U_672] :
( U_673 != U_672
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),U_672)),U_683)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),U_673)),U_683)) ) )
& ! [U_682,U_680,U_678] :
( ! [U_671,U_670] :
( ! [U_669] :
( U_670 = U_669
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_669)),U_682)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_670)),U_682)) )
| ~ c_Relation_Osingle__valued(U_678,U_680,U_682) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_674,sK41(U_683,U_681,U_679))],[f_111_3]) ).
fof(f_111_5,plain,
( ! [U_683,U_681,U_679] :
( c_Relation_Osingle__valued(U_679,U_681,U_683)
| ( ? [U_672] :
( sK42(U_683,U_681,U_679) != U_672
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),U_672)),U_683)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),sK42(U_683,U_681,U_679))),U_683)) ) )
& ! [U_682,U_680,U_678] :
( ! [U_671,U_670] :
( ! [U_669] :
( U_670 = U_669
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_669)),U_682)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_670)),U_682)) )
| ~ c_Relation_Osingle__valued(U_678,U_680,U_682) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_673,sK42(U_683,U_681,U_679))],[f_111_4]) ).
fof(f_111_6,plain,
( ! [U_683,U_681,U_679] :
( c_Relation_Osingle__valued(U_679,U_681,U_683)
| ( sK42(U_683,U_681,U_679) != sK43(U_683,U_681,U_679)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),sK43(U_683,U_681,U_679))),U_683))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),sK42(U_683,U_681,U_679))),U_683)) ) )
& ! [U_682,U_680,U_678] :
( ! [U_671,U_670] :
( ! [U_669] :
( U_670 = U_669
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_669)),U_682)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_670)),U_682)) )
| ~ c_Relation_Osingle__valued(U_678,U_680,U_682) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_672,sK43(U_683,U_681,U_679))],[f_111_5]) ).
cnf(f_111_7,plain,
( U_670 = U_669
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_669)),U_682))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_678,U_680)),hAPP(hAPP(c_Product__Type_OPair(U_678,U_680),U_671),U_670)),U_682))
| ~ c_Relation_Osingle__valued(U_678,U_680,U_682) ),
inference(clausify,[status(thm)],[f_111_6]) ).
cnf(f_111_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),sK42(U_683,U_681,U_679))),U_683))
| c_Relation_Osingle__valued(U_679,U_681,U_683) ),
inference(clausify,[status(thm)],[f_111_6]) ).
cnf(f_111_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_679,U_681)),hAPP(hAPP(c_Product__Type_OPair(U_679,U_681),sK41(U_683,U_681,U_679)),sK43(U_683,U_681,U_679))),U_683))
| c_Relation_Osingle__valued(U_679,U_681,U_683) ),
inference(clausify,[status(thm)],[f_111_6]) ).
cnf(f_111_10,plain,
( sK42(U_683,U_681,U_679) != sK43(U_683,U_681,U_679)
| c_Relation_Osingle__valued(U_679,U_681,U_683) ),
inference(clausify,[status(thm)],[f_111_6]) ).
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_687,U_686,U_685,U_684] :
( ( c_Predicate_ODomainP(U_684,U_685,hAPP(hAPP(c_COMBC(U_684,tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_fun(U_685,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_685,tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_fun(U_685,tc_HOL_Obool)),U_684),c_COMBC(U_685,tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_685,tc_prod(U_684,U_685)),tc_fun(U_685,tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool)),U_684),hAPP(c_COMBB(tc_prod(U_684,U_685),tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool),U_685),c_member(tc_prod(U_684,U_685)))),c_Product__Type_OPair(U_684,U_685)))),U_686),U_687)
| ~ hBOOL(hAPP(hAPP(c_member(U_684),U_687),c_Relation_ODomain(U_684,U_685,U_686))) )
& ( hBOOL(hAPP(hAPP(c_member(U_684),U_687),c_Relation_ODomain(U_684,U_685,U_686)))
| ~ c_Predicate_ODomainP(U_684,U_685,hAPP(hAPP(c_COMBC(U_684,tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_fun(U_685,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_685,tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_fun(U_685,tc_HOL_Obool)),U_684),c_COMBC(U_685,tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_685,tc_prod(U_684,U_685)),tc_fun(U_685,tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool)),U_684),hAPP(c_COMBB(tc_prod(U_684,U_685),tc_fun(tc_fun(tc_prod(U_684,U_685),tc_HOL_Obool),tc_HOL_Obool),U_685),c_member(tc_prod(U_684,U_685)))),c_Product__Type_OPair(U_684,U_685)))),U_686),U_687) ) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
( ! [U_695,U_693,U_691,U_689] :
( c_Predicate_ODomainP(U_689,U_691,hAPP(hAPP(c_COMBC(U_689,tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_fun(U_691,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_691,tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_fun(U_691,tc_HOL_Obool)),U_689),c_COMBC(U_691,tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_691,tc_prod(U_689,U_691)),tc_fun(U_691,tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool)),U_689),hAPP(c_COMBB(tc_prod(U_689,U_691),tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool),U_691),c_member(tc_prod(U_689,U_691)))),c_Product__Type_OPair(U_689,U_691)))),U_693),U_695)
| ~ hBOOL(hAPP(hAPP(c_member(U_689),U_695),c_Relation_ODomain(U_689,U_691,U_693))) )
& ! [U_694,U_692,U_690,U_688] :
( hBOOL(hAPP(hAPP(c_member(U_688),U_694),c_Relation_ODomain(U_688,U_690,U_692)))
| ~ c_Predicate_ODomainP(U_688,U_690,hAPP(hAPP(c_COMBC(U_688,tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_fun(U_690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_690,tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_fun(U_690,tc_HOL_Obool)),U_688),c_COMBC(U_690,tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_690,tc_prod(U_688,U_690)),tc_fun(U_690,tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool)),U_688),hAPP(c_COMBB(tc_prod(U_688,U_690),tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool),U_690),c_member(tc_prod(U_688,U_690)))),c_Product__Type_OPair(U_688,U_690)))),U_692),U_694) ) ),
inference(miniscope,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_688),U_694),c_Relation_ODomain(U_688,U_690,U_692)))
| ~ c_Predicate_ODomainP(U_688,U_690,hAPP(hAPP(c_COMBC(U_688,tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_fun(U_690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_690,tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_fun(U_690,tc_HOL_Obool)),U_688),c_COMBC(U_690,tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_690,tc_prod(U_688,U_690)),tc_fun(U_690,tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool)),U_688),hAPP(c_COMBB(tc_prod(U_688,U_690),tc_fun(tc_fun(tc_prod(U_688,U_690),tc_HOL_Obool),tc_HOL_Obool),U_690),c_member(tc_prod(U_688,U_690)))),c_Product__Type_OPair(U_688,U_690)))),U_692),U_694) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_5,plain,
( c_Predicate_ODomainP(U_689,U_691,hAPP(hAPP(c_COMBC(U_689,tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_fun(U_691,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_691,tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_fun(U_691,tc_HOL_Obool)),U_689),c_COMBC(U_691,tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_691,tc_prod(U_689,U_691)),tc_fun(U_691,tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool)),U_689),hAPP(c_COMBB(tc_prod(U_689,U_691),tc_fun(tc_fun(tc_prod(U_689,U_691),tc_HOL_Obool),tc_HOL_Obool),U_691),c_member(tc_prod(U_689,U_691)))),c_Product__Type_OPair(U_689,U_691)))),U_693),U_695)
| ~ hBOOL(hAPP(hAPP(c_member(U_689),U_695),c_Relation_ODomain(U_689,U_691,U_693))) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_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_113_2,plain,
! [U_707,U_706,U_705,U_704] :
( ( c_Recdef_Oadm__wf(U_704,U_705,U_706,U_707)
| ? [U_703,U_702,U_701] :
( hAPP(hAPP(U_707,U_703),U_701) != hAPP(hAPP(U_707,U_702),U_701)
& ! [U_700] :
( hAPP(U_703,U_700) = hAPP(U_702,U_700)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_704,U_704)),hAPP(hAPP(c_Product__Type_OPair(U_704,U_704),U_700),U_701)),U_706)) ) ) )
& ( ! [U_699,U_698,U_697] :
( hAPP(hAPP(U_707,U_699),U_697) = hAPP(hAPP(U_707,U_698),U_697)
| ? [U_696] :
( hAPP(U_699,U_696) != hAPP(U_698,U_696)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_704,U_704)),hAPP(hAPP(c_Product__Type_OPair(U_704,U_704),U_696),U_697)),U_706)) ) )
| ~ c_Recdef_Oadm__wf(U_704,U_705,U_706,U_707) ) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_715,U_713,U_711,U_709] :
( c_Recdef_Oadm__wf(U_709,U_711,U_713,U_715)
| ? [U_703,U_702,U_701] :
( hAPP(hAPP(U_715,U_703),U_701) != hAPP(hAPP(U_715,U_702),U_701)
& ! [U_700] :
( hAPP(U_703,U_700) = hAPP(U_702,U_700)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_709,U_709)),hAPP(hAPP(c_Product__Type_OPair(U_709,U_709),U_700),U_701)),U_713)) ) ) )
& ! [U_714,U_712,U_710,U_708] :
( ! [U_699,U_698,U_697] :
( hAPP(hAPP(U_714,U_699),U_697) = hAPP(hAPP(U_714,U_698),U_697)
| ? [U_696] :
( hAPP(U_699,U_696) != hAPP(U_698,U_696)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_708,U_708)),hAPP(hAPP(c_Product__Type_OPair(U_708,U_708),U_696),U_697)),U_712)) ) )
| ~ c_Recdef_Oadm__wf(U_708,U_710,U_712,U_714) ) ),
inference(miniscope,[status(thm)],[f_113_2]) ).
fof(f_113_4,plain,
( ! [U_715,U_713,U_711,U_709] :
( c_Recdef_Oadm__wf(U_709,U_711,U_713,U_715)
| ? [U_703,U_702,U_701] :
( hAPP(hAPP(U_715,U_703),U_701) != hAPP(hAPP(U_715,U_702),U_701)
& ! [U_700] :
( hAPP(U_703,U_700) = hAPP(U_702,U_700)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_709,U_709)),hAPP(hAPP(c_Product__Type_OPair(U_709,U_709),U_700),U_701)),U_713)) ) ) )
& ! [U_714,U_712,U_710,U_708] :
( ! [U_699,U_698,U_697] :
( hAPP(hAPP(U_714,U_699),U_697) = hAPP(hAPP(U_714,U_698),U_697)
| ( hAPP(U_699,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)) != hAPP(U_698,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_708,U_708)),hAPP(hAPP(c_Product__Type_OPair(U_708,U_708),sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)),U_697)),U_712)) ) )
| ~ c_Recdef_Oadm__wf(U_708,U_710,U_712,U_714) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_696,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697))],[f_113_3]) ).
fof(f_113_5,plain,
( ! [U_715,U_713,U_711,U_709] :
( c_Recdef_Oadm__wf(U_709,U_711,U_713,U_715)
| ? [U_702,U_701] :
( hAPP(hAPP(U_715,sK45(U_715,U_713,U_711,U_709)),U_701) != hAPP(hAPP(U_715,U_702),U_701)
& ! [U_700] :
( hAPP(sK45(U_715,U_713,U_711,U_709),U_700) = hAPP(U_702,U_700)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_709,U_709)),hAPP(hAPP(c_Product__Type_OPair(U_709,U_709),U_700),U_701)),U_713)) ) ) )
& ! [U_714,U_712,U_710,U_708] :
( ! [U_699,U_698,U_697] :
( hAPP(hAPP(U_714,U_699),U_697) = hAPP(hAPP(U_714,U_698),U_697)
| ( hAPP(U_699,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)) != hAPP(U_698,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_708,U_708)),hAPP(hAPP(c_Product__Type_OPair(U_708,U_708),sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)),U_697)),U_712)) ) )
| ~ c_Recdef_Oadm__wf(U_708,U_710,U_712,U_714) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_703,sK45(U_715,U_713,U_711,U_709))],[f_113_4]) ).
fof(f_113_6,plain,
( ! [U_715,U_713,U_711,U_709] :
( c_Recdef_Oadm__wf(U_709,U_711,U_713,U_715)
| ? [U_701] :
( hAPP(hAPP(U_715,sK45(U_715,U_713,U_711,U_709)),U_701) != hAPP(hAPP(U_715,sK46(U_715,U_713,U_711,U_709)),U_701)
& ! [U_700] :
( hAPP(sK45(U_715,U_713,U_711,U_709),U_700) = hAPP(sK46(U_715,U_713,U_711,U_709),U_700)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_709,U_709)),hAPP(hAPP(c_Product__Type_OPair(U_709,U_709),U_700),U_701)),U_713)) ) ) )
& ! [U_714,U_712,U_710,U_708] :
( ! [U_699,U_698,U_697] :
( hAPP(hAPP(U_714,U_699),U_697) = hAPP(hAPP(U_714,U_698),U_697)
| ( hAPP(U_699,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)) != hAPP(U_698,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_708,U_708)),hAPP(hAPP(c_Product__Type_OPair(U_708,U_708),sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)),U_697)),U_712)) ) )
| ~ c_Recdef_Oadm__wf(U_708,U_710,U_712,U_714) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_702,sK46(U_715,U_713,U_711,U_709))],[f_113_5]) ).
fof(f_113_7,plain,
( ! [U_715,U_713,U_711,U_709] :
( c_Recdef_Oadm__wf(U_709,U_711,U_713,U_715)
| ( hAPP(hAPP(U_715,sK45(U_715,U_713,U_711,U_709)),sK47(U_715,U_713,U_711,U_709)) != hAPP(hAPP(U_715,sK46(U_715,U_713,U_711,U_709)),sK47(U_715,U_713,U_711,U_709))
& ! [U_700] :
( hAPP(sK45(U_715,U_713,U_711,U_709),U_700) = hAPP(sK46(U_715,U_713,U_711,U_709),U_700)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_709,U_709)),hAPP(hAPP(c_Product__Type_OPair(U_709,U_709),U_700),sK47(U_715,U_713,U_711,U_709))),U_713)) ) ) )
& ! [U_714,U_712,U_710,U_708] :
( ! [U_699,U_698,U_697] :
( hAPP(hAPP(U_714,U_699),U_697) = hAPP(hAPP(U_714,U_698),U_697)
| ( hAPP(U_699,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)) != hAPP(U_698,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_708,U_708)),hAPP(hAPP(c_Product__Type_OPair(U_708,U_708),sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)),U_697)),U_712)) ) )
| ~ c_Recdef_Oadm__wf(U_708,U_710,U_712,U_714) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_701,sK47(U_715,U_713,U_711,U_709))],[f_113_6]) ).
cnf(f_113_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_708,U_708)),hAPP(hAPP(c_Product__Type_OPair(U_708,U_708),sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)),U_697)),U_712))
| hAPP(hAPP(U_714,U_699),U_697) = hAPP(hAPP(U_714,U_698),U_697)
| ~ c_Recdef_Oadm__wf(U_708,U_710,U_712,U_714) ),
inference(clausify,[status(thm)],[f_113_7]) ).
cnf(f_113_9,plain,
( hAPP(U_699,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697)) != hAPP(U_698,sK44(U_714,U_712,U_710,U_708,U_699,U_698,U_697))
| hAPP(hAPP(U_714,U_699),U_697) = hAPP(hAPP(U_714,U_698),U_697)
| ~ c_Recdef_Oadm__wf(U_708,U_710,U_712,U_714) ),
inference(clausify,[status(thm)],[f_113_7]) ).
cnf(f_113_10,plain,
( hAPP(sK45(U_715,U_713,U_711,U_709),U_700) = hAPP(sK46(U_715,U_713,U_711,U_709),U_700)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_709,U_709)),hAPP(hAPP(c_Product__Type_OPair(U_709,U_709),U_700),sK47(U_715,U_713,U_711,U_709))),U_713))
| c_Recdef_Oadm__wf(U_709,U_711,U_713,U_715) ),
inference(clausify,[status(thm)],[f_113_7]) ).
cnf(f_113_11,plain,
( hAPP(hAPP(U_715,sK45(U_715,U_713,U_711,U_709)),sK47(U_715,U_713,U_711,U_709)) != hAPP(hAPP(U_715,sK46(U_715,U_713,U_711,U_709)),sK47(U_715,U_713,U_711,U_709))
| c_Recdef_Oadm__wf(U_709,U_711,U_713,U_715) ),
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_721,U_720,U_719,U_718,U_717,U_716] :
( hAPP(U_718,U_721) = c_HOL_Oundefined(U_717)
| hBOOL(hAPP(hAPP(c_member(U_716),U_721),U_719))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_716,U_717)),U_718),c_FuncSet_Oextensional__funcset(U_716,U_717,U_719,U_720))) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( hAPP(U_718,U_721) = c_HOL_Oundefined(U_717)
| hBOOL(hAPP(hAPP(c_member(U_716),U_721),U_719))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_716,U_717)),U_718),c_FuncSet_Oextensional__funcset(U_716,U_717,U_719,U_720))) ),
inference(clausify,[status(thm)],[f_114_2]) ).
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_726,U_725,U_724,U_723,U_722] :
( c_Predicate_ODomainP(U_725,U_726,U_722,U_723)
| ~ hBOOL(hAPP(hAPP(U_722,U_723),U_724)) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( c_Predicate_ODomainP(U_725,U_726,U_722,U_723)
| ~ hBOOL(hAPP(hAPP(U_722,U_723),U_724)) ),
inference(clausify,[status(thm)],[f_115_2]) ).
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_732,U_731,U_730,U_729,U_728,U_727] :
( hBOOL(hAPP(hAPP(c_member(U_728),hAPP(U_729,U_732)),U_731))
| ~ hBOOL(hAPP(hAPP(c_member(U_727),U_732),U_730))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_727,U_728)),U_729),c_FuncSet_Oextensional__funcset(U_727,U_728,U_730,U_731))) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_728),hAPP(U_729,U_732)),U_731))
| ~ hBOOL(hAPP(hAPP(c_member(U_727),U_732),U_730))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_727,U_728)),U_729),c_FuncSet_Oextensional__funcset(U_727,U_728,U_730,U_731))) ),
inference(clausify,[status(thm)],[f_116_2]) ).
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_736,U_735] :
( ( c_Relation_Oirrefl(U_735,U_736)
| ? [U_734] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_735,U_735)),hAPP(hAPP(c_Product__Type_OPair(U_735,U_735),U_734),U_734)),U_736)) )
& ( ! [U_733] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_735,U_735)),hAPP(hAPP(c_Product__Type_OPair(U_735,U_735),U_733),U_733)),U_736))
| ~ c_Relation_Oirrefl(U_735,U_736) ) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_740,U_738] :
( c_Relation_Oirrefl(U_738,U_740)
| ? [U_734] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_738,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_738,U_738),U_734),U_734)),U_740)) )
& ! [U_739,U_737] :
( ! [U_733] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_737,U_737)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_737),U_733),U_733)),U_739))
| ~ c_Relation_Oirrefl(U_737,U_739) ) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
fof(f_117_4,plain,
( ! [U_740,U_738] :
( c_Relation_Oirrefl(U_738,U_740)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_738,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_738,U_738),sK48(U_740,U_738)),sK48(U_740,U_738))),U_740)) )
& ! [U_739,U_737] :
( ! [U_733] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_737,U_737)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_737),U_733),U_733)),U_739))
| ~ c_Relation_Oirrefl(U_737,U_739) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_734,sK48(U_740,U_738))],[f_117_3]) ).
cnf(f_117_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_737,U_737)),hAPP(hAPP(c_Product__Type_OPair(U_737,U_737),U_733),U_733)),U_739))
| ~ c_Relation_Oirrefl(U_737,U_739) ),
inference(clausify,[status(thm)],[f_117_4]) ).
cnf(f_117_6,plain,
( c_Relation_Oirrefl(U_738,U_740)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_738,U_738)),hAPP(hAPP(c_Product__Type_OPair(U_738,U_738),sK48(U_740,U_738)),sK48(U_740,U_738))),U_740)) ),
inference(clausify,[status(thm)],[f_117_4]) ).
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_745,U_744,U_743,U_742] :
( ? [U_741] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_742,U_744)),hAPP(hAPP(c_Product__Type_OPair(U_742,U_744),U_743),U_741)),U_745))
| ~ hBOOL(hAPP(hAPP(c_member(U_742),U_743),c_Relation_ODomain(U_742,U_744,U_745))) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_745,U_744,U_743,U_742] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_742,U_744)),hAPP(hAPP(c_Product__Type_OPair(U_742,U_744),U_743),sK49(U_745,U_744,U_743,U_742))),U_745))
| ~ hBOOL(hAPP(hAPP(c_member(U_742),U_743),c_Relation_ODomain(U_742,U_744,U_745))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_741,sK49(U_745,U_744,U_743,U_742))],[f_118_2]) ).
cnf(f_118_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_742,U_744)),hAPP(hAPP(c_Product__Type_OPair(U_742,U_744),U_743),sK49(U_745,U_744,U_743,U_742))),U_745))
| ~ hBOOL(hAPP(hAPP(c_member(U_742),U_743),c_Relation_ODomain(U_742,U_744,U_745))) ),
inference(clausify,[status(thm)],[f_118_3]) ).
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_750,U_749,U_748,U_747,U_746] :
( hBOOL(hAPP(hAPP(c_member(U_747),U_749),c_Relation_ORange(U_746,U_747,U_750)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_746,U_747)),hAPP(hAPP(c_Product__Type_OPair(U_746,U_747),U_748),U_749)),U_750)) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_747),U_749),c_Relation_ORange(U_746,U_747,U_750)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_746,U_747)),hAPP(hAPP(c_Product__Type_OPair(U_746,U_747),U_748),U_749)),U_750)) ),
inference(clausify,[status(thm)],[f_119_2]) ).
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_754,U_753,U_752,U_751] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_751,U_751)),hAPP(hAPP(c_Product__Type_OPair(U_751,U_751),U_752),U_753)),c_Relation_OId__on(U_751,U_754)))
| ~ hBOOL(hAPP(hAPP(c_member(U_751),U_752),U_754))
| U_752 != U_753 )
& ( ( hBOOL(hAPP(hAPP(c_member(U_751),U_752),U_754))
& U_752 = U_753 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_751,U_751)),hAPP(hAPP(c_Product__Type_OPair(U_751,U_751),U_752),U_753)),c_Relation_OId__on(U_751,U_754))) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_762,U_760,U_758,U_756] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_756,U_756)),hAPP(hAPP(c_Product__Type_OPair(U_756,U_756),U_758),U_760)),c_Relation_OId__on(U_756,U_762)))
| ~ hBOOL(hAPP(hAPP(c_member(U_756),U_758),U_762))
| U_758 != U_760 )
& ! [U_761,U_759,U_757,U_755] :
( ( hBOOL(hAPP(hAPP(c_member(U_755),U_757),U_761))
& U_757 = U_759 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_755,U_755)),hAPP(hAPP(c_Product__Type_OPair(U_755,U_755),U_757),U_759)),c_Relation_OId__on(U_755,U_761))) ) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( U_757 = U_759
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_755,U_755)),hAPP(hAPP(c_Product__Type_OPair(U_755,U_755),U_757),U_759)),c_Relation_OId__on(U_755,U_761))) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_755),U_757),U_761))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_755,U_755)),hAPP(hAPP(c_Product__Type_OPair(U_755,U_755),U_757),U_759)),c_Relation_OId__on(U_755,U_761))) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_756,U_756)),hAPP(hAPP(c_Product__Type_OPair(U_756,U_756),U_758),U_760)),c_Relation_OId__on(U_756,U_762)))
| ~ hBOOL(hAPP(hAPP(c_member(U_756),U_758),U_762))
| U_758 != U_760 ),
inference(clausify,[status(thm)],[f_120_3]) ).
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_766,U_765,U_764,U_763] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_765,U_765)),hAPP(hAPP(c_Product__Type_OPair(U_765,U_765),U_763),U_764)),c_Relation_OId__on(U_765,U_766)))
| ~ hBOOL(hAPP(hAPP(c_member(U_765),U_763),U_766))
| U_763 != U_764 ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_765,U_765)),hAPP(hAPP(c_Product__Type_OPair(U_765,U_765),U_763),U_764)),c_Relation_OId__on(U_765,U_766)))
| ~ hBOOL(hAPP(hAPP(c_member(U_765),U_763),U_766))
| U_763 != U_764 ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_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_122_2,plain,
! [U_775,U_774,U_773,U_772,U_771,U_770,U_769] :
( ? [U_768,U_767] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_768),U_767)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_768),U_767))),U_775)) )
| hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772) = hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775))) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_775,U_774,U_773,U_772,U_771,U_770,U_769] :
( ? [U_767] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),sK50(U_775,U_774,U_773,U_772,U_771,U_770,U_769)),U_767)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),sK50(U_775,U_774,U_773,U_772,U_771,U_770,U_769)),U_767))),U_775)) )
| hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772) = hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_768,sK50(U_775,U_774,U_773,U_772,U_771,U_770,U_769))],[f_122_2]) ).
fof(f_122_4,plain,
! [U_775,U_774,U_773,U_772,U_771,U_770,U_769] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),sK50(U_775,U_774,U_773,U_772,U_771,U_770,U_769)),sK51(U_775,U_774,U_773,U_772,U_771,U_770,U_769))),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),sK50(U_775,U_774,U_773,U_772,U_771,U_770,U_769)),sK51(U_775,U_774,U_773,U_772,U_771,U_770,U_769)))),U_775)) )
| hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772) = hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_767,sK51(U_775,U_774,U_773,U_772,U_771,U_770,U_769))],[f_122_3]) ).
cnf(f_122_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),sK50(U_775,U_774,U_773,U_772,U_771,U_770,U_769)),sK51(U_775,U_774,U_773,U_772,U_771,U_770,U_769)))),U_775))
| hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772) = hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775))) ),
inference(clausify,[status(thm)],[f_122_4]) ).
cnf(f_122_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),sK50(U_775,U_774,U_773,U_772,U_771,U_770,U_769)),sK51(U_775,U_774,U_773,U_772,U_771,U_770,U_769))),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775)))
| hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772) = hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_769,U_770),tc_prod(U_769,U_770))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_769,U_770),tc_prod(U_769,U_770)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_771),U_772)),hAPP(hAPP(c_Product__Type_OPair(U_769,U_770),U_773),U_774))),c_Transitive__Closure_Ortrancl(tc_prod(U_769,U_770),U_775))) ),
inference(clausify,[status(thm)],[f_122_4]) ).
fof(f_123_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_123_2,plain,
! [U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780] :
( hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ? [U_779,U_778,U_777,U_776] :
( ~ hBOOL(hAPP(hAPP(U_787,U_779),U_778))
& hBOOL(hAPP(hAPP(U_787,U_777),U_776))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_777),U_776)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_779),U_778)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_777),U_776))),U_786)) )
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780] :
( hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ? [U_778,U_777,U_776] :
( ~ hBOOL(hAPP(hAPP(U_787,sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),U_778))
& hBOOL(hAPP(hAPP(U_787,U_777),U_776))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_777),U_776)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),U_778)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_777),U_776))),U_786)) )
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_779,sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))],[f_123_2]) ).
fof(f_123_4,plain,
! [U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780] :
( hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ? [U_777,U_776] :
( ~ hBOOL(hAPP(hAPP(U_787,sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))
& hBOOL(hAPP(hAPP(U_787,U_777),U_776))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_777),U_776)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_777),U_776))),U_786)) )
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_778,sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))],[f_123_3]) ).
fof(f_123_5,plain,
! [U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780] :
( hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ? [U_776] :
( ~ hBOOL(hAPP(hAPP(U_787,sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))
& hBOOL(hAPP(hAPP(U_787,sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),U_776))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),U_776)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),U_776))),U_786)) )
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_777,sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))],[f_123_4]) ).
fof(f_123_6,plain,
! [U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780] :
( hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ( ~ hBOOL(hAPP(hAPP(U_787,sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))
& hBOOL(hAPP(hAPP(U_787,sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK55(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK55(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK55(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))),U_786)) )
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_776,sK55(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))],[f_123_5]) ).
cnf(f_123_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK55(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))),U_786))
| hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(clausify,[status(thm)],[f_123_6]) ).
cnf(f_123_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK55(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780))),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786)))
| hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(clausify,[status(thm)],[f_123_6]) ).
cnf(f_123_9,plain,
( hBOOL(hAPP(hAPP(U_787,sK54(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK55(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))
| hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(clausify,[status(thm)],[f_123_6]) ).
cnf(f_123_10,plain,
( ~ hBOOL(hAPP(hAPP(U_787,sK52(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)),sK53(U_787,U_786,U_785,U_784,U_783,U_782,U_781,U_780)))
| hBOOL(hAPP(hAPP(U_787,U_782),U_783))
| ~ hBOOL(hAPP(hAPP(U_787,U_784),U_785))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_780,U_781),tc_prod(U_780,U_781))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_780,U_781),tc_prod(U_780,U_781)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_782),U_783)),hAPP(hAPP(c_Product__Type_OPair(U_780,U_781),U_784),U_785))),c_Transitive__Closure_Ortrancl(tc_prod(U_780,U_781),U_786))) ),
inference(clausify,[status(thm)],[f_123_6]) ).
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_789,U_788] : c_Relation_ORange(U_788,U_788,c_Relation_OId__on(U_788,U_789)) = U_789,
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
c_Relation_ORange(U_788,U_788,c_Relation_OId__on(U_788,U_789)) = U_789,
inference(clausify,[status(thm)],[f_124_2]) ).
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_791,U_790] : c_Relation_ODomain(U_790,U_790,c_Relation_OId__on(U_790,U_791)) = U_791,
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
c_Relation_ODomain(U_790,U_790,c_Relation_OId__on(U_790,U_791)) = U_791,
inference(clausify,[status(thm)],[f_125_2]) ).
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_793,U_792] : c_Relation_Osingle__valued(U_792,U_792,c_Relation_OId__on(U_792,U_793)),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
c_Relation_Osingle__valued(U_792,U_792,c_Relation_OId__on(U_792,U_793)),
inference(clausify,[status(thm)],[f_126_2]) ).
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_799,U_798,U_797,U_796] :
( ( hBOOL(hAPP(hAPP(c_member(U_796),U_797),c_Relation_ORange(U_798,U_796,U_799)))
| ! [U_795] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_798,U_796)),hAPP(hAPP(c_Product__Type_OPair(U_798,U_796),U_795),U_797)),U_799)) )
& ( ? [U_794] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_798,U_796)),hAPP(hAPP(c_Product__Type_OPair(U_798,U_796),U_794),U_797)),U_799))
| ~ hBOOL(hAPP(hAPP(c_member(U_796),U_797),c_Relation_ORange(U_798,U_796,U_799))) ) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( ! [U_807,U_805,U_803,U_801] :
( hBOOL(hAPP(hAPP(c_member(U_801),U_803),c_Relation_ORange(U_805,U_801,U_807)))
| ! [U_795] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_805,U_801)),hAPP(hAPP(c_Product__Type_OPair(U_805,U_801),U_795),U_803)),U_807)) )
& ! [U_806,U_804,U_802,U_800] :
( ? [U_794] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_804,U_800)),hAPP(hAPP(c_Product__Type_OPair(U_804,U_800),U_794),U_802)),U_806))
| ~ hBOOL(hAPP(hAPP(c_member(U_800),U_802),c_Relation_ORange(U_804,U_800,U_806))) ) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
fof(f_127_4,plain,
( ! [U_807,U_805,U_803,U_801] :
( hBOOL(hAPP(hAPP(c_member(U_801),U_803),c_Relation_ORange(U_805,U_801,U_807)))
| ! [U_795] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_805,U_801)),hAPP(hAPP(c_Product__Type_OPair(U_805,U_801),U_795),U_803)),U_807)) )
& ! [U_806,U_804,U_802,U_800] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_804,U_800)),hAPP(hAPP(c_Product__Type_OPair(U_804,U_800),sK56(U_806,U_804,U_802,U_800)),U_802)),U_806))
| ~ hBOOL(hAPP(hAPP(c_member(U_800),U_802),c_Relation_ORange(U_804,U_800,U_806))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_794,sK56(U_806,U_804,U_802,U_800))],[f_127_3]) ).
cnf(f_127_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_804,U_800)),hAPP(hAPP(c_Product__Type_OPair(U_804,U_800),sK56(U_806,U_804,U_802,U_800)),U_802)),U_806))
| ~ hBOOL(hAPP(hAPP(c_member(U_800),U_802),c_Relation_ORange(U_804,U_800,U_806))) ),
inference(clausify,[status(thm)],[f_127_4]) ).
cnf(f_127_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_801),U_803),c_Relation_ORange(U_805,U_801,U_807)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_805,U_801)),hAPP(hAPP(c_Product__Type_OPair(U_805,U_801),U_795),U_803)),U_807)) ),
inference(clausify,[status(thm)],[f_127_4]) ).
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_811,U_810,U_809,U_808] :
( ( c_Predicate_ORangeP(U_808,U_809,hAPP(hAPP(c_COMBC(U_808,tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_fun(U_809,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_809,tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_fun(U_809,tc_HOL_Obool)),U_808),c_COMBC(U_809,tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_809,tc_prod(U_808,U_809)),tc_fun(U_809,tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool)),U_808),hAPP(c_COMBB(tc_prod(U_808,U_809),tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool),U_809),c_member(tc_prod(U_808,U_809)))),c_Product__Type_OPair(U_808,U_809)))),U_810),U_811)
| ~ hBOOL(hAPP(hAPP(c_member(U_809),U_811),c_Relation_ORange(U_808,U_809,U_810))) )
& ( hBOOL(hAPP(hAPP(c_member(U_809),U_811),c_Relation_ORange(U_808,U_809,U_810)))
| ~ c_Predicate_ORangeP(U_808,U_809,hAPP(hAPP(c_COMBC(U_808,tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_fun(U_809,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_809,tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_fun(U_809,tc_HOL_Obool)),U_808),c_COMBC(U_809,tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_809,tc_prod(U_808,U_809)),tc_fun(U_809,tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool)),U_808),hAPP(c_COMBB(tc_prod(U_808,U_809),tc_fun(tc_fun(tc_prod(U_808,U_809),tc_HOL_Obool),tc_HOL_Obool),U_809),c_member(tc_prod(U_808,U_809)))),c_Product__Type_OPair(U_808,U_809)))),U_810),U_811) ) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_819,U_817,U_815,U_813] :
( c_Predicate_ORangeP(U_813,U_815,hAPP(hAPP(c_COMBC(U_813,tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_fun(U_815,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_815,tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_fun(U_815,tc_HOL_Obool)),U_813),c_COMBC(U_815,tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_815,tc_prod(U_813,U_815)),tc_fun(U_815,tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool)),U_813),hAPP(c_COMBB(tc_prod(U_813,U_815),tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool),U_815),c_member(tc_prod(U_813,U_815)))),c_Product__Type_OPair(U_813,U_815)))),U_817),U_819)
| ~ hBOOL(hAPP(hAPP(c_member(U_815),U_819),c_Relation_ORange(U_813,U_815,U_817))) )
& ! [U_818,U_816,U_814,U_812] :
( hBOOL(hAPP(hAPP(c_member(U_814),U_818),c_Relation_ORange(U_812,U_814,U_816)))
| ~ c_Predicate_ORangeP(U_812,U_814,hAPP(hAPP(c_COMBC(U_812,tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_fun(U_814,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_814,tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_fun(U_814,tc_HOL_Obool)),U_812),c_COMBC(U_814,tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_814,tc_prod(U_812,U_814)),tc_fun(U_814,tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool)),U_812),hAPP(c_COMBB(tc_prod(U_812,U_814),tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool),U_814),c_member(tc_prod(U_812,U_814)))),c_Product__Type_OPair(U_812,U_814)))),U_816),U_818) ) ),
inference(miniscope,[status(thm)],[f_128_2]) ).
cnf(f_128_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_814),U_818),c_Relation_ORange(U_812,U_814,U_816)))
| ~ c_Predicate_ORangeP(U_812,U_814,hAPP(hAPP(c_COMBC(U_812,tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_fun(U_814,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_814,tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_fun(U_814,tc_HOL_Obool)),U_812),c_COMBC(U_814,tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_814,tc_prod(U_812,U_814)),tc_fun(U_814,tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool)),U_812),hAPP(c_COMBB(tc_prod(U_812,U_814),tc_fun(tc_fun(tc_prod(U_812,U_814),tc_HOL_Obool),tc_HOL_Obool),U_814),c_member(tc_prod(U_812,U_814)))),c_Product__Type_OPair(U_812,U_814)))),U_816),U_818) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( c_Predicate_ORangeP(U_813,U_815,hAPP(hAPP(c_COMBC(U_813,tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_fun(U_815,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_815,tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_fun(U_815,tc_HOL_Obool)),U_813),c_COMBC(U_815,tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_815,tc_prod(U_813,U_815)),tc_fun(U_815,tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool)),U_813),hAPP(c_COMBB(tc_prod(U_813,U_815),tc_fun(tc_fun(tc_prod(U_813,U_815),tc_HOL_Obool),tc_HOL_Obool),U_815),c_member(tc_prod(U_813,U_815)))),c_Product__Type_OPair(U_813,U_815)))),U_817),U_819)
| ~ hBOOL(hAPP(hAPP(c_member(U_815),U_819),c_Relation_ORange(U_813,U_815,U_817))) ),
inference(clausify,[status(thm)],[f_128_3]) ).
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_823,U_822,U_821] :
( ? [U_820] :
( U_822 = hAPP(hAPP(c_Product__Type_OPair(U_821,U_821),U_820),U_820)
& hBOOL(hAPP(hAPP(c_member(U_821),U_820),U_823)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_821,U_821)),U_822),c_Relation_OId__on(U_821,U_823))) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_823,U_822,U_821] :
( ( U_822 = hAPP(hAPP(c_Product__Type_OPair(U_821,U_821),sK57(U_823,U_822,U_821)),sK57(U_823,U_822,U_821))
& hBOOL(hAPP(hAPP(c_member(U_821),sK57(U_823,U_822,U_821)),U_823)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_821,U_821)),U_822),c_Relation_OId__on(U_821,U_823))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_820,sK57(U_823,U_822,U_821))],[f_129_2]) ).
cnf(f_129_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_821),sK57(U_823,U_822,U_821)),U_823))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_821,U_821)),U_822),c_Relation_OId__on(U_821,U_823))) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_5,plain,
( U_822 = hAPP(hAPP(c_Product__Type_OPair(U_821,U_821),sK57(U_823,U_822,U_821)),sK57(U_823,U_822,U_821))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_821,U_821)),U_822),c_Relation_OId__on(U_821,U_823))) ),
inference(clausify,[status(thm)],[f_129_3]) ).
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_828,U_827,U_826,U_825] :
( ? [U_824] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_827,U_825)),hAPP(hAPP(c_Product__Type_OPair(U_827,U_825),U_824),U_826)),U_828))
| ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),c_Relation_ORange(U_827,U_825,U_828))) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_828,U_827,U_826,U_825] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_827,U_825)),hAPP(hAPP(c_Product__Type_OPair(U_827,U_825),sK58(U_828,U_827,U_826,U_825)),U_826)),U_828))
| ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),c_Relation_ORange(U_827,U_825,U_828))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_824,sK58(U_828,U_827,U_826,U_825))],[f_130_2]) ).
cnf(f_130_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_827,U_825)),hAPP(hAPP(c_Product__Type_OPair(U_827,U_825),sK58(U_828,U_827,U_826,U_825)),U_826)),U_828))
| ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),c_Relation_ORange(U_827,U_825,U_828))) ),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_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_131_2,plain,
! [U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833] :
( hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ? [U_832,U_831] :
( ? [U_830,U_829] :
( ~ hBOOL(hAPP(hAPP(U_840,U_830),U_829))
& hBOOL(hAPP(hAPP(U_840,U_832),U_831))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_832),U_831)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_830),U_829))),U_839)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_832),U_831))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) )
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833] :
( hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ? [U_831] :
( ? [U_830,U_829] :
( ~ hBOOL(hAPP(hAPP(U_840,U_830),U_829))
& hBOOL(hAPP(hAPP(U_840,sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),U_831))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),U_831)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_830),U_829))),U_839)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),U_831))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) )
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_832,sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))],[f_131_2]) ).
fof(f_131_4,plain,
! [U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833] :
( hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ( ? [U_830,U_829] :
( ~ hBOOL(hAPP(hAPP(U_840,U_830),U_829))
& hBOOL(hAPP(hAPP(U_840,sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_830),U_829))),U_839)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) )
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_831,sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))],[f_131_3]) ).
fof(f_131_5,plain,
! [U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833] :
( hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ( ? [U_829] :
( ~ hBOOL(hAPP(hAPP(U_840,sK61(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),U_829))
& hBOOL(hAPP(hAPP(U_840,sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK61(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),U_829))),U_839)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) )
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_830,sK61(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))],[f_131_4]) ).
fof(f_131_6,plain,
! [U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833] :
( hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ( ~ hBOOL(hAPP(hAPP(U_840,sK61(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK62(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))
& hBOOL(hAPP(hAPP(U_840,sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK61(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK62(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))),U_839))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) )
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_829,sK62(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))],[f_131_5]) ).
cnf(f_131_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839)))
| hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(clausify,[status(thm)],[f_131_6]) ).
cnf(f_131_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833))),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),sK61(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK62(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))),U_839))
| hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(clausify,[status(thm)],[f_131_6]) ).
cnf(f_131_9,plain,
( hBOOL(hAPP(hAPP(U_840,sK59(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK60(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))
| hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(clausify,[status(thm)],[f_131_6]) ).
cnf(f_131_10,plain,
( ~ hBOOL(hAPP(hAPP(U_840,sK61(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)),sK62(U_840,U_839,U_838,U_837,U_836,U_835,U_834,U_833)))
| hBOOL(hAPP(hAPP(U_840,U_837),U_838))
| ~ hBOOL(hAPP(hAPP(U_840,U_835),U_836))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_833,U_834),tc_prod(U_833,U_834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_833,U_834),tc_prod(U_833,U_834)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_835),U_836)),hAPP(hAPP(c_Product__Type_OPair(U_833,U_834),U_837),U_838))),c_Transitive__Closure_Ortrancl(tc_prod(U_833,U_834),U_839))) ),
inference(clausify,[status(thm)],[f_131_6]) ).
fof(f_132_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_132_2,plain,
! [U_847,U_846,U_845,U_844,U_843,U_842] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_842,U_845,U_844,U_846,U_843),hAPP(hAPP(U_846,U_847),U_843)))
| ? [U_841] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_842,U_845,U_844,U_846,U_841),hAPP(U_847,U_841)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_842,U_842)),hAPP(hAPP(c_Product__Type_OPair(U_842,U_842),U_841),U_843)),U_844)) ) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_847,U_846,U_845,U_844,U_843,U_842] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_842,U_845,U_844,U_846,U_843),hAPP(hAPP(U_846,U_847),U_843)))
| ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_842,U_845,U_844,U_846,sK63(U_847,U_846,U_845,U_844,U_843,U_842)),hAPP(U_847,sK63(U_847,U_846,U_845,U_844,U_843,U_842))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_842,U_842)),hAPP(hAPP(c_Product__Type_OPair(U_842,U_842),sK63(U_847,U_846,U_845,U_844,U_843,U_842)),U_843)),U_844)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_841,sK63(U_847,U_846,U_845,U_844,U_843,U_842))],[f_132_2]) ).
cnf(f_132_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_842,U_842)),hAPP(hAPP(c_Product__Type_OPair(U_842,U_842),sK63(U_847,U_846,U_845,U_844,U_843,U_842)),U_843)),U_844))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(U_842,U_845,U_844,U_846,U_843),hAPP(hAPP(U_846,U_847),U_843))) ),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_5,plain,
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_842,U_845,U_844,U_846,sK63(U_847,U_846,U_845,U_844,U_843,U_842)),hAPP(U_847,sK63(U_847,U_846,U_845,U_844,U_843,U_842))))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(U_842,U_845,U_844,U_846,U_843),hAPP(hAPP(U_846,U_847),U_843))) ),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_857,U_856,U_855,U_854,U_853,U_852] :
( ( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_852,U_853,U_854,U_855,U_856),U_857))
| ! [U_851] :
( ? [U_850] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_852,U_853,U_854,U_855,U_850),hAPP(U_851,U_850)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_852,U_852)),hAPP(hAPP(c_Product__Type_OPair(U_852,U_852),U_850),U_856)),U_854)) )
| U_857 != hAPP(hAPP(U_855,U_851),U_856) ) )
& ( ? [U_849] :
( ! [U_848] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_852,U_853,U_854,U_855,U_848),hAPP(U_849,U_848)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_852,U_852)),hAPP(hAPP(c_Product__Type_OPair(U_852,U_852),U_848),U_856)),U_854)) )
& U_857 = hAPP(hAPP(U_855,U_849),U_856) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_852,U_853,U_854,U_855,U_856),U_857)) ) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
( ! [U_869,U_867,U_865,U_863,U_861,U_859] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,U_867),U_869))
| ! [U_851] :
( ? [U_850] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,U_850),hAPP(U_851,U_850)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_859,U_859)),hAPP(hAPP(c_Product__Type_OPair(U_859,U_859),U_850),U_867)),U_863)) )
| U_869 != hAPP(hAPP(U_865,U_851),U_867) ) )
& ! [U_868,U_866,U_864,U_862,U_860,U_858] :
( ? [U_849] :
( ! [U_848] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_848),hAPP(U_849,U_848)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),U_848),U_866)),U_862)) )
& U_868 = hAPP(hAPP(U_864,U_849),U_866) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_866),U_868)) ) ),
inference(miniscope,[status(thm)],[f_133_2]) ).
fof(f_133_4,plain,
( ! [U_869,U_867,U_865,U_863,U_861,U_859] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,U_867),U_869))
| ! [U_851] :
( ? [U_850] :
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,U_850),hAPP(U_851,U_850)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_859,U_859)),hAPP(hAPP(c_Product__Type_OPair(U_859,U_859),U_850),U_867)),U_863)) )
| U_869 != hAPP(hAPP(U_865,U_851),U_867) ) )
& ! [U_868,U_866,U_864,U_862,U_860,U_858] :
( ( ! [U_848] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_848),hAPP(sK64(U_868,U_866,U_864,U_862,U_860,U_858),U_848)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),U_848),U_866)),U_862)) )
& U_868 = hAPP(hAPP(U_864,sK64(U_868,U_866,U_864,U_862,U_860,U_858)),U_866) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_866),U_868)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_849,sK64(U_868,U_866,U_864,U_862,U_860,U_858))],[f_133_3]) ).
fof(f_133_5,plain,
( ! [U_869,U_867,U_865,U_863,U_861,U_859] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,U_867),U_869))
| ! [U_851] :
( ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,sK65(U_869,U_867,U_865,U_863,U_861,U_859,U_851)),hAPP(U_851,sK65(U_869,U_867,U_865,U_863,U_861,U_859,U_851))))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_859,U_859)),hAPP(hAPP(c_Product__Type_OPair(U_859,U_859),sK65(U_869,U_867,U_865,U_863,U_861,U_859,U_851)),U_867)),U_863)) )
| U_869 != hAPP(hAPP(U_865,U_851),U_867) ) )
& ! [U_868,U_866,U_864,U_862,U_860,U_858] :
( ( ! [U_848] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_848),hAPP(sK64(U_868,U_866,U_864,U_862,U_860,U_858),U_848)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),U_848),U_866)),U_862)) )
& U_868 = hAPP(hAPP(U_864,sK64(U_868,U_866,U_864,U_862,U_860,U_858)),U_866) )
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_866),U_868)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_850,sK65(U_869,U_867,U_865,U_863,U_861,U_859,U_851))],[f_133_4]) ).
cnf(f_133_6,plain,
( U_868 = hAPP(hAPP(U_864,sK64(U_868,U_866,U_864,U_862,U_860,U_858)),U_866)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_866),U_868)) ),
inference(clausify,[status(thm)],[f_133_5]) ).
cnf(f_133_7,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_848),hAPP(sK64(U_868,U_866,U_864,U_862,U_860,U_858),U_848)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_858,U_858)),hAPP(hAPP(c_Product__Type_OPair(U_858,U_858),U_848),U_866)),U_862))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_858,U_860,U_862,U_864,U_866),U_868)) ),
inference(clausify,[status(thm)],[f_133_5]) ).
cnf(f_133_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_859,U_859)),hAPP(hAPP(c_Product__Type_OPair(U_859,U_859),sK65(U_869,U_867,U_865,U_863,U_861,U_859,U_851)),U_867)),U_863))
| U_869 != hAPP(hAPP(U_865,U_851),U_867)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,U_867),U_869)) ),
inference(clausify,[status(thm)],[f_133_5]) ).
cnf(f_133_9,plain,
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,sK65(U_869,U_867,U_865,U_863,U_861,U_859,U_851)),hAPP(U_851,sK65(U_869,U_867,U_865,U_863,U_861,U_859,U_851))))
| U_869 != hAPP(hAPP(U_865,U_851),U_867)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(U_859,U_861,U_863,U_865,U_867),U_869)) ),
inference(clausify,[status(thm)],[f_133_5]) ).
fof(f_134_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_134_2,plain,
! [U_875,U_874,U_873,U_872,U_871] :
( U_873 = U_875
| ? [U_870] :
( hAPP(U_873,U_870) != hAPP(U_875,U_870)
& hBOOL(hAPP(hAPP(c_member(U_871),U_870),U_874)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_875),c_FuncSet_Oextensional(U_871,U_872,U_874)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_873),c_FuncSet_Oextensional(U_871,U_872,U_874))) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_875,U_874,U_873,U_872,U_871] :
( U_873 = U_875
| ( hAPP(U_873,sK66(U_875,U_874,U_873,U_872,U_871)) != hAPP(U_875,sK66(U_875,U_874,U_873,U_872,U_871))
& hBOOL(hAPP(hAPP(c_member(U_871),sK66(U_875,U_874,U_873,U_872,U_871)),U_874)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_875),c_FuncSet_Oextensional(U_871,U_872,U_874)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_873),c_FuncSet_Oextensional(U_871,U_872,U_874))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_870,sK66(U_875,U_874,U_873,U_872,U_871))],[f_134_2]) ).
cnf(f_134_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_871),sK66(U_875,U_874,U_873,U_872,U_871)),U_874))
| U_873 = U_875
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_875),c_FuncSet_Oextensional(U_871,U_872,U_874)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_873),c_FuncSet_Oextensional(U_871,U_872,U_874))) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_5,plain,
( hAPP(U_873,sK66(U_875,U_874,U_873,U_872,U_871)) != hAPP(U_875,sK66(U_875,U_874,U_873,U_872,U_871))
| U_873 = U_875
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_875),c_FuncSet_Oextensional(U_871,U_872,U_874)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_871,U_872)),U_873),c_FuncSet_Oextensional(U_871,U_872,U_874))) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_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_135_2,plain,
! [U_880,U_879,U_878,U_877,U_876] :
( c_Predicate_ORangeP(U_879,U_880,U_876,U_878)
| ~ hBOOL(hAPP(hAPP(U_876,U_877),U_878)) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( c_Predicate_ORangeP(U_879,U_880,U_876,U_878)
| ~ hBOOL(hAPP(hAPP(U_876,U_877),U_878)) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_886,U_885,U_884,U_883] :
( ( c_Predicate_ORangeP(U_883,U_884,U_885,U_886)
| ! [U_882] : ~ hBOOL(hAPP(hAPP(U_885,U_882),U_886)) )
& ( ? [U_881] : hBOOL(hAPP(hAPP(U_885,U_881),U_886))
| ~ c_Predicate_ORangeP(U_883,U_884,U_885,U_886) ) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_894,U_892] :
( ! [U_890,U_888] : c_Predicate_ORangeP(U_888,U_890,U_892,U_894)
| ! [U_882] : ~ hBOOL(hAPP(hAPP(U_892,U_882),U_894)) )
& ! [U_893,U_891] :
( ! [U_889,U_887] : ~ c_Predicate_ORangeP(U_887,U_889,U_891,U_893)
| ? [U_881] : hBOOL(hAPP(hAPP(U_891,U_881),U_893)) ) ),
inference(miniscope,[status(thm)],[f_136_2]) ).
fof(f_136_4,plain,
( ! [U_894,U_892] :
( ! [U_890,U_888] : c_Predicate_ORangeP(U_888,U_890,U_892,U_894)
| ! [U_882] : ~ hBOOL(hAPP(hAPP(U_892,U_882),U_894)) )
& ! [U_893,U_891] :
( ! [U_889,U_887] : ~ c_Predicate_ORangeP(U_887,U_889,U_891,U_893)
| hBOOL(hAPP(hAPP(U_891,sK67(U_893,U_891)),U_893)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_881,sK67(U_893,U_891))],[f_136_3]) ).
cnf(f_136_5,plain,
( ~ c_Predicate_ORangeP(U_887,U_889,U_891,U_893)
| hBOOL(hAPP(hAPP(U_891,sK67(U_893,U_891)),U_893)) ),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_6,plain,
( c_Predicate_ORangeP(U_888,U_890,U_892,U_894)
| ~ hBOOL(hAPP(hAPP(U_892,U_882),U_894)) ),
inference(clausify,[status(thm)],[f_136_4]) ).
fof(f_137_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_137_2,plain,
! [U_900,U_899,U_898] :
( c_Relation_Osingle__valued(U_898,U_899,U_900)
| ? [U_897,U_896] :
( ? [U_895] :
( U_896 != U_895
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),U_897),U_895)),U_900)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),U_897),U_896)),U_900)) ) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_900,U_899,U_898] :
( c_Relation_Osingle__valued(U_898,U_899,U_900)
| ? [U_896] :
( ? [U_895] :
( U_896 != U_895
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),U_895)),U_900)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),U_896)),U_900)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_897,sK68(U_900,U_899,U_898))],[f_137_2]) ).
fof(f_137_4,plain,
! [U_900,U_899,U_898] :
( c_Relation_Osingle__valued(U_898,U_899,U_900)
| ( ? [U_895] :
( sK69(U_900,U_899,U_898) != U_895
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),U_895)),U_900)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),sK69(U_900,U_899,U_898))),U_900)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_896,sK69(U_900,U_899,U_898))],[f_137_3]) ).
fof(f_137_5,plain,
! [U_900,U_899,U_898] :
( c_Relation_Osingle__valued(U_898,U_899,U_900)
| ( sK69(U_900,U_899,U_898) != sK70(U_900,U_899,U_898)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),sK70(U_900,U_899,U_898))),U_900))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),sK69(U_900,U_899,U_898))),U_900)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_895,sK70(U_900,U_899,U_898))],[f_137_4]) ).
cnf(f_137_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),sK69(U_900,U_899,U_898))),U_900))
| c_Relation_Osingle__valued(U_898,U_899,U_900) ),
inference(clausify,[status(thm)],[f_137_5]) ).
cnf(f_137_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_898,U_899)),hAPP(hAPP(c_Product__Type_OPair(U_898,U_899),sK68(U_900,U_899,U_898)),sK70(U_900,U_899,U_898))),U_900))
| c_Relation_Osingle__valued(U_898,U_899,U_900) ),
inference(clausify,[status(thm)],[f_137_5]) ).
cnf(f_137_8,plain,
( sK69(U_900,U_899,U_898) != sK70(U_900,U_899,U_898)
| c_Relation_Osingle__valued(U_898,U_899,U_900) ),
inference(clausify,[status(thm)],[f_137_5]) ).
fof(f_138_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_138_2,plain,
! [U_904,U_903,U_902,U_901] : c_FuncSet_Oextensional__funcset(U_901,U_902,U_903,U_904) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_901,U_902),tc_HOL_Obool),c_FuncSet_OPi(U_901,U_902,U_903,c_COMBK(tc_fun(U_902,tc_HOL_Obool),U_901,U_904)),c_FuncSet_Oextensional(U_901,U_902,U_903)),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
c_FuncSet_Oextensional__funcset(U_901,U_902,U_903,U_904) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_901,U_902),tc_HOL_Obool),c_FuncSet_OPi(U_901,U_902,U_903,c_COMBK(tc_fun(U_902,tc_HOL_Obool),U_901,U_904)),c_FuncSet_Oextensional(U_901,U_902,U_903)),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_911,U_910,U_909,U_908,U_907] :
( hBOOL(hAPP(U_911,U_909))
| ? [U_906] :
( ? [U_905] :
( ~ hBOOL(hAPP(U_911,U_905))
& hBOOL(hAPP(U_911,U_906))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_906),U_905)),U_910)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_906)),c_Transitive__Closure_Ortrancl(U_907,U_910))) )
| ~ hBOOL(hAPP(U_911,U_908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_909)),c_Transitive__Closure_Ortrancl(U_907,U_910))) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_911,U_910,U_909,U_908,U_907] :
( hBOOL(hAPP(U_911,U_909))
| ( ? [U_905] :
( ~ hBOOL(hAPP(U_911,U_905))
& hBOOL(hAPP(U_911,sK71(U_911,U_910,U_909,U_908,U_907)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),sK71(U_911,U_910,U_909,U_908,U_907)),U_905)),U_910)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),sK71(U_911,U_910,U_909,U_908,U_907))),c_Transitive__Closure_Ortrancl(U_907,U_910))) )
| ~ hBOOL(hAPP(U_911,U_908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_909)),c_Transitive__Closure_Ortrancl(U_907,U_910))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_906,sK71(U_911,U_910,U_909,U_908,U_907))],[f_139_2]) ).
fof(f_139_4,plain,
! [U_911,U_910,U_909,U_908,U_907] :
( hBOOL(hAPP(U_911,U_909))
| ( ~ hBOOL(hAPP(U_911,sK72(U_911,U_910,U_909,U_908,U_907)))
& hBOOL(hAPP(U_911,sK71(U_911,U_910,U_909,U_908,U_907)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),sK71(U_911,U_910,U_909,U_908,U_907)),sK72(U_911,U_910,U_909,U_908,U_907))),U_910))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),sK71(U_911,U_910,U_909,U_908,U_907))),c_Transitive__Closure_Ortrancl(U_907,U_910))) )
| ~ hBOOL(hAPP(U_911,U_908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_909)),c_Transitive__Closure_Ortrancl(U_907,U_910))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_905,sK72(U_911,U_910,U_909,U_908,U_907))],[f_139_3]) ).
cnf(f_139_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),sK71(U_911,U_910,U_909,U_908,U_907))),c_Transitive__Closure_Ortrancl(U_907,U_910)))
| hBOOL(hAPP(U_911,U_909))
| ~ hBOOL(hAPP(U_911,U_908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_909)),c_Transitive__Closure_Ortrancl(U_907,U_910))) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),sK71(U_911,U_910,U_909,U_908,U_907)),sK72(U_911,U_910,U_909,U_908,U_907))),U_910))
| hBOOL(hAPP(U_911,U_909))
| ~ hBOOL(hAPP(U_911,U_908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_909)),c_Transitive__Closure_Ortrancl(U_907,U_910))) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_7,plain,
( hBOOL(hAPP(U_911,sK71(U_911,U_910,U_909,U_908,U_907)))
| hBOOL(hAPP(U_911,U_909))
| ~ hBOOL(hAPP(U_911,U_908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_909)),c_Transitive__Closure_Ortrancl(U_907,U_910))) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_8,plain,
( ~ hBOOL(hAPP(U_911,sK72(U_911,U_910,U_909,U_908,U_907)))
| hBOOL(hAPP(U_911,U_909))
| ~ hBOOL(hAPP(U_911,U_908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_907,U_907)),hAPP(hAPP(c_Product__Type_OPair(U_907,U_907),U_908),U_909)),c_Transitive__Closure_Ortrancl(U_907,U_910))) ),
inference(clausify,[status(thm)],[f_139_4]) ).
fof(f_140_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_140_2,plain,
! [U_918,U_917,U_916,U_915,U_914] :
( hBOOL(hAPP(U_918,U_915))
| ? [U_913,U_912] :
( ~ hBOOL(hAPP(U_918,U_913))
& hBOOL(hAPP(U_918,U_912))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_912),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_913),U_912)),U_917)) )
| ~ hBOOL(hAPP(U_918,U_916))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_915),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917))) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_918,U_917,U_916,U_915,U_914] :
( hBOOL(hAPP(U_918,U_915))
| ? [U_912] :
( ~ hBOOL(hAPP(U_918,sK73(U_918,U_917,U_916,U_915,U_914)))
& hBOOL(hAPP(U_918,U_912))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_912),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),sK73(U_918,U_917,U_916,U_915,U_914)),U_912)),U_917)) )
| ~ hBOOL(hAPP(U_918,U_916))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_915),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_913,sK73(U_918,U_917,U_916,U_915,U_914))],[f_140_2]) ).
fof(f_140_4,plain,
! [U_918,U_917,U_916,U_915,U_914] :
( hBOOL(hAPP(U_918,U_915))
| ( ~ hBOOL(hAPP(U_918,sK73(U_918,U_917,U_916,U_915,U_914)))
& hBOOL(hAPP(U_918,sK74(U_918,U_917,U_916,U_915,U_914)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),sK74(U_918,U_917,U_916,U_915,U_914)),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),sK73(U_918,U_917,U_916,U_915,U_914)),sK74(U_918,U_917,U_916,U_915,U_914))),U_917)) )
| ~ hBOOL(hAPP(U_918,U_916))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_915),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_912,sK74(U_918,U_917,U_916,U_915,U_914))],[f_140_3]) ).
cnf(f_140_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),sK73(U_918,U_917,U_916,U_915,U_914)),sK74(U_918,U_917,U_916,U_915,U_914))),U_917))
| hBOOL(hAPP(U_918,U_915))
| ~ hBOOL(hAPP(U_918,U_916))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_915),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917))) ),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),sK74(U_918,U_917,U_916,U_915,U_914)),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917)))
| hBOOL(hAPP(U_918,U_915))
| ~ hBOOL(hAPP(U_918,U_916))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_915),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917))) ),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_7,plain,
( hBOOL(hAPP(U_918,sK74(U_918,U_917,U_916,U_915,U_914)))
| hBOOL(hAPP(U_918,U_915))
| ~ hBOOL(hAPP(U_918,U_916))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_915),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917))) ),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_8,plain,
( ~ hBOOL(hAPP(U_918,sK73(U_918,U_917,U_916,U_915,U_914)))
| hBOOL(hAPP(U_918,U_915))
| ~ hBOOL(hAPP(U_918,U_916))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_914,U_914)),hAPP(hAPP(c_Product__Type_OPair(U_914,U_914),U_915),U_916)),c_Transitive__Closure_Ortrancl(U_914,U_917))) ),
inference(clausify,[status(thm)],[f_140_4]) ).
fof(f_141_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_141_2,plain,
! [U_923,U_922,U_921,U_920] :
( ? [U_919] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_919),U_922)),c_Transitive__Closure_Ortrancl(U_920,U_923)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_921),U_919)),U_923)) )
| U_921 = U_922
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_921),U_922)),c_Transitive__Closure_Ortrancl(U_920,U_923))) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_923,U_922,U_921,U_920] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),sK75(U_923,U_922,U_921,U_920)),U_922)),c_Transitive__Closure_Ortrancl(U_920,U_923)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_921),sK75(U_923,U_922,U_921,U_920))),U_923)) )
| U_921 = U_922
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_921),U_922)),c_Transitive__Closure_Ortrancl(U_920,U_923))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_919,sK75(U_923,U_922,U_921,U_920))],[f_141_2]) ).
cnf(f_141_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_921),sK75(U_923,U_922,U_921,U_920))),U_923))
| U_921 = U_922
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_921),U_922)),c_Transitive__Closure_Ortrancl(U_920,U_923))) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),sK75(U_923,U_922,U_921,U_920)),U_922)),c_Transitive__Closure_Ortrancl(U_920,U_923)))
| U_921 = U_922
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_920,U_920)),hAPP(hAPP(c_Product__Type_OPair(U_920,U_920),U_921),U_922)),c_Transitive__Closure_Ortrancl(U_920,U_923))) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_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_142_2,plain,
! [U_928,U_927,U_926,U_925] :
( ? [U_924] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_924),U_927)),U_928))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_926),U_924)),c_Transitive__Closure_Ortrancl(U_925,U_928))) )
| U_926 = U_927
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_926),U_927)),c_Transitive__Closure_Ortrancl(U_925,U_928))) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_928,U_927,U_926,U_925] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),sK76(U_928,U_927,U_926,U_925)),U_927)),U_928))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_926),sK76(U_928,U_927,U_926,U_925))),c_Transitive__Closure_Ortrancl(U_925,U_928))) )
| U_926 = U_927
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_926),U_927)),c_Transitive__Closure_Ortrancl(U_925,U_928))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_924,sK76(U_928,U_927,U_926,U_925))],[f_142_2]) ).
cnf(f_142_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_926),sK76(U_928,U_927,U_926,U_925))),c_Transitive__Closure_Ortrancl(U_925,U_928)))
| U_926 = U_927
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_926),U_927)),c_Transitive__Closure_Ortrancl(U_925,U_928))) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),sK76(U_928,U_927,U_926,U_925)),U_927)),U_928))
| U_926 = U_927
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_925,U_925)),hAPP(hAPP(c_Product__Type_OPair(U_925,U_925),U_926),U_927)),c_Transitive__Closure_Ortrancl(U_925,U_928))) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_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_143_2,plain,
! [U_932,U_931,U_930,U_929] :
( ( hBOOL(hAPP(U_931,U_932))
& hBOOL(hAPP(U_930,U_932)) )
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_929,tc_HOL_Obool),U_930,U_931),U_932)) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_932,U_931,U_930] :
( ! [U_929] : ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_929,tc_HOL_Obool),U_930,U_931),U_932))
| ( hBOOL(hAPP(U_931,U_932))
& hBOOL(hAPP(U_930,U_932)) ) ),
inference(miniscope,[status(thm)],[f_143_2]) ).
cnf(f_143_4,plain,
( hBOOL(hAPP(U_930,U_932))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_929,tc_HOL_Obool),U_930,U_931),U_932)) ),
inference(clausify,[status(thm)],[f_143_3]) ).
cnf(f_143_5,plain,
( hBOOL(hAPP(U_931,U_932))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_929,tc_HOL_Obool),U_930,U_931),U_932)) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_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_144_2,plain,
! [U_936,U_935,U_934,U_933] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_936,tc_HOL_Obool),U_933,U_935),U_934))
| ~ hBOOL(hAPP(U_935,U_934))
| ~ hBOOL(hAPP(U_933,U_934)) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_936,tc_HOL_Obool),U_933,U_935),U_934))
| ~ hBOOL(hAPP(U_935,U_934))
| ~ hBOOL(hAPP(U_933,U_934)) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_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_145_2,plain,
! [U_940,U_939,U_938,U_937] :
( ( hBOOL(hAPP(hAPP(c_member(U_937),U_938),U_940))
& hBOOL(hAPP(hAPP(c_member(U_937),U_938),U_939)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_937),U_938),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_937,tc_HOL_Obool),U_939,U_940))) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_937),U_938),U_939))
| ~ hBOOL(hAPP(hAPP(c_member(U_937),U_938),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_937,tc_HOL_Obool),U_939,U_940))) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_937),U_938),U_940))
| ~ hBOOL(hAPP(hAPP(c_member(U_937),U_938),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_937,tc_HOL_Obool),U_939,U_940))) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_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_146_2,plain,
! [U_944,U_943,U_942,U_941] :
( hBOOL(hAPP(hAPP(c_member(U_941),U_942),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_941,tc_HOL_Obool),U_943,U_944)))
| ~ hBOOL(hAPP(hAPP(c_member(U_941),U_942),U_944))
| ~ hBOOL(hAPP(hAPP(c_member(U_941),U_942),U_943)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_941),U_942),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_941,tc_HOL_Obool),U_943,U_944)))
| ~ hBOOL(hAPP(hAPP(c_member(U_941),U_942),U_944))
| ~ hBOOL(hAPP(hAPP(c_member(U_941),U_942),U_943)) ),
inference(clausify,[status(thm)],[f_146_2]) ).
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_948,U_947,U_946,U_945] :
( hBOOL(hAPP(U_947,U_948))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_945,tc_HOL_Obool),U_946,U_947),U_948)) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_948,U_947] :
( ! [U_946,U_945] : ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_945,tc_HOL_Obool),U_946,U_947),U_948))
| hBOOL(hAPP(U_947,U_948)) ),
inference(miniscope,[status(thm)],[f_147_2]) ).
cnf(f_147_4,plain,
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_945,tc_HOL_Obool),U_946,U_947),U_948))
| hBOOL(hAPP(U_947,U_948)) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_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_148_2,plain,
! [U_952,U_951,U_950,U_949] :
( hBOOL(hAPP(U_950,U_952))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_949,tc_HOL_Obool),U_950,U_951),U_952)) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_952,U_951,U_950] :
( ! [U_949] : ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_949,tc_HOL_Obool),U_950,U_951),U_952))
| hBOOL(hAPP(U_950,U_952)) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
cnf(f_148_4,plain,
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_949,tc_HOL_Obool),U_950,U_951),U_952))
| hBOOL(hAPP(U_950,U_952)) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_956,U_955,U_954,U_953] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),U_954,U_955),U_956) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),U_954,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),U_955,U_956)),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),U_954,U_955),U_956) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),U_954,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_953,tc_HOL_Obool),U_955,U_956)),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_960,U_959,U_958,U_957] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_958,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_959,U_960)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_959,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_958,U_960)),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_958,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_959,U_960)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_959,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_957,tc_HOL_Obool),U_958,U_960)),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_963,U_962,U_961] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_961,tc_HOL_Obool),U_962,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_961,tc_HOL_Obool),U_962,U_963)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_961,tc_HOL_Obool),U_962,U_963),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_961,tc_HOL_Obool),U_962,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_961,tc_HOL_Obool),U_962,U_963)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_961,tc_HOL_Obool),U_962,U_963),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_152_2,plain,
! [U_966,U_965,U_964] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_964,tc_HOL_Obool),U_965,U_966) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_964,tc_HOL_Obool),U_966,U_965),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_964,tc_HOL_Obool),U_965,U_966) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_964,tc_HOL_Obool),U_966,U_965),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_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_153_2,plain,
! [U_968,U_967] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_967,tc_HOL_Obool),U_968,U_968) = U_968,
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_967,tc_HOL_Obool),U_968,U_968) = U_968,
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_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_154_2,plain,
! [U_972,U_971,U_970,U_969] :
( hBOOL(hAPP(hAPP(c_member(U_969),U_970),U_972))
| ~ hBOOL(hAPP(hAPP(c_member(U_969),U_970),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_969,tc_HOL_Obool),U_971,U_972))) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_969),U_970),U_972))
| ~ hBOOL(hAPP(hAPP(c_member(U_969),U_970),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_969,tc_HOL_Obool),U_971,U_972))) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_976,U_975,U_974,U_973] :
( hBOOL(hAPP(hAPP(c_member(U_973),U_974),U_975))
| ~ hBOOL(hAPP(hAPP(c_member(U_973),U_974),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_973,tc_HOL_Obool),U_975,U_976))) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_973),U_974),U_975))
| ~ hBOOL(hAPP(hAPP(c_member(U_973),U_974),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_973,tc_HOL_Obool),U_975,U_976))) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_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_156_2,plain,
! [U_980,U_979,U_978,U_977] :
( ( hBOOL(hAPP(hAPP(c_member(U_977),U_978),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_977,tc_HOL_Obool),U_979,U_980)))
| ~ hBOOL(hAPP(hAPP(c_member(U_977),U_978),U_980))
| ~ hBOOL(hAPP(hAPP(c_member(U_977),U_978),U_979)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_977),U_978),U_980))
& hBOOL(hAPP(hAPP(c_member(U_977),U_978),U_979)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_977),U_978),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_977,tc_HOL_Obool),U_979,U_980))) ) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ! [U_988,U_986,U_984,U_982] :
( hBOOL(hAPP(hAPP(c_member(U_982),U_984),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_982,tc_HOL_Obool),U_986,U_988)))
| ~ hBOOL(hAPP(hAPP(c_member(U_982),U_984),U_988))
| ~ hBOOL(hAPP(hAPP(c_member(U_982),U_984),U_986)) )
& ! [U_987,U_985,U_983,U_981] :
( ( hBOOL(hAPP(hAPP(c_member(U_981),U_983),U_987))
& hBOOL(hAPP(hAPP(c_member(U_981),U_983),U_985)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_981),U_983),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool),U_985,U_987))) ) ),
inference(miniscope,[status(thm)],[f_156_2]) ).
cnf(f_156_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_981),U_983),U_985))
| ~ hBOOL(hAPP(hAPP(c_member(U_981),U_983),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool),U_985,U_987))) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_981),U_983),U_987))
| ~ hBOOL(hAPP(hAPP(c_member(U_981),U_983),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool),U_985,U_987))) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_982),U_984),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_982,tc_HOL_Obool),U_986,U_988)))
| ~ hBOOL(hAPP(hAPP(c_member(U_982),U_984),U_988))
| ~ hBOOL(hAPP(hAPP(c_member(U_982),U_984),U_986)) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_992,U_991,U_990,U_989] :
( ( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_989,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_989,tc_fun(U_989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_989)),U_990),hAPP(hAPP(c_COMBC(U_989,tc_fun(U_989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_989)),U_991)),U_992))
| ~ hBOOL(hAPP(hAPP(c_member(U_989),U_992),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_989,tc_HOL_Obool),U_990,U_991))) )
& ( hBOOL(hAPP(hAPP(c_member(U_989),U_992),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_989,tc_HOL_Obool),U_990,U_991)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_989,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_989,tc_fun(U_989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_989)),U_990),hAPP(hAPP(c_COMBC(U_989,tc_fun(U_989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_989)),U_991)),U_992)) ) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_1000,U_998,U_996,U_994] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_994,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_994,tc_fun(U_994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_994)),U_996),hAPP(hAPP(c_COMBC(U_994,tc_fun(U_994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_994)),U_998)),U_1000))
| ~ hBOOL(hAPP(hAPP(c_member(U_994),U_1000),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_994,tc_HOL_Obool),U_996,U_998))) )
& ! [U_999,U_997,U_995,U_993] :
( hBOOL(hAPP(hAPP(c_member(U_993),U_999),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_993,tc_HOL_Obool),U_995,U_997)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_993,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_993,tc_fun(U_993,tc_HOL_Obool),tc_HOL_Obool),c_member(U_993)),U_995),hAPP(hAPP(c_COMBC(U_993,tc_fun(U_993,tc_HOL_Obool),tc_HOL_Obool),c_member(U_993)),U_997)),U_999)) ) ),
inference(miniscope,[status(thm)],[f_157_2]) ).
cnf(f_157_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_993),U_999),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_993,tc_HOL_Obool),U_995,U_997)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_993,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_993,tc_fun(U_993,tc_HOL_Obool),tc_HOL_Obool),c_member(U_993)),U_995),hAPP(hAPP(c_COMBC(U_993,tc_fun(U_993,tc_HOL_Obool),tc_HOL_Obool),c_member(U_993)),U_997)),U_999)) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_994,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_994,tc_fun(U_994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_994)),U_996),hAPP(hAPP(c_COMBC(U_994,tc_fun(U_994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_994)),U_998)),U_1000))
| ~ hBOOL(hAPP(hAPP(c_member(U_994),U_1000),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_994,tc_HOL_Obool),U_996,U_998))) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_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_158_2,plain,
! [U_1005,U_1004,U_1003,U_1002,U_1001] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1002,U_1001),U_1003,U_1004),U_1005) = c_Lattices_Osemilattice__inf__class_Oinf(U_1001,hAPP(U_1003,U_1005),hAPP(U_1004,U_1005))
| ~ class_Lattices_Olattice(U_1001) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1002,U_1001),U_1003,U_1004),U_1005) = c_Lattices_Osemilattice__inf__class_Oinf(U_1001,hAPP(U_1003,U_1005),hAPP(U_1004,U_1005))
| ~ class_Lattices_Olattice(U_1001) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_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_159_2,plain,
! [U_1010,U_1009,U_1008,U_1007,U_1006] :
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,U_1006),U_1008,U_1009),U_1010) = c_Lattices_Osemilattice__inf__class_Oinf(U_1006,hAPP(U_1008,U_1010),hAPP(U_1009,U_1010))
| ~ class_Lattices_Olattice(U_1006) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,U_1006),U_1008,U_1009),U_1010) = c_Lattices_Osemilattice__inf__class_Oinf(U_1006,hAPP(U_1008,U_1010),hAPP(U_1009,U_1010))
| ~ class_Lattices_Olattice(U_1006) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_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_160_2,plain,
! [U_1017,U_1016,U_1015] :
( ( c_Relation_Ototal__on(U_1015,U_1016,U_1017)
| ? [U_1014] :
( ? [U_1013] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),U_1013),U_1014)),U_1017))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),U_1014),U_1013)),U_1017))
& U_1014 != U_1013
& hBOOL(hAPP(hAPP(c_member(U_1015),U_1013),U_1016)) )
& hBOOL(hAPP(hAPP(c_member(U_1015),U_1014),U_1016)) ) )
& ( ! [U_1012] :
( ! [U_1011] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),U_1011),U_1012)),U_1017))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1015,U_1015)),hAPP(hAPP(c_Product__Type_OPair(U_1015,U_1015),U_1012),U_1011)),U_1017))
| U_1012 = U_1011
| ~ hBOOL(hAPP(hAPP(c_member(U_1015),U_1011),U_1016)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1015),U_1012),U_1016)) )
| ~ c_Relation_Ototal__on(U_1015,U_1016,U_1017) ) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
( ! [U_1023,U_1021,U_1019] :
( c_Relation_Ototal__on(U_1019,U_1021,U_1023)
| ? [U_1014] :
( ? [U_1013] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),U_1013),U_1014)),U_1023))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),U_1014),U_1013)),U_1023))
& U_1014 != U_1013
& hBOOL(hAPP(hAPP(c_member(U_1019),U_1013),U_1021)) )
& hBOOL(hAPP(hAPP(c_member(U_1019),U_1014),U_1021)) ) )
& ! [U_1022,U_1020,U_1018] :
( ! [U_1012] :
( ! [U_1011] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1011),U_1012)),U_1022))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1012),U_1011)),U_1022))
| U_1012 = U_1011
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1011),U_1020)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1012),U_1020)) )
| ~ c_Relation_Ototal__on(U_1018,U_1020,U_1022) ) ),
inference(miniscope,[status(thm)],[f_160_2]) ).
fof(f_160_4,plain,
( ! [U_1023,U_1021,U_1019] :
( c_Relation_Ototal__on(U_1019,U_1021,U_1023)
| ( ? [U_1013] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),U_1013),sK77(U_1023,U_1021,U_1019))),U_1023))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),sK77(U_1023,U_1021,U_1019)),U_1013)),U_1023))
& sK77(U_1023,U_1021,U_1019) != U_1013
& hBOOL(hAPP(hAPP(c_member(U_1019),U_1013),U_1021)) )
& hBOOL(hAPP(hAPP(c_member(U_1019),sK77(U_1023,U_1021,U_1019)),U_1021)) ) )
& ! [U_1022,U_1020,U_1018] :
( ! [U_1012] :
( ! [U_1011] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1011),U_1012)),U_1022))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1012),U_1011)),U_1022))
| U_1012 = U_1011
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1011),U_1020)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1012),U_1020)) )
| ~ c_Relation_Ototal__on(U_1018,U_1020,U_1022) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1014,sK77(U_1023,U_1021,U_1019))],[f_160_3]) ).
fof(f_160_5,plain,
( ! [U_1023,U_1021,U_1019] :
( c_Relation_Ototal__on(U_1019,U_1021,U_1023)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),sK78(U_1023,U_1021,U_1019)),sK77(U_1023,U_1021,U_1019))),U_1023))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),sK77(U_1023,U_1021,U_1019)),sK78(U_1023,U_1021,U_1019))),U_1023))
& sK77(U_1023,U_1021,U_1019) != sK78(U_1023,U_1021,U_1019)
& hBOOL(hAPP(hAPP(c_member(U_1019),sK78(U_1023,U_1021,U_1019)),U_1021))
& hBOOL(hAPP(hAPP(c_member(U_1019),sK77(U_1023,U_1021,U_1019)),U_1021)) ) )
& ! [U_1022,U_1020,U_1018] :
( ! [U_1012] :
( ! [U_1011] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1011),U_1012)),U_1022))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1012),U_1011)),U_1022))
| U_1012 = U_1011
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1011),U_1020)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1012),U_1020)) )
| ~ c_Relation_Ototal__on(U_1018,U_1020,U_1022) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1013,sK78(U_1023,U_1021,U_1019))],[f_160_4]) ).
cnf(f_160_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1011),U_1012)),U_1022))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1018,U_1018)),hAPP(hAPP(c_Product__Type_OPair(U_1018,U_1018),U_1012),U_1011)),U_1022))
| U_1012 = U_1011
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1011),U_1020))
| ~ hBOOL(hAPP(hAPP(c_member(U_1018),U_1012),U_1020))
| ~ c_Relation_Ototal__on(U_1018,U_1020,U_1022) ),
inference(clausify,[status(thm)],[f_160_5]) ).
cnf(f_160_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_1019),sK77(U_1023,U_1021,U_1019)),U_1021))
| c_Relation_Ototal__on(U_1019,U_1021,U_1023) ),
inference(clausify,[status(thm)],[f_160_5]) ).
cnf(f_160_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1019),sK78(U_1023,U_1021,U_1019)),U_1021))
| c_Relation_Ototal__on(U_1019,U_1021,U_1023) ),
inference(clausify,[status(thm)],[f_160_5]) ).
cnf(f_160_9,plain,
( sK77(U_1023,U_1021,U_1019) != sK78(U_1023,U_1021,U_1019)
| c_Relation_Ototal__on(U_1019,U_1021,U_1023) ),
inference(clausify,[status(thm)],[f_160_5]) ).
cnf(f_160_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),sK77(U_1023,U_1021,U_1019)),sK78(U_1023,U_1021,U_1019))),U_1023))
| c_Relation_Ototal__on(U_1019,U_1021,U_1023) ),
inference(clausify,[status(thm)],[f_160_5]) ).
cnf(f_160_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1019,U_1019)),hAPP(hAPP(c_Product__Type_OPair(U_1019,U_1019),sK78(U_1023,U_1021,U_1019)),sK77(U_1023,U_1021,U_1019))),U_1023))
| c_Relation_Ototal__on(U_1019,U_1021,U_1023) ),
inference(clausify,[status(thm)],[f_160_5]) ).
fof(f_161_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_161_2,plain,
! [U_1029,U_1028,U_1027,U_1026,U_1025,U_1024] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1024,U_1024)),hAPP(hAPP(c_Product__Type_OPair(U_1024,U_1024),U_1025),U_1026)),hAPP(hAPP(c_Relation_Oinv__image(U_1027,U_1024),U_1028),U_1029)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1027,U_1027)),hAPP(hAPP(c_Product__Type_OPair(U_1027,U_1027),hAPP(U_1029,U_1025)),hAPP(U_1029,U_1026))),U_1028)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1027,U_1027)),hAPP(hAPP(c_Product__Type_OPair(U_1027,U_1027),hAPP(U_1029,U_1025)),hAPP(U_1029,U_1026))),U_1028))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1024,U_1024)),hAPP(hAPP(c_Product__Type_OPair(U_1024,U_1024),U_1025),U_1026)),hAPP(hAPP(c_Relation_Oinv__image(U_1027,U_1024),U_1028),U_1029))) ) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
( ! [U_1041,U_1039,U_1037,U_1035,U_1033] :
( ! [U_1031] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1031,U_1031)),hAPP(hAPP(c_Product__Type_OPair(U_1031,U_1031),U_1033),U_1035)),hAPP(hAPP(c_Relation_Oinv__image(U_1037,U_1031),U_1039),U_1041)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1037,U_1037)),hAPP(hAPP(c_Product__Type_OPair(U_1037,U_1037),hAPP(U_1041,U_1033)),hAPP(U_1041,U_1035))),U_1039)) )
& ! [U_1040,U_1038,U_1036,U_1034,U_1032] :
( ! [U_1030] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1030,U_1030)),hAPP(hAPP(c_Product__Type_OPair(U_1030,U_1030),U_1032),U_1034)),hAPP(hAPP(c_Relation_Oinv__image(U_1036,U_1030),U_1038),U_1040)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1036,U_1036)),hAPP(hAPP(c_Product__Type_OPair(U_1036,U_1036),hAPP(U_1040,U_1032)),hAPP(U_1040,U_1034))),U_1038)) ) ),
inference(miniscope,[status(thm)],[f_161_2]) ).
cnf(f_161_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1030,U_1030)),hAPP(hAPP(c_Product__Type_OPair(U_1030,U_1030),U_1032),U_1034)),hAPP(hAPP(c_Relation_Oinv__image(U_1036,U_1030),U_1038),U_1040)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1036,U_1036)),hAPP(hAPP(c_Product__Type_OPair(U_1036,U_1036),hAPP(U_1040,U_1032)),hAPP(U_1040,U_1034))),U_1038)) ),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1031,U_1031)),hAPP(hAPP(c_Product__Type_OPair(U_1031,U_1031),U_1033),U_1035)),hAPP(hAPP(c_Relation_Oinv__image(U_1037,U_1031),U_1039),U_1041)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1037,U_1037)),hAPP(hAPP(c_Product__Type_OPair(U_1037,U_1037),hAPP(U_1041,U_1033)),hAPP(U_1041,U_1035))),U_1039)) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_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_162_2,plain,
! [U_1046,U_1045,U_1044,U_1043,U_1042] :
( hBOOL(hAPP(hAPP(c_member(U_1042),U_1046),U_1043))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1042,U_1042)),hAPP(hAPP(c_Product__Type_OPair(U_1042,U_1042),U_1045),U_1046)),U_1044))
| ~ c_Relation_Orefl__on(U_1042,U_1043,U_1044) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_1042),U_1046),U_1043))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1042,U_1042)),hAPP(hAPP(c_Product__Type_OPair(U_1042,U_1042),U_1045),U_1046)),U_1044))
| ~ c_Relation_Orefl__on(U_1042,U_1043,U_1044) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_1051,U_1050,U_1049,U_1048,U_1047] :
( hBOOL(hAPP(hAPP(c_member(U_1047),U_1050),U_1048))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1047,U_1047)),hAPP(hAPP(c_Product__Type_OPair(U_1047,U_1047),U_1050),U_1051)),U_1049))
| ~ c_Relation_Orefl__on(U_1047,U_1048,U_1049) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_1047),U_1050),U_1048))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1047,U_1047)),hAPP(hAPP(c_Product__Type_OPair(U_1047,U_1047),U_1050),U_1051)),U_1049))
| ~ c_Relation_Orefl__on(U_1047,U_1048,U_1049) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_1057,U_1056,U_1055,U_1054,U_1053,U_1052] :
( ( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1052,tc_fun(U_1053,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1052,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),U_1052),c_COMBC(U_1053,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_prod(U_1052,U_1053)),tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),U_1052),hAPP(c_COMBB(tc_prod(U_1052,U_1053),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool),U_1053),c_member(tc_prod(U_1052,U_1053)))),c_Product__Type_OPair(U_1052,U_1053)))),U_1054),hAPP(hAPP(c_COMBC(U_1052,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),U_1052),c_COMBC(U_1053,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_prod(U_1052,U_1053)),tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),U_1052),hAPP(c_COMBB(tc_prod(U_1052,U_1053),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool),U_1053),c_member(tc_prod(U_1052,U_1053)))),c_Product__Type_OPair(U_1052,U_1053)))),U_1055)),U_1056),U_1057))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1052,U_1053)),hAPP(hAPP(c_Product__Type_OPair(U_1052,U_1053),U_1056),U_1057)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),U_1054,U_1055))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1052,U_1053)),hAPP(hAPP(c_Product__Type_OPair(U_1052,U_1053),U_1056),U_1057)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),U_1054,U_1055)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1052,tc_fun(U_1053,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1052,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),U_1052),c_COMBC(U_1053,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_prod(U_1052,U_1053)),tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),U_1052),hAPP(c_COMBB(tc_prod(U_1052,U_1053),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool),U_1053),c_member(tc_prod(U_1052,U_1053)))),c_Product__Type_OPair(U_1052,U_1053)))),U_1054),hAPP(hAPP(c_COMBC(U_1052,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_fun(U_1053,tc_HOL_Obool)),U_1052),c_COMBC(U_1053,tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1053,tc_prod(U_1052,U_1053)),tc_fun(U_1053,tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool)),U_1052),hAPP(c_COMBB(tc_prod(U_1052,U_1053),tc_fun(tc_fun(tc_prod(U_1052,U_1053),tc_HOL_Obool),tc_HOL_Obool),U_1053),c_member(tc_prod(U_1052,U_1053)))),c_Product__Type_OPair(U_1052,U_1053)))),U_1055)),U_1056),U_1057)) ) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
( ! [U_1069,U_1067,U_1065,U_1063,U_1061,U_1059] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1059,tc_fun(U_1061,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1059,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),U_1059),c_COMBC(U_1061,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_prod(U_1059,U_1061)),tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),U_1059),hAPP(c_COMBB(tc_prod(U_1059,U_1061),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool),U_1061),c_member(tc_prod(U_1059,U_1061)))),c_Product__Type_OPair(U_1059,U_1061)))),U_1063),hAPP(hAPP(c_COMBC(U_1059,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),U_1059),c_COMBC(U_1061,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_prod(U_1059,U_1061)),tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),U_1059),hAPP(c_COMBB(tc_prod(U_1059,U_1061),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool),U_1061),c_member(tc_prod(U_1059,U_1061)))),c_Product__Type_OPair(U_1059,U_1061)))),U_1065)),U_1067),U_1069))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1059,U_1061)),hAPP(hAPP(c_Product__Type_OPair(U_1059,U_1061),U_1067),U_1069)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),U_1063,U_1065))) )
& ! [U_1068,U_1066,U_1064,U_1062,U_1060,U_1058] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1058,U_1060)),hAPP(hAPP(c_Product__Type_OPair(U_1058,U_1060),U_1066),U_1068)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),U_1062,U_1064)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1058,tc_fun(U_1060,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1058,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),U_1058),c_COMBC(U_1060,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_prod(U_1058,U_1060)),tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),U_1058),hAPP(c_COMBB(tc_prod(U_1058,U_1060),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool),U_1060),c_member(tc_prod(U_1058,U_1060)))),c_Product__Type_OPair(U_1058,U_1060)))),U_1062),hAPP(hAPP(c_COMBC(U_1058,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),U_1058),c_COMBC(U_1060,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_prod(U_1058,U_1060)),tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),U_1058),hAPP(c_COMBB(tc_prod(U_1058,U_1060),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool),U_1060),c_member(tc_prod(U_1058,U_1060)))),c_Product__Type_OPair(U_1058,U_1060)))),U_1064)),U_1066),U_1068)) ) ),
inference(miniscope,[status(thm)],[f_164_2]) ).
cnf(f_164_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1058,U_1060)),hAPP(hAPP(c_Product__Type_OPair(U_1058,U_1060),U_1066),U_1068)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),U_1062,U_1064)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1058,tc_fun(U_1060,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1058,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),U_1058),c_COMBC(U_1060,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_prod(U_1058,U_1060)),tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),U_1058),hAPP(c_COMBB(tc_prod(U_1058,U_1060),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool),U_1060),c_member(tc_prod(U_1058,U_1060)))),c_Product__Type_OPair(U_1058,U_1060)))),U_1062),hAPP(hAPP(c_COMBC(U_1058,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_fun(U_1060,tc_HOL_Obool)),U_1058),c_COMBC(U_1060,tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1060,tc_prod(U_1058,U_1060)),tc_fun(U_1060,tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool)),U_1058),hAPP(c_COMBB(tc_prod(U_1058,U_1060),tc_fun(tc_fun(tc_prod(U_1058,U_1060),tc_HOL_Obool),tc_HOL_Obool),U_1060),c_member(tc_prod(U_1058,U_1060)))),c_Product__Type_OPair(U_1058,U_1060)))),U_1064)),U_1066),U_1068)) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_5,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1059,tc_fun(U_1061,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1059,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),U_1059),c_COMBC(U_1061,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_prod(U_1059,U_1061)),tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),U_1059),hAPP(c_COMBB(tc_prod(U_1059,U_1061),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool),U_1061),c_member(tc_prod(U_1059,U_1061)))),c_Product__Type_OPair(U_1059,U_1061)))),U_1063),hAPP(hAPP(c_COMBC(U_1059,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_fun(U_1061,tc_HOL_Obool)),U_1059),c_COMBC(U_1061,tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1061,tc_prod(U_1059,U_1061)),tc_fun(U_1061,tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool)),U_1059),hAPP(c_COMBB(tc_prod(U_1059,U_1061),tc_fun(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),tc_HOL_Obool),U_1061),c_member(tc_prod(U_1059,U_1061)))),c_Product__Type_OPair(U_1059,U_1061)))),U_1065)),U_1067),U_1069))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1059,U_1061)),hAPP(hAPP(c_Product__Type_OPair(U_1059,U_1061),U_1067),U_1069)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1059,U_1061),tc_HOL_Obool),U_1063,U_1065))) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_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_165_2,plain,
! [U_1074,U_1073,U_1072,U_1071,U_1070] :
( c_Relation_Orefl__on(U_1070,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1070,tc_HOL_Obool),U_1071,U_1073),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1070,U_1070),tc_HOL_Obool),U_1072,U_1074))
| ~ c_Relation_Orefl__on(U_1070,U_1073,U_1074)
| ~ c_Relation_Orefl__on(U_1070,U_1071,U_1072) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( c_Relation_Orefl__on(U_1070,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1070,tc_HOL_Obool),U_1071,U_1073),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1070,U_1070),tc_HOL_Obool),U_1072,U_1074))
| ~ c_Relation_Orefl__on(U_1070,U_1073,U_1074)
| ~ c_Relation_Orefl__on(U_1070,U_1071,U_1072) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_1076,U_1075] : c_Relation_Orefl__on(U_1075,U_1076,c_Relation_OId__on(U_1075,U_1076)),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
c_Relation_Orefl__on(U_1075,U_1076,c_Relation_OId__on(U_1075,U_1076)),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_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_167_2,plain,
! [U_1080,U_1079,U_1078,U_1077] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1077,c_Lattices_Osemilattice__inf__class_Oinf(U_1077,U_1078,U_1079),U_1080) = c_Lattices_Osemilattice__inf__class_Oinf(U_1077,U_1078,c_Lattices_Osemilattice__inf__class_Oinf(U_1077,U_1079,U_1080))
| ~ class_Lattices_Osemilattice__inf(U_1077) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1077,c_Lattices_Osemilattice__inf__class_Oinf(U_1077,U_1078,U_1079),U_1080) = c_Lattices_Osemilattice__inf__class_Oinf(U_1077,U_1078,c_Lattices_Osemilattice__inf__class_Oinf(U_1077,U_1079,U_1080))
| ~ class_Lattices_Osemilattice__inf(U_1077) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_168_2,plain,
! [U_1084,U_1083,U_1082,U_1081] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1081,c_Lattices_Osemilattice__inf__class_Oinf(U_1081,U_1082,U_1083),U_1084) = c_Lattices_Osemilattice__inf__class_Oinf(U_1081,U_1082,c_Lattices_Osemilattice__inf__class_Oinf(U_1081,U_1083,U_1084))
| ~ class_Lattices_Olattice(U_1081) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1081,c_Lattices_Osemilattice__inf__class_Oinf(U_1081,U_1082,U_1083),U_1084) = c_Lattices_Osemilattice__inf__class_Oinf(U_1081,U_1082,c_Lattices_Osemilattice__inf__class_Oinf(U_1081,U_1083,U_1084))
| ~ class_Lattices_Olattice(U_1081) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_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_169_2,plain,
! [U_1088,U_1087,U_1086,U_1085] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1085,c_Lattices_Osemilattice__inf__class_Oinf(U_1085,U_1086,U_1087),U_1088) = c_Lattices_Osemilattice__inf__class_Oinf(U_1085,U_1086,c_Lattices_Osemilattice__inf__class_Oinf(U_1085,U_1087,U_1088))
| ~ class_Lattices_Osemilattice__inf(U_1085) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1085,c_Lattices_Osemilattice__inf__class_Oinf(U_1085,U_1086,U_1087),U_1088) = c_Lattices_Osemilattice__inf__class_Oinf(U_1085,U_1086,c_Lattices_Osemilattice__inf__class_Oinf(U_1085,U_1087,U_1088))
| ~ class_Lattices_Osemilattice__inf(U_1085) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_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_170_2,plain,
! [U_1092,U_1091,U_1090,U_1089] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1090,c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1091,U_1092)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1091,c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1090,U_1092))
| ~ class_Lattices_Osemilattice__inf(U_1089) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1090,c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1091,U_1092)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1091,c_Lattices_Osemilattice__inf__class_Oinf(U_1089,U_1090,U_1092))
| ~ class_Lattices_Osemilattice__inf(U_1089) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_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_171_2,plain,
! [U_1096,U_1095,U_1094,U_1093] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1094,c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1095,U_1096)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1095,c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1094,U_1096))
| ~ class_Lattices_Olattice(U_1093) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1094,c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1095,U_1096)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1095,c_Lattices_Osemilattice__inf__class_Oinf(U_1093,U_1094,U_1096))
| ~ class_Lattices_Olattice(U_1093) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_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_172_2,plain,
! [U_1100,U_1099,U_1098,U_1097] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1098,c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1099,U_1100)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1099,c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1098,U_1100))
| ~ class_Lattices_Osemilattice__inf(U_1097) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1098,c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1099,U_1100)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1099,c_Lattices_Osemilattice__inf__class_Oinf(U_1097,U_1098,U_1100))
| ~ class_Lattices_Osemilattice__inf(U_1097) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_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_173_2,plain,
! [U_1103,U_1102,U_1101] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1101,U_1102,c_Lattices_Osemilattice__inf__class_Oinf(U_1101,U_1102,U_1103)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1101,U_1102,U_1103)
| ~ class_Lattices_Osemilattice__inf(U_1101) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1101,U_1102,c_Lattices_Osemilattice__inf__class_Oinf(U_1101,U_1102,U_1103)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1101,U_1102,U_1103)
| ~ class_Lattices_Osemilattice__inf(U_1101) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_1106,U_1105,U_1104] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1104,U_1105,c_Lattices_Osemilattice__inf__class_Oinf(U_1104,U_1105,U_1106)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1104,U_1105,U_1106)
| ~ class_Lattices_Olattice(U_1104) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1104,U_1105,c_Lattices_Osemilattice__inf__class_Oinf(U_1104,U_1105,U_1106)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1104,U_1105,U_1106)
| ~ class_Lattices_Olattice(U_1104) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_1109,U_1108,U_1107] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1107,U_1108,c_Lattices_Osemilattice__inf__class_Oinf(U_1107,U_1108,U_1109)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1107,U_1108,U_1109)
| ~ class_Lattices_Osemilattice__inf(U_1107) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1107,U_1108,c_Lattices_Osemilattice__inf__class_Oinf(U_1107,U_1108,U_1109)) = c_Lattices_Osemilattice__inf__class_Oinf(U_1107,U_1108,U_1109)
| ~ class_Lattices_Osemilattice__inf(U_1107) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_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_176_2,plain,
! [U_1112,U_1111,U_1110] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1110,U_1111,U_1112) = c_Lattices_Osemilattice__inf__class_Oinf(U_1110,U_1112,U_1111)
| ~ class_Lattices_Osemilattice__inf(U_1110) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1110,U_1111,U_1112) = c_Lattices_Osemilattice__inf__class_Oinf(U_1110,U_1112,U_1111)
| ~ class_Lattices_Osemilattice__inf(U_1110) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_1115,U_1114,U_1113] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1113,U_1114,U_1115) = c_Lattices_Osemilattice__inf__class_Oinf(U_1113,U_1115,U_1114)
| ~ class_Lattices_Olattice(U_1113) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1113,U_1114,U_1115) = c_Lattices_Osemilattice__inf__class_Oinf(U_1113,U_1115,U_1114)
| ~ class_Lattices_Olattice(U_1113) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_1118,U_1117,U_1116] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1116,U_1117,U_1118) = c_Lattices_Osemilattice__inf__class_Oinf(U_1116,U_1118,U_1117)
| ~ class_Lattices_Osemilattice__inf(U_1116) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1116,U_1117,U_1118) = c_Lattices_Osemilattice__inf__class_Oinf(U_1116,U_1118,U_1117)
| ~ class_Lattices_Osemilattice__inf(U_1116) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_1120,U_1119] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1119,U_1120,U_1120) = U_1120
| ~ class_Lattices_Osemilattice__inf(U_1119) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1119,U_1120,U_1120) = U_1120
| ~ class_Lattices_Osemilattice__inf(U_1119) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_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_180_2,plain,
! [U_1122,U_1121] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1121,U_1122,U_1122) = U_1122
| ~ class_Lattices_Osemilattice__inf(U_1121) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1121,U_1122,U_1122) = U_1122
| ~ class_Lattices_Osemilattice__inf(U_1121) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_1126,U_1125,U_1124,U_1123] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1123,U_1123)),hAPP(hAPP(c_Product__Type_OPair(U_1123,U_1123),U_1126),U_1126)),U_1125))
| ~ hBOOL(hAPP(hAPP(c_member(U_1123),U_1126),U_1124))
| ~ c_Relation_Orefl__on(U_1123,U_1124,U_1125) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1123,U_1123)),hAPP(hAPP(c_Product__Type_OPair(U_1123,U_1123),U_1126),U_1126)),U_1125))
| ~ hBOOL(hAPP(hAPP(c_member(U_1123),U_1126),U_1124))
| ~ c_Relation_Orefl__on(U_1123,U_1124,U_1125) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_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_182_2,plain,
! [U_1130,U_1129,U_1128,U_1127] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1127,U_1127)),hAPP(hAPP(c_Product__Type_OPair(U_1127,U_1127),U_1128),U_1129)),c_Transitive__Closure_Ortrancl(U_1127,U_1130)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1127,U_1127)),hAPP(hAPP(c_Product__Type_OPair(U_1127,U_1127),U_1128),U_1129)),c_Transitive__Closure_Otrancl(U_1127,U_1130))) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1127,U_1127)),hAPP(hAPP(c_Product__Type_OPair(U_1127,U_1127),U_1128),U_1129)),c_Transitive__Closure_Ortrancl(U_1127,U_1130)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1127,U_1127)),hAPP(hAPP(c_Product__Type_OPair(U_1127,U_1127),U_1128),U_1129)),c_Transitive__Closure_Otrancl(U_1127,U_1130))) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_1134,U_1133,U_1132,U_1131] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1131,hAPP(hAPP(c_COMBC(U_1131,tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_fun(U_1131,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1131,tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_fun(U_1131,tc_HOL_Obool)),U_1131),c_COMBC(U_1131,tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1131,tc_prod(U_1131,U_1131)),tc_fun(U_1131,tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool)),U_1131),hAPP(c_COMBB(tc_prod(U_1131,U_1131),tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool),U_1131),c_member(tc_prod(U_1131,U_1131)))),c_Product__Type_OPair(U_1131,U_1131)))),U_1132)),U_1133),U_1134))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1131,U_1131)),hAPP(hAPP(c_Product__Type_OPair(U_1131,U_1131),U_1133),U_1134)),c_Transitive__Closure_Ortrancl(U_1131,U_1132))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1131,U_1131)),hAPP(hAPP(c_Product__Type_OPair(U_1131,U_1131),U_1133),U_1134)),c_Transitive__Closure_Ortrancl(U_1131,U_1132)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1131,hAPP(hAPP(c_COMBC(U_1131,tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_fun(U_1131,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1131,tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_fun(U_1131,tc_HOL_Obool)),U_1131),c_COMBC(U_1131,tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1131,tc_prod(U_1131,U_1131)),tc_fun(U_1131,tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool)),U_1131),hAPP(c_COMBB(tc_prod(U_1131,U_1131),tc_fun(tc_fun(tc_prod(U_1131,U_1131),tc_HOL_Obool),tc_HOL_Obool),U_1131),c_member(tc_prod(U_1131,U_1131)))),c_Product__Type_OPair(U_1131,U_1131)))),U_1132)),U_1133),U_1134)) ) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_1142,U_1140,U_1138,U_1136] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1136,hAPP(hAPP(c_COMBC(U_1136,tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_fun(U_1136,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1136,tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_fun(U_1136,tc_HOL_Obool)),U_1136),c_COMBC(U_1136,tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1136,tc_prod(U_1136,U_1136)),tc_fun(U_1136,tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool)),U_1136),hAPP(c_COMBB(tc_prod(U_1136,U_1136),tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool),U_1136),c_member(tc_prod(U_1136,U_1136)))),c_Product__Type_OPair(U_1136,U_1136)))),U_1138)),U_1140),U_1142))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1136,U_1136)),hAPP(hAPP(c_Product__Type_OPair(U_1136,U_1136),U_1140),U_1142)),c_Transitive__Closure_Ortrancl(U_1136,U_1138))) )
& ! [U_1141,U_1139,U_1137,U_1135] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1135,U_1135)),hAPP(hAPP(c_Product__Type_OPair(U_1135,U_1135),U_1139),U_1141)),c_Transitive__Closure_Ortrancl(U_1135,U_1137)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1135,hAPP(hAPP(c_COMBC(U_1135,tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_fun(U_1135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1135,tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_fun(U_1135,tc_HOL_Obool)),U_1135),c_COMBC(U_1135,tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1135,tc_prod(U_1135,U_1135)),tc_fun(U_1135,tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool)),U_1135),hAPP(c_COMBB(tc_prod(U_1135,U_1135),tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool),U_1135),c_member(tc_prod(U_1135,U_1135)))),c_Product__Type_OPair(U_1135,U_1135)))),U_1137)),U_1139),U_1141)) ) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1135,U_1135)),hAPP(hAPP(c_Product__Type_OPair(U_1135,U_1135),U_1139),U_1141)),c_Transitive__Closure_Ortrancl(U_1135,U_1137)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1135,hAPP(hAPP(c_COMBC(U_1135,tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_fun(U_1135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1135,tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_fun(U_1135,tc_HOL_Obool)),U_1135),c_COMBC(U_1135,tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1135,tc_prod(U_1135,U_1135)),tc_fun(U_1135,tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool)),U_1135),hAPP(c_COMBB(tc_prod(U_1135,U_1135),tc_fun(tc_fun(tc_prod(U_1135,U_1135),tc_HOL_Obool),tc_HOL_Obool),U_1135),c_member(tc_prod(U_1135,U_1135)))),c_Product__Type_OPair(U_1135,U_1135)))),U_1137)),U_1139),U_1141)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1136,hAPP(hAPP(c_COMBC(U_1136,tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_fun(U_1136,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1136,tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_fun(U_1136,tc_HOL_Obool)),U_1136),c_COMBC(U_1136,tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1136,tc_prod(U_1136,U_1136)),tc_fun(U_1136,tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool)),U_1136),hAPP(c_COMBB(tc_prod(U_1136,U_1136),tc_fun(tc_fun(tc_prod(U_1136,U_1136),tc_HOL_Obool),tc_HOL_Obool),U_1136),c_member(tc_prod(U_1136,U_1136)))),c_Product__Type_OPair(U_1136,U_1136)))),U_1138)),U_1140),U_1142))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1136,U_1136)),hAPP(hAPP(c_Product__Type_OPair(U_1136,U_1136),U_1140),U_1142)),c_Transitive__Closure_Ortrancl(U_1136,U_1138))) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_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_184_2,plain,
! [U_1147,U_1146,U_1145,U_1144,U_1143] : c_Nitpick_Owf__wfrec_H(U_1143,U_1144,U_1145,U_1146,U_1147) = hAPP(hAPP(U_1146,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1143,U_1144),c_Nitpick_Owf__wfrec(U_1143,U_1144,U_1145,U_1146)),U_1145),U_1147)),U_1147),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
c_Nitpick_Owf__wfrec_H(U_1143,U_1144,U_1145,U_1146,U_1147) = hAPP(hAPP(U_1146,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1143,U_1144),c_Nitpick_Owf__wfrec(U_1143,U_1144,U_1145,U_1146)),U_1145),U_1147)),U_1147),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [V_x,T_a] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x) = V_x
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem]) ).
fof(f_185_2,plain,
! [U_1149,U_1148] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1148,U_1149,U_1149) = U_1149
| ~ class_Lattices_Olattice(U_1148) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1148,U_1149,U_1149) = U_1149
| ~ class_Lattices_Olattice(U_1148) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [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_Relation_OId(T_a))),
inference(fof_nnf,[status(thm)],[fact_IdI]) ).
fof(f_186_2,plain,
! [U_1151,U_1150] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1150,U_1150)),hAPP(hAPP(c_Product__Type_OPair(U_1150,U_1150),U_1151),U_1151)),c_Relation_OId(U_1150))),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(U_1150,U_1150)),hAPP(hAPP(c_Product__Type_OPair(U_1150,U_1150),U_1151),U_1151)),c_Relation_OId(U_1150))),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [T_b,V_g_2,V_f_2,V_A_2,T_a] :
( c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2) = c_FuncSet_Orestrict(T_a,T_b,V_g_2,V_A_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)) ) ),
inference(fof_nnf,[status(thm)],[fact_restrict__ext]) ).
fof(f_187_2,plain,
! [U_1157,U_1156,U_1155,U_1154,U_1153] :
( c_FuncSet_Orestrict(U_1153,U_1157,U_1155,U_1154) = c_FuncSet_Orestrict(U_1153,U_1157,U_1156,U_1154)
| ? [U_1152] :
( hAPP(U_1155,U_1152) != hAPP(U_1156,U_1152)
& hBOOL(hAPP(hAPP(c_member(U_1153),U_1152),U_1154)) ) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_1157,U_1156,U_1155,U_1154,U_1153] :
( c_FuncSet_Orestrict(U_1153,U_1157,U_1155,U_1154) = c_FuncSet_Orestrict(U_1153,U_1157,U_1156,U_1154)
| ( hAPP(U_1155,sK79(U_1157,U_1156,U_1155,U_1154,U_1153)) != hAPP(U_1156,sK79(U_1157,U_1156,U_1155,U_1154,U_1153))
& hBOOL(hAPP(hAPP(c_member(U_1153),sK79(U_1157,U_1156,U_1155,U_1154,U_1153)),U_1154)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1152,sK79(U_1157,U_1156,U_1155,U_1154,U_1153))],[f_187_2]) ).
cnf(f_187_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1153),sK79(U_1157,U_1156,U_1155,U_1154,U_1153)),U_1154))
| c_FuncSet_Orestrict(U_1153,U_1157,U_1155,U_1154) = c_FuncSet_Orestrict(U_1153,U_1157,U_1156,U_1154) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_5,plain,
( hAPP(U_1155,sK79(U_1157,U_1156,U_1155,U_1154,U_1153)) != hAPP(U_1156,sK79(U_1157,U_1156,U_1155,U_1154,U_1153))
| c_FuncSet_Orestrict(U_1153,U_1157,U_1155,U_1154) = c_FuncSet_Orestrict(U_1153,U_1157,U_1156,U_1154) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_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_188_2,plain,
! [U_1161,U_1160,U_1159,U_1158] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1161,U_1158),U_1159),U_1160))
| ~ hBOOL(hAPP(hAPP(U_1158,U_1159),U_1160)) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1161,U_1158),U_1159),U_1160))
| ~ hBOOL(hAPP(hAPP(U_1158,U_1159),U_1160)) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_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_189_2,plain,
! [U_1164,U_1163,U_1162] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1162,U_1163),U_1164),U_1164)),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1162,U_1163),U_1164),U_1164)),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_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_190_2,plain,
! [U_1170,U_1169,U_1168,U_1167,U_1166,U_1165] :
( ( hBOOL(hAPP(hAPP(U_1168,U_1169),U_1170))
& hBOOL(hAPP(hAPP(U_1167,U_1169),U_1170)) )
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1165,tc_fun(U_1166,tc_HOL_Obool)),U_1167,U_1168),U_1169),U_1170)) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_1170,U_1169,U_1168,U_1167] :
( ! [U_1166,U_1165] : ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1165,tc_fun(U_1166,tc_HOL_Obool)),U_1167,U_1168),U_1169),U_1170))
| ( hBOOL(hAPP(hAPP(U_1168,U_1169),U_1170))
& hBOOL(hAPP(hAPP(U_1167,U_1169),U_1170)) ) ),
inference(miniscope,[status(thm)],[f_190_2]) ).
cnf(f_190_4,plain,
( hBOOL(hAPP(hAPP(U_1167,U_1169),U_1170))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1165,tc_fun(U_1166,tc_HOL_Obool)),U_1167,U_1168),U_1169),U_1170)) ),
inference(clausify,[status(thm)],[f_190_3]) ).
cnf(f_190_5,plain,
( hBOOL(hAPP(hAPP(U_1168,U_1169),U_1170))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1165,tc_fun(U_1166,tc_HOL_Obool)),U_1167,U_1168),U_1169),U_1170)) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_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_191_2,plain,
! [U_1176,U_1175,U_1174,U_1173,U_1172,U_1171] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1175,tc_fun(U_1176,tc_HOL_Obool)),U_1171,U_1174),U_1172),U_1173))
| ~ hBOOL(hAPP(hAPP(U_1174,U_1172),U_1173))
| ~ hBOOL(hAPP(hAPP(U_1171,U_1172),U_1173)) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1175,tc_fun(U_1176,tc_HOL_Obool)),U_1171,U_1174),U_1172),U_1173))
| ~ hBOOL(hAPP(hAPP(U_1174,U_1172),U_1173))
| ~ hBOOL(hAPP(hAPP(U_1171,U_1172),U_1173)) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_1180,U_1179,U_1178,U_1177] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1177,U_1177)),hAPP(hAPP(c_Product__Type_OPair(U_1177,U_1177),U_1178),U_1179)),c_Transitive__Closure_Otrancl(U_1177,U_1180)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1177,U_1177)),hAPP(hAPP(c_Product__Type_OPair(U_1177,U_1177),U_1178),U_1179)),U_1180)) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1177,U_1177)),hAPP(hAPP(c_Product__Type_OPair(U_1177,U_1177),U_1178),U_1179)),c_Transitive__Closure_Otrancl(U_1177,U_1180)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1177,U_1177)),hAPP(hAPP(c_Product__Type_OPair(U_1177,U_1177),U_1178),U_1179)),U_1180)) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_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_193_2,plain,
! [U_1182,U_1181] : c_Transitive__Closure_Ortranclp(U_1181,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1181,tc_fun(U_1181,tc_HOL_Obool)),U_1182,hAPP(hAPP(c_COMBB(tc_fun(U_1181,tc_HOL_Obool),tc_fun(U_1181,tc_HOL_Obool),U_1181),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_1181),c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(U_1181,U_1182),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
c_Transitive__Closure_Ortranclp(U_1181,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1181,tc_fun(U_1181,tc_HOL_Obool)),U_1182,hAPP(hAPP(c_COMBB(tc_fun(U_1181,tc_HOL_Obool),tc_fun(U_1181,tc_HOL_Obool),U_1181),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_1181),c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(U_1181,U_1182),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_194_2,plain,
! [U_1188,U_1187,U_1186,U_1185,U_1184,U_1183] :
( hBOOL(hAPP(hAPP(U_1186,U_1187),U_1188))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_fun(U_1184,tc_HOL_Obool)),U_1185,U_1186),U_1187),U_1188)) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_1188,U_1187,U_1186] :
( ! [U_1185,U_1184,U_1183] : ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_fun(U_1184,tc_HOL_Obool)),U_1185,U_1186),U_1187),U_1188))
| hBOOL(hAPP(hAPP(U_1186,U_1187),U_1188)) ),
inference(miniscope,[status(thm)],[f_194_2]) ).
cnf(f_194_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_fun(U_1184,tc_HOL_Obool)),U_1185,U_1186),U_1187),U_1188))
| hBOOL(hAPP(hAPP(U_1186,U_1187),U_1188)) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_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_195_2,plain,
! [U_1194,U_1193,U_1192,U_1191,U_1190,U_1189] :
( hBOOL(hAPP(hAPP(U_1191,U_1193),U_1194))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1189,tc_fun(U_1190,tc_HOL_Obool)),U_1191,U_1192),U_1193),U_1194)) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_1194,U_1193,U_1192,U_1191] :
( ! [U_1190,U_1189] : ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1189,tc_fun(U_1190,tc_HOL_Obool)),U_1191,U_1192),U_1193),U_1194))
| hBOOL(hAPP(hAPP(U_1191,U_1193),U_1194)) ),
inference(miniscope,[status(thm)],[f_195_2]) ).
cnf(f_195_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1189,tc_fun(U_1190,tc_HOL_Obool)),U_1191,U_1192),U_1193),U_1194))
| hBOOL(hAPP(hAPP(U_1191,U_1193),U_1194)) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_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_196_2,plain,
! [U_1199,U_1198,U_1197,U_1196,U_1195] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1195,U_1196),U_1197),U_1199))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1195,U_1196),U_1198),U_1199))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1195,U_1196),U_1197),U_1198)) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1195,U_1196),U_1197),U_1199))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1195,U_1196),U_1198),U_1199))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1195,U_1196),U_1197),U_1198)) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_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_197_2,plain,
! [U_1204,U_1203,U_1202,U_1201,U_1200] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1200,U_1201),U_1202),U_1204))
| ~ hBOOL(hAPP(hAPP(U_1201,U_1203),U_1204))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1200,U_1201),U_1202),U_1203)) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1200,U_1201),U_1202),U_1204))
| ~ hBOOL(hAPP(hAPP(U_1201,U_1203),U_1204))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1200,U_1201),U_1202),U_1203)) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_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_198_2,plain,
! [U_1209,U_1208,U_1207,U_1206,U_1205] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1208,U_1205),U_1206),U_1209))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1208,U_1205),U_1207),U_1209))
| ~ hBOOL(hAPP(hAPP(U_1205,U_1206),U_1207)) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1208,U_1205),U_1206),U_1209))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1208,U_1205),U_1207),U_1209))
| ~ hBOOL(hAPP(hAPP(U_1205,U_1206),U_1207)) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_1215,U_1214,U_1213,U_1212] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1212,U_1213),U_1214),U_1215))
| ( ! [U_1211] :
( ~ hBOOL(hAPP(hAPP(U_1213,U_1211),U_1215))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1212,U_1213),U_1214),U_1211)) )
& U_1215 != U_1214 ) )
& ( ? [U_1210] :
( hBOOL(hAPP(hAPP(U_1213,U_1210),U_1215))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1212,U_1213),U_1214),U_1210)) )
| U_1215 = U_1214
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1212,U_1213),U_1214),U_1215)) ) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
( ! [U_1223,U_1221,U_1219,U_1217] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1217,U_1219),U_1221),U_1223))
| ( ! [U_1211] :
( ~ hBOOL(hAPP(hAPP(U_1219,U_1211),U_1223))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1217,U_1219),U_1221),U_1211)) )
& U_1223 != U_1221 ) )
& ! [U_1222,U_1220,U_1218,U_1216] :
( ? [U_1210] :
( hBOOL(hAPP(hAPP(U_1218,U_1210),U_1222))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1216,U_1218),U_1220),U_1210)) )
| U_1222 = U_1220
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1216,U_1218),U_1220),U_1222)) ) ),
inference(miniscope,[status(thm)],[f_199_2]) ).
fof(f_199_4,plain,
( ! [U_1223,U_1221,U_1219,U_1217] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1217,U_1219),U_1221),U_1223))
| ( ! [U_1211] :
( ~ hBOOL(hAPP(hAPP(U_1219,U_1211),U_1223))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1217,U_1219),U_1221),U_1211)) )
& U_1223 != U_1221 ) )
& ! [U_1222,U_1220,U_1218,U_1216] :
( ( hBOOL(hAPP(hAPP(U_1218,sK80(U_1222,U_1220,U_1218,U_1216)),U_1222))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1216,U_1218),U_1220),sK80(U_1222,U_1220,U_1218,U_1216))) )
| U_1222 = U_1220
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1216,U_1218),U_1220),U_1222)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1210,sK80(U_1222,U_1220,U_1218,U_1216))],[f_199_3]) ).
cnf(f_199_5,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1216,U_1218),U_1220),sK80(U_1222,U_1220,U_1218,U_1216)))
| U_1222 = U_1220
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1216,U_1218),U_1220),U_1222)) ),
inference(clausify,[status(thm)],[f_199_4]) ).
cnf(f_199_6,plain,
( hBOOL(hAPP(hAPP(U_1218,sK80(U_1222,U_1220,U_1218,U_1216)),U_1222))
| U_1222 = U_1220
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1216,U_1218),U_1220),U_1222)) ),
inference(clausify,[status(thm)],[f_199_4]) ).
cnf(f_199_7,plain,
( U_1223 != U_1221
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1217,U_1219),U_1221),U_1223)) ),
inference(clausify,[status(thm)],[f_199_4]) ).
cnf(f_199_8,plain,
( ~ hBOOL(hAPP(hAPP(U_1219,U_1211),U_1223))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1217,U_1219),U_1221),U_1211))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1217,U_1219),U_1221),U_1223)) ),
inference(clausify,[status(thm)],[f_199_4]) ).
fof(f_200_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_200_2,plain,
! [U_1226,U_1225,U_1224] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1224,U_1225),U_1226),U_1226)),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1224,U_1225),U_1226),U_1226)),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_1228,U_1227] : c_Transitive__Closure_Ortranclp(U_1227,c_Transitive__Closure_Ortranclp(U_1227,U_1228)) = c_Transitive__Closure_Ortranclp(U_1227,U_1228),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
c_Transitive__Closure_Ortranclp(U_1227,c_Transitive__Closure_Ortranclp(U_1227,U_1228)) = c_Transitive__Closure_Ortranclp(U_1227,U_1228),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_1231,U_1230,U_1229] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),U_1230),c_Transitive__Closure_Otrancl(U_1229,U_1231)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),U_1230),U_1231)) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),U_1230),c_Transitive__Closure_Otrancl(U_1229,U_1231)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1229,U_1229)),U_1230),U_1231)) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_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_203_2,plain,
! [U_1233,U_1232] : c_Transitive__Closure_Ortrancl(U_1232,c_Transitive__Closure_Otrancl(U_1232,U_1233)) = c_Transitive__Closure_Ortrancl(U_1232,U_1233),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
c_Transitive__Closure_Ortrancl(U_1232,c_Transitive__Closure_Otrancl(U_1232,U_1233)) = c_Transitive__Closure_Ortrancl(U_1232,U_1233),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_204_2,plain,
! [U_1235,U_1234] : c_Transitive__Closure_Otrancl(U_1234,c_Transitive__Closure_Ortrancl(U_1234,U_1235)) = c_Transitive__Closure_Ortrancl(U_1234,U_1235),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
c_Transitive__Closure_Otrancl(U_1234,c_Transitive__Closure_Ortrancl(U_1234,U_1235)) = c_Transitive__Closure_Ortrancl(U_1234,U_1235),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_1237,U_1236] : c_Relation_ODomain(U_1236,U_1236,c_Transitive__Closure_Otrancl(U_1236,U_1237)) = c_Relation_ODomain(U_1236,U_1236,U_1237),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
c_Relation_ODomain(U_1236,U_1236,c_Transitive__Closure_Otrancl(U_1236,U_1237)) = c_Relation_ODomain(U_1236,U_1236,U_1237),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_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_206_2,plain,
! [U_1239,U_1238] : c_Relation_ORange(U_1238,U_1238,c_Transitive__Closure_Otrancl(U_1238,U_1239)) = c_Relation_ORange(U_1238,U_1238,U_1239),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
c_Relation_ORange(U_1238,U_1238,c_Transitive__Closure_Otrancl(U_1238,U_1239)) = c_Relation_ORange(U_1238,U_1238,U_1239),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_1243,U_1242,U_1241,U_1240] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1240,U_1241),U_1242))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1240,U_1241),U_1243))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1240,U_1241),U_1242),U_1243)) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1240,U_1241),U_1242))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1240,U_1241),U_1243))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1240,U_1241),U_1242),U_1243)) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_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_208_2,plain,
! [U_1247,U_1246,U_1245,U_1244] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1244,U_1245),U_1247))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1244,U_1245),U_1247),U_1246))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1244,U_1245),U_1246)) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1244,U_1245),U_1247))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1244,U_1245),U_1247),U_1246))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1244,U_1245),U_1246)) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)),
inference(fof_nnf,[status(thm)],[fact_single__valued__Id]) ).
fof(f_209_2,plain,
! [U_1248] : c_Relation_Osingle__valued(U_1248,U_1248,c_Relation_OId(U_1248)),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
c_Relation_Osingle__valued(U_1248,U_1248,c_Relation_OId(U_1248)),
inference(clausify,[status(thm)],[f_209_2]) ).
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_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_210_2,plain,
! [U_1253,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_1253)),c_Transitive__Closure_Otrancl(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_1251),U_1253)),c_Transitive__Closure_Otrancl(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))) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1249,U_1249)),hAPP(hAPP(c_Product__Type_OPair(U_1249,U_1249),U_1250),U_1253)),c_Transitive__Closure_Otrancl(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_1251),U_1253)),c_Transitive__Closure_Otrancl(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))) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_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_211_2,plain,
! [U_1258,U_1257,U_1256,U_1255,U_1254] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1255),U_1258)),c_Transitive__Closure_Otrancl(U_1254,U_1257)))
| ~ 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)),U_1257))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1255),U_1256)),c_Transitive__Closure_Otrancl(U_1254,U_1257))) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1255),U_1258)),c_Transitive__Closure_Otrancl(U_1254,U_1257)))
| ~ 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)),U_1257))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1254,U_1254)),hAPP(hAPP(c_Product__Type_OPair(U_1254,U_1254),U_1255),U_1256)),c_Transitive__Closure_Otrancl(U_1254,U_1257))) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_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_212_2,plain,
! [U_1263,U_1262,U_1261,U_1260,U_1259] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1259,U_1259)),hAPP(hAPP(c_Product__Type_OPair(U_1259,U_1259),U_1260),U_1263)),c_Transitive__Closure_Otrancl(U_1259,U_1262)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1259,U_1259)),hAPP(hAPP(c_Product__Type_OPair(U_1259,U_1259),U_1261),U_1263)),c_Transitive__Closure_Otrancl(U_1259,U_1262)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1259,U_1259)),hAPP(hAPP(c_Product__Type_OPair(U_1259,U_1259),U_1260),U_1261)),U_1262)) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1259,U_1259)),hAPP(hAPP(c_Product__Type_OPair(U_1259,U_1259),U_1260),U_1263)),c_Transitive__Closure_Otrancl(U_1259,U_1262)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1259,U_1259)),hAPP(hAPP(c_Product__Type_OPair(U_1259,U_1259),U_1261),U_1263)),c_Transitive__Closure_Otrancl(U_1259,U_1262)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1259,U_1259)),hAPP(hAPP(c_Product__Type_OPair(U_1259,U_1259),U_1260),U_1261)),U_1262)) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_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_213_2,plain,
! [U_1268,U_1267,U_1266,U_1265,U_1264] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1264,U_1264)),hAPP(hAPP(c_Product__Type_OPair(U_1264,U_1264),U_1265),U_1268)),c_Transitive__Closure_Otrancl(U_1264,U_1267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1264,U_1264)),hAPP(hAPP(c_Product__Type_OPair(U_1264,U_1264),U_1266),U_1268)),U_1267))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1264,U_1264)),hAPP(hAPP(c_Product__Type_OPair(U_1264,U_1264),U_1265),U_1266)),U_1267)) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1264,U_1264)),hAPP(hAPP(c_Product__Type_OPair(U_1264,U_1264),U_1265),U_1268)),c_Transitive__Closure_Otrancl(U_1264,U_1267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1264,U_1264)),hAPP(hAPP(c_Product__Type_OPair(U_1264,U_1264),U_1266),U_1268)),U_1267))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1264,U_1264)),hAPP(hAPP(c_Product__Type_OPair(U_1264,U_1264),U_1265),U_1266)),U_1267)) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [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_Relation_OId(T_a)))
| 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_Relation_OId(T_a))) ) ),
inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv]) ).
fof(f_214_2,plain,
! [U_1271,U_1270,U_1269] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1269,U_1269)),hAPP(hAPP(c_Product__Type_OPair(U_1269,U_1269),U_1270),U_1271)),c_Relation_OId(U_1269)))
| U_1270 != U_1271 )
& ( U_1270 = U_1271
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1269,U_1269)),hAPP(hAPP(c_Product__Type_OPair(U_1269,U_1269),U_1270),U_1271)),c_Relation_OId(U_1269))) ) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
( ! [U_1277,U_1275] :
( ! [U_1273] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1273,U_1273)),hAPP(hAPP(c_Product__Type_OPair(U_1273,U_1273),U_1275),U_1277)),c_Relation_OId(U_1273)))
| U_1275 != U_1277 )
& ! [U_1276,U_1274] :
( ! [U_1272] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1272,U_1272)),hAPP(hAPP(c_Product__Type_OPair(U_1272,U_1272),U_1274),U_1276)),c_Relation_OId(U_1272)))
| U_1274 = U_1276 ) ),
inference(miniscope,[status(thm)],[f_214_2]) ).
cnf(f_214_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1272,U_1272)),hAPP(hAPP(c_Product__Type_OPair(U_1272,U_1272),U_1274),U_1276)),c_Relation_OId(U_1272)))
| U_1274 = U_1276 ),
inference(clausify,[status(thm)],[f_214_3]) ).
cnf(f_214_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1273,U_1273)),hAPP(hAPP(c_Product__Type_OPair(U_1273,U_1273),U_1275),U_1277)),c_Relation_OId(U_1273)))
| U_1275 != U_1277 ),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_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_215_2,plain,
! [U_1282,U_1281,U_1280,U_1279,U_1278] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1278,U_1278)),hAPP(hAPP(c_Product__Type_OPair(U_1278,U_1278),U_1279),U_1282)),c_Transitive__Closure_Otrancl(U_1278,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1278,U_1278)),hAPP(hAPP(c_Product__Type_OPair(U_1278,U_1278),U_1280),U_1282)),c_Transitive__Closure_Otrancl(U_1278,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1278,U_1278)),hAPP(hAPP(c_Product__Type_OPair(U_1278,U_1278),U_1279),U_1280)),c_Transitive__Closure_Ortrancl(U_1278,U_1281))) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1278,U_1278)),hAPP(hAPP(c_Product__Type_OPair(U_1278,U_1278),U_1279),U_1282)),c_Transitive__Closure_Otrancl(U_1278,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1278,U_1278)),hAPP(hAPP(c_Product__Type_OPair(U_1278,U_1278),U_1280),U_1282)),c_Transitive__Closure_Otrancl(U_1278,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1278,U_1278)),hAPP(hAPP(c_Product__Type_OPair(U_1278,U_1278),U_1279),U_1280)),c_Transitive__Closure_Ortrancl(U_1278,U_1281))) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_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_216_2,plain,
! [U_1287,U_1286,U_1285,U_1284,U_1283] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1283,U_1283)),hAPP(hAPP(c_Product__Type_OPair(U_1283,U_1283),U_1284),U_1287)),c_Transitive__Closure_Otrancl(U_1283,U_1286)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1283,U_1283)),hAPP(hAPP(c_Product__Type_OPair(U_1283,U_1283),U_1285),U_1287)),c_Transitive__Closure_Ortrancl(U_1283,U_1286)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1283,U_1283)),hAPP(hAPP(c_Product__Type_OPair(U_1283,U_1283),U_1284),U_1285)),c_Transitive__Closure_Otrancl(U_1283,U_1286))) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1283,U_1283)),hAPP(hAPP(c_Product__Type_OPair(U_1283,U_1283),U_1284),U_1287)),c_Transitive__Closure_Otrancl(U_1283,U_1286)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1283,U_1283)),hAPP(hAPP(c_Product__Type_OPair(U_1283,U_1283),U_1285),U_1287)),c_Transitive__Closure_Ortrancl(U_1283,U_1286)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1283,U_1283)),hAPP(hAPP(c_Product__Type_OPair(U_1283,U_1283),U_1284),U_1285)),c_Transitive__Closure_Otrancl(U_1283,U_1286))) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_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_217_2,plain,
! [U_1292,U_1291,U_1290,U_1289,U_1288] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1288,U_1288)),hAPP(hAPP(c_Product__Type_OPair(U_1288,U_1288),U_1289),U_1292)),c_Transitive__Closure_Otrancl(U_1288,U_1291)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1288,U_1288)),hAPP(hAPP(c_Product__Type_OPair(U_1288,U_1288),U_1290),U_1292)),U_1291))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1288,U_1288)),hAPP(hAPP(c_Product__Type_OPair(U_1288,U_1288),U_1289),U_1290)),c_Transitive__Closure_Ortrancl(U_1288,U_1291))) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1288,U_1288)),hAPP(hAPP(c_Product__Type_OPair(U_1288,U_1288),U_1289),U_1292)),c_Transitive__Closure_Otrancl(U_1288,U_1291)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1288,U_1288)),hAPP(hAPP(c_Product__Type_OPair(U_1288,U_1288),U_1290),U_1292)),U_1291))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1288,U_1288)),hAPP(hAPP(c_Product__Type_OPair(U_1288,U_1288),U_1289),U_1290)),c_Transitive__Closure_Ortrancl(U_1288,U_1291))) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_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_218_2,plain,
! [U_1296,U_1295,U_1294,U_1293] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1293,U_1293)),hAPP(hAPP(c_Product__Type_OPair(U_1293,U_1293),U_1294),U_1295)),c_Transitive__Closure_Otrancl(U_1293,U_1296)))
& U_1294 != U_1295 )
| U_1294 = U_1295
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1293,U_1293)),hAPP(hAPP(c_Product__Type_OPair(U_1293,U_1293),U_1294),U_1295)),c_Transitive__Closure_Ortrancl(U_1293,U_1296))) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( U_1294 != U_1295
| U_1294 = U_1295
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1293,U_1293)),hAPP(hAPP(c_Product__Type_OPair(U_1293,U_1293),U_1294),U_1295)),c_Transitive__Closure_Ortrancl(U_1293,U_1296))) ),
inference(clausify,[status(thm)],[f_218_2]) ).
cnf(f_218_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1293,U_1293)),hAPP(hAPP(c_Product__Type_OPair(U_1293,U_1293),U_1294),U_1295)),c_Transitive__Closure_Otrancl(U_1293,U_1296)))
| U_1294 = U_1295
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1293,U_1293)),hAPP(hAPP(c_Product__Type_OPair(U_1293,U_1293),U_1294),U_1295)),c_Transitive__Closure_Ortrancl(U_1293,U_1296))) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_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_219_2,plain,
! [U_1301,U_1300,U_1299,U_1298,U_1297] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1298),U_1301)),c_Transitive__Closure_Otrancl(U_1297,U_1300)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1299),U_1301)),c_Transitive__Closure_Ortrancl(U_1297,U_1300)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1298),U_1299)),U_1300)) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1298),U_1301)),c_Transitive__Closure_Otrancl(U_1297,U_1300)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1299),U_1301)),c_Transitive__Closure_Ortrancl(U_1297,U_1300)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1297,U_1297)),hAPP(hAPP(c_Product__Type_OPair(U_1297,U_1297),U_1298),U_1299)),U_1300)) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_1305,U_1304,U_1303,U_1302] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1302,U_1302)),hAPP(hAPP(c_Product__Type_OPair(U_1302,U_1302),U_1303),U_1304)),c_Transitive__Closure_Ortrancl(U_1302,U_1305)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1302,U_1302)),hAPP(hAPP(c_Product__Type_OPair(U_1302,U_1302),U_1303),U_1304)),c_Transitive__Closure_Otrancl(U_1302,U_1305)))
| U_1303 = U_1304 )
& U_1303 != U_1304 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1302,U_1302)),hAPP(hAPP(c_Product__Type_OPair(U_1302,U_1302),U_1303),U_1304)),c_Transitive__Closure_Otrancl(U_1302,U_1305)))
& U_1303 != U_1304 )
| U_1303 = U_1304
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1302,U_1302)),hAPP(hAPP(c_Product__Type_OPair(U_1302,U_1302),U_1303),U_1304)),c_Transitive__Closure_Ortrancl(U_1302,U_1305))) ) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
( ! [U_1313,U_1311,U_1309,U_1307] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1307,U_1307)),hAPP(hAPP(c_Product__Type_OPair(U_1307,U_1307),U_1309),U_1311)),c_Transitive__Closure_Ortrancl(U_1307,U_1313)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1307,U_1307)),hAPP(hAPP(c_Product__Type_OPair(U_1307,U_1307),U_1309),U_1311)),c_Transitive__Closure_Otrancl(U_1307,U_1313)))
| U_1309 = U_1311 )
& U_1309 != U_1311 ) )
& ! [U_1312,U_1310,U_1308,U_1306] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1306,U_1306)),hAPP(hAPP(c_Product__Type_OPair(U_1306,U_1306),U_1308),U_1310)),c_Transitive__Closure_Otrancl(U_1306,U_1312)))
& U_1308 != U_1310 )
| U_1308 = U_1310
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1306,U_1306)),hAPP(hAPP(c_Product__Type_OPair(U_1306,U_1306),U_1308),U_1310)),c_Transitive__Closure_Ortrancl(U_1306,U_1312))) ) ),
inference(miniscope,[status(thm)],[f_220_2]) ).
cnf(f_220_4,plain,
( U_1308 != U_1310
| U_1308 = U_1310
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1306,U_1306)),hAPP(hAPP(c_Product__Type_OPair(U_1306,U_1306),U_1308),U_1310)),c_Transitive__Closure_Ortrancl(U_1306,U_1312))) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1306,U_1306)),hAPP(hAPP(c_Product__Type_OPair(U_1306,U_1306),U_1308),U_1310)),c_Transitive__Closure_Otrancl(U_1306,U_1312)))
| U_1308 = U_1310
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1306,U_1306)),hAPP(hAPP(c_Product__Type_OPair(U_1306,U_1306),U_1308),U_1310)),c_Transitive__Closure_Ortrancl(U_1306,U_1312))) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_6,plain,
( U_1309 != U_1311
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1307,U_1307)),hAPP(hAPP(c_Product__Type_OPair(U_1307,U_1307),U_1309),U_1311)),c_Transitive__Closure_Ortrancl(U_1307,U_1313))) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1307,U_1307)),hAPP(hAPP(c_Product__Type_OPair(U_1307,U_1307),U_1309),U_1311)),c_Transitive__Closure_Otrancl(U_1307,U_1313)))
| U_1309 = U_1311
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1307,U_1307)),hAPP(hAPP(c_Product__Type_OPair(U_1307,U_1307),U_1309),U_1311)),c_Transitive__Closure_Ortrancl(U_1307,U_1313))) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_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_221_2,plain,
! [U_1318,U_1317,U_1316,U_1315] :
( ? [U_1314] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1314),U_1317)),c_Transitive__Closure_Ortrancl(U_1315,U_1318)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1316),U_1314)),U_1318)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1316),U_1317)),c_Transitive__Closure_Otrancl(U_1315,U_1318))) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_1318,U_1317,U_1316,U_1315] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),sK81(U_1318,U_1317,U_1316,U_1315)),U_1317)),c_Transitive__Closure_Ortrancl(U_1315,U_1318)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1316),sK81(U_1318,U_1317,U_1316,U_1315))),U_1318)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1316),U_1317)),c_Transitive__Closure_Otrancl(U_1315,U_1318))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_1314,sK81(U_1318,U_1317,U_1316,U_1315))],[f_221_2]) ).
cnf(f_221_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1316),sK81(U_1318,U_1317,U_1316,U_1315))),U_1318))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1316),U_1317)),c_Transitive__Closure_Otrancl(U_1315,U_1318))) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),sK81(U_1318,U_1317,U_1316,U_1315)),U_1317)),c_Transitive__Closure_Ortrancl(U_1315,U_1318)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1315,U_1315)),hAPP(hAPP(c_Product__Type_OPair(U_1315,U_1315),U_1316),U_1317)),c_Transitive__Closure_Otrancl(U_1315,U_1318))) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_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_222_2,plain,
! [U_1323,U_1322,U_1321,U_1320] :
( ? [U_1319] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1319),U_1322)),U_1323))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1321),U_1319)),c_Transitive__Closure_Ortrancl(U_1320,U_1323))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1321),U_1322)),c_Transitive__Closure_Otrancl(U_1320,U_1323))) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_1323,U_1322,U_1321,U_1320] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),sK82(U_1323,U_1322,U_1321,U_1320)),U_1322)),U_1323))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1321),sK82(U_1323,U_1322,U_1321,U_1320))),c_Transitive__Closure_Ortrancl(U_1320,U_1323))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1321),U_1322)),c_Transitive__Closure_Otrancl(U_1320,U_1323))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_1319,sK82(U_1323,U_1322,U_1321,U_1320))],[f_222_2]) ).
cnf(f_222_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1321),sK82(U_1323,U_1322,U_1321,U_1320))),c_Transitive__Closure_Ortrancl(U_1320,U_1323)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1321),U_1322)),c_Transitive__Closure_Otrancl(U_1320,U_1323))) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),sK82(U_1323,U_1322,U_1321,U_1320)),U_1322)),U_1323))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1320,U_1320)),hAPP(hAPP(c_Product__Type_OPair(U_1320,U_1320),U_1321),U_1322)),c_Transitive__Closure_Otrancl(U_1320,U_1323))) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [V_p_2,T_a] :
( ? [B_x] : V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) ),
inference(fof_nnf,[status(thm)],[fact_IdE]) ).
fof(f_223_2,plain,
! [U_1326,U_1325] :
( ? [U_1324] : U_1326 = hAPP(hAPP(c_Product__Type_OPair(U_1325,U_1325),U_1324),U_1324)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1325,U_1325)),U_1326),c_Relation_OId(U_1325))) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_1326,U_1325] :
( U_1326 = hAPP(hAPP(c_Product__Type_OPair(U_1325,U_1325),sK83(U_1326,U_1325)),sK83(U_1326,U_1325))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1325,U_1325)),U_1326),c_Relation_OId(U_1325))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_1324,sK83(U_1326,U_1325))],[f_223_2]) ).
cnf(f_223_4,plain,
( U_1326 = hAPP(hAPP(c_Product__Type_OPair(U_1325,U_1325),sK83(U_1326,U_1325)),sK83(U_1326,U_1325))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1325,U_1325)),U_1326),c_Relation_OId(U_1325))) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_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_224_2,plain,
! [U_1330,U_1329] :
( ( c_Wellfounded_Oacyclic(U_1329,U_1330)
| ? [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_1328)),c_Transitive__Closure_Otrancl(U_1329,U_1330))) )
& ( ! [U_1327] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1329,U_1329)),hAPP(hAPP(c_Product__Type_OPair(U_1329,U_1329),U_1327),U_1327)),c_Transitive__Closure_Otrancl(U_1329,U_1330)))
| ~ c_Wellfounded_Oacyclic(U_1329,U_1330) ) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
( ! [U_1334,U_1332] :
( c_Wellfounded_Oacyclic(U_1332,U_1334)
| ? [U_1328] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1332,U_1332)),hAPP(hAPP(c_Product__Type_OPair(U_1332,U_1332),U_1328),U_1328)),c_Transitive__Closure_Otrancl(U_1332,U_1334))) )
& ! [U_1333,U_1331] :
( ! [U_1327] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1331,U_1331)),hAPP(hAPP(c_Product__Type_OPair(U_1331,U_1331),U_1327),U_1327)),c_Transitive__Closure_Otrancl(U_1331,U_1333)))
| ~ c_Wellfounded_Oacyclic(U_1331,U_1333) ) ),
inference(miniscope,[status(thm)],[f_224_2]) ).
fof(f_224_4,plain,
( ! [U_1334,U_1332] :
( c_Wellfounded_Oacyclic(U_1332,U_1334)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1332,U_1332)),hAPP(hAPP(c_Product__Type_OPair(U_1332,U_1332),sK84(U_1334,U_1332)),sK84(U_1334,U_1332))),c_Transitive__Closure_Otrancl(U_1332,U_1334))) )
& ! [U_1333,U_1331] :
( ! [U_1327] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1331,U_1331)),hAPP(hAPP(c_Product__Type_OPair(U_1331,U_1331),U_1327),U_1327)),c_Transitive__Closure_Otrancl(U_1331,U_1333)))
| ~ c_Wellfounded_Oacyclic(U_1331,U_1333) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_1328,sK84(U_1334,U_1332))],[f_224_3]) ).
cnf(f_224_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1331,U_1331)),hAPP(hAPP(c_Product__Type_OPair(U_1331,U_1331),U_1327),U_1327)),c_Transitive__Closure_Otrancl(U_1331,U_1333)))
| ~ c_Wellfounded_Oacyclic(U_1331,U_1333) ),
inference(clausify,[status(thm)],[f_224_4]) ).
cnf(f_224_6,plain,
( c_Wellfounded_Oacyclic(U_1332,U_1334)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1332,U_1332)),hAPP(hAPP(c_Product__Type_OPair(U_1332,U_1332),sK84(U_1334,U_1332)),sK84(U_1334,U_1332))),c_Transitive__Closure_Otrancl(U_1332,U_1334))) ),
inference(clausify,[status(thm)],[f_224_4]) ).
fof(f_225_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_225_2,plain,
! [U_1339,U_1338,U_1337,U_1336] :
( ? [U_1335] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1335),U_1338)),U_1339))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1335)),c_Transitive__Closure_Otrancl(U_1336,U_1339))) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),U_1339))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),c_Transitive__Closure_Otrancl(U_1336,U_1339))) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_1339,U_1338,U_1337,U_1336] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),sK85(U_1339,U_1338,U_1337,U_1336)),U_1338)),U_1339))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),sK85(U_1339,U_1338,U_1337,U_1336))),c_Transitive__Closure_Otrancl(U_1336,U_1339))) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),U_1339))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),c_Transitive__Closure_Otrancl(U_1336,U_1339))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_1335,sK85(U_1339,U_1338,U_1337,U_1336))],[f_225_2]) ).
cnf(f_225_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),sK85(U_1339,U_1338,U_1337,U_1336))),c_Transitive__Closure_Otrancl(U_1336,U_1339)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),U_1339))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),c_Transitive__Closure_Otrancl(U_1336,U_1339))) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),sK85(U_1339,U_1338,U_1337,U_1336)),U_1338)),U_1339))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),U_1339))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1336,U_1336)),hAPP(hAPP(c_Product__Type_OPair(U_1336,U_1336),U_1337),U_1338)),c_Transitive__Closure_Otrancl(U_1336,U_1339))) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_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_226_2,plain,
! [U_1342,U_1341] :
( c_Wellfounded_Oacyclic(U_1341,U_1342)
| ? [U_1340] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1341,U_1341)),hAPP(hAPP(c_Product__Type_OPair(U_1341,U_1341),U_1340),U_1340)),c_Transitive__Closure_Otrancl(U_1341,U_1342))) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_1342,U_1341] :
( c_Wellfounded_Oacyclic(U_1341,U_1342)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1341,U_1341)),hAPP(hAPP(c_Product__Type_OPair(U_1341,U_1341),sK86(U_1342,U_1341)),sK86(U_1342,U_1341))),c_Transitive__Closure_Otrancl(U_1341,U_1342))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_1340,sK86(U_1342,U_1341))],[f_226_2]) ).
cnf(f_226_4,plain,
( c_Wellfounded_Oacyclic(U_1341,U_1342)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1341,U_1341)),hAPP(hAPP(c_Product__Type_OPair(U_1341,U_1341),sK86(U_1342,U_1341)),sK86(U_1342,U_1341))),c_Transitive__Closure_Otrancl(U_1341,U_1342))) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_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_227_2,plain,
! [U_1346,U_1345,U_1344,U_1343] :
( ( c_Wellfounded_Oacyclic(U_1343,c_Set_Oinsert(tc_prod(U_1343,U_1343),hAPP(hAPP(c_Product__Type_OPair(U_1343,U_1343),U_1344),U_1345),U_1346))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1343,U_1343)),hAPP(hAPP(c_Product__Type_OPair(U_1343,U_1343),U_1345),U_1344)),c_Transitive__Closure_Ortrancl(U_1343,U_1346)))
| ~ c_Wellfounded_Oacyclic(U_1343,U_1346) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1343,U_1343)),hAPP(hAPP(c_Product__Type_OPair(U_1343,U_1343),U_1345),U_1344)),c_Transitive__Closure_Ortrancl(U_1343,U_1346)))
& c_Wellfounded_Oacyclic(U_1343,U_1346) )
| ~ c_Wellfounded_Oacyclic(U_1343,c_Set_Oinsert(tc_prod(U_1343,U_1343),hAPP(hAPP(c_Product__Type_OPair(U_1343,U_1343),U_1344),U_1345),U_1346)) ) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
( ! [U_1354,U_1352,U_1350,U_1348] :
( c_Wellfounded_Oacyclic(U_1348,c_Set_Oinsert(tc_prod(U_1348,U_1348),hAPP(hAPP(c_Product__Type_OPair(U_1348,U_1348),U_1350),U_1352),U_1354))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1348,U_1348)),hAPP(hAPP(c_Product__Type_OPair(U_1348,U_1348),U_1352),U_1350)),c_Transitive__Closure_Ortrancl(U_1348,U_1354)))
| ~ c_Wellfounded_Oacyclic(U_1348,U_1354) )
& ! [U_1353,U_1351,U_1349,U_1347] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1347,U_1347)),hAPP(hAPP(c_Product__Type_OPair(U_1347,U_1347),U_1351),U_1349)),c_Transitive__Closure_Ortrancl(U_1347,U_1353)))
& c_Wellfounded_Oacyclic(U_1347,U_1353) )
| ~ c_Wellfounded_Oacyclic(U_1347,c_Set_Oinsert(tc_prod(U_1347,U_1347),hAPP(hAPP(c_Product__Type_OPair(U_1347,U_1347),U_1349),U_1351),U_1353)) ) ),
inference(miniscope,[status(thm)],[f_227_2]) ).
cnf(f_227_4,plain,
( c_Wellfounded_Oacyclic(U_1347,U_1353)
| ~ c_Wellfounded_Oacyclic(U_1347,c_Set_Oinsert(tc_prod(U_1347,U_1347),hAPP(hAPP(c_Product__Type_OPair(U_1347,U_1347),U_1349),U_1351),U_1353)) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1347,U_1347)),hAPP(hAPP(c_Product__Type_OPair(U_1347,U_1347),U_1351),U_1349)),c_Transitive__Closure_Ortrancl(U_1347,U_1353)))
| ~ c_Wellfounded_Oacyclic(U_1347,c_Set_Oinsert(tc_prod(U_1347,U_1347),hAPP(hAPP(c_Product__Type_OPair(U_1347,U_1347),U_1349),U_1351),U_1353)) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_6,plain,
( c_Wellfounded_Oacyclic(U_1348,c_Set_Oinsert(tc_prod(U_1348,U_1348),hAPP(hAPP(c_Product__Type_OPair(U_1348,U_1348),U_1350),U_1352),U_1354))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1348,U_1348)),hAPP(hAPP(c_Product__Type_OPair(U_1348,U_1348),U_1352),U_1350)),c_Transitive__Closure_Ortrancl(U_1348,U_1354)))
| ~ c_Wellfounded_Oacyclic(U_1348,U_1354) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_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_228_2,plain,
! [U_1359,U_1358,U_1357,U_1356] :
( U_1358 != U_1359
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1356,U_1356)),hAPP(hAPP(c_Product__Type_OPair(U_1356,U_1356),U_1358),U_1359)),U_1357))
| ? [U_1355] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1356,U_1356)),hAPP(hAPP(c_Product__Type_OPair(U_1356,U_1356),U_1355),U_1355)),c_Transitive__Closure_Otrancl(U_1356,U_1357))) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_1359,U_1358,U_1357,U_1356] :
( U_1358 != U_1359
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1356,U_1356)),hAPP(hAPP(c_Product__Type_OPair(U_1356,U_1356),U_1358),U_1359)),U_1357))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1356,U_1356)),hAPP(hAPP(c_Product__Type_OPair(U_1356,U_1356),sK87(U_1359,U_1358,U_1357,U_1356)),sK87(U_1359,U_1358,U_1357,U_1356))),c_Transitive__Closure_Otrancl(U_1356,U_1357))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_1355,sK87(U_1359,U_1358,U_1357,U_1356))],[f_228_2]) ).
cnf(f_228_4,plain,
( U_1358 != U_1359
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1356,U_1356)),hAPP(hAPP(c_Product__Type_OPair(U_1356,U_1356),U_1358),U_1359)),U_1357))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1356,U_1356)),hAPP(hAPP(c_Product__Type_OPair(U_1356,U_1356),sK87(U_1359,U_1358,U_1357,U_1356)),sK87(U_1359,U_1358,U_1357,U_1356))),c_Transitive__Closure_Otrancl(U_1356,U_1357))) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_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_229_2,plain,
! [U_1364,U_1363,U_1362,U_1361] :
( ? [U_1360] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1360),U_1363)),c_Transitive__Closure_Otrancl(U_1361,U_1364)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1360)),U_1364)) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),U_1364))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),c_Transitive__Closure_Otrancl(U_1361,U_1364))) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_1364,U_1363,U_1362,U_1361] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),sK88(U_1364,U_1363,U_1362,U_1361)),U_1363)),c_Transitive__Closure_Otrancl(U_1361,U_1364)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),sK88(U_1364,U_1363,U_1362,U_1361))),U_1364)) )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),U_1364))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),c_Transitive__Closure_Otrancl(U_1361,U_1364))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_1360,sK88(U_1364,U_1363,U_1362,U_1361))],[f_229_2]) ).
cnf(f_229_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),sK88(U_1364,U_1363,U_1362,U_1361))),U_1364))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),U_1364))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),c_Transitive__Closure_Otrancl(U_1361,U_1364))) ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),sK88(U_1364,U_1363,U_1362,U_1361)),U_1363)),c_Transitive__Closure_Otrancl(U_1361,U_1364)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),U_1364))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1361,U_1361)),hAPP(hAPP(c_Product__Type_OPair(U_1361,U_1361),U_1362),U_1363)),c_Transitive__Closure_Otrancl(U_1361,U_1364))) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_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_230_2,plain,
! [U_1368,U_1367,U_1366,U_1365] :
( hBOOL(hAPP(hAPP(c_member(U_1365),U_1366),U_1368))
| U_1366 = U_1367
| ~ hBOOL(hAPP(hAPP(c_member(U_1365),U_1366),c_Set_Oinsert(U_1365,U_1367,U_1368))) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_1365),U_1366),U_1368))
| U_1366 = U_1367
| ~ hBOOL(hAPP(hAPP(c_member(U_1365),U_1366),c_Set_Oinsert(U_1365,U_1367,U_1368))) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_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_231_2,plain,
! [U_1372,U_1371,U_1370,U_1369] :
( hBOOL(hAPP(hAPP(c_member(U_1369),U_1370),c_Set_Oinsert(U_1369,U_1372,U_1371)))
| ( U_1370 != U_1372
& ~ hBOOL(hAPP(hAPP(c_member(U_1369),U_1370),U_1371)) ) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1369),U_1370),U_1371))
| hBOOL(hAPP(hAPP(c_member(U_1369),U_1370),c_Set_Oinsert(U_1369,U_1372,U_1371))) ),
inference(clausify,[status(thm)],[f_231_2]) ).
cnf(f_231_4,plain,
( U_1370 != U_1372
| hBOOL(hAPP(hAPP(c_member(U_1369),U_1370),c_Set_Oinsert(U_1369,U_1372,U_1371))) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_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_232_2,plain,
! [U_1377,U_1376,U_1375,U_1374,U_1373] : c_Relation_ODomain(U_1373,U_1374,c_Set_Oinsert(tc_prod(U_1373,U_1374),hAPP(hAPP(c_Product__Type_OPair(U_1373,U_1374),U_1375),U_1376),U_1377)) = c_Set_Oinsert(U_1373,U_1375,c_Relation_ODomain(U_1373,U_1374,U_1377)),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
c_Relation_ODomain(U_1373,U_1374,c_Set_Oinsert(tc_prod(U_1373,U_1374),hAPP(hAPP(c_Product__Type_OPair(U_1373,U_1374),U_1375),U_1376),U_1377)) = c_Set_Oinsert(U_1373,U_1375,c_Relation_ODomain(U_1373,U_1374,U_1377)),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_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_233_2,plain,
! [U_1382,U_1381,U_1380,U_1379,U_1378] : c_Relation_ORange(U_1378,U_1379,c_Set_Oinsert(tc_prod(U_1378,U_1379),hAPP(hAPP(c_Product__Type_OPair(U_1378,U_1379),U_1380),U_1381),U_1382)) = c_Set_Oinsert(U_1379,U_1381,c_Relation_ORange(U_1378,U_1379,U_1382)),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
c_Relation_ORange(U_1378,U_1379,c_Set_Oinsert(tc_prod(U_1378,U_1379),hAPP(hAPP(c_Product__Type_OPair(U_1378,U_1379),U_1380),U_1381),U_1382)) = c_Set_Oinsert(U_1379,U_1381,c_Relation_ORange(U_1378,U_1379,U_1382)),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_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_234_2,plain,
! [U_1386,U_1385,U_1384,U_1383] :
( ( hBOOL(hAPP(c_Set_Oinsert(U_1383,U_1384,U_1385),U_1386))
| ( ~ hBOOL(hAPP(U_1385,U_1386))
& U_1384 != U_1386 ) )
& ( hBOOL(hAPP(U_1385,U_1386))
| U_1384 = U_1386
| ~ hBOOL(hAPP(c_Set_Oinsert(U_1383,U_1384,U_1385),U_1386)) ) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
( ! [U_1394,U_1392,U_1390] :
( ! [U_1388] : hBOOL(hAPP(c_Set_Oinsert(U_1388,U_1390,U_1392),U_1394))
| ( ~ hBOOL(hAPP(U_1392,U_1394))
& U_1390 != U_1394 ) )
& ! [U_1393,U_1391,U_1389] :
( ! [U_1387] : ~ hBOOL(hAPP(c_Set_Oinsert(U_1387,U_1389,U_1391),U_1393))
| hBOOL(hAPP(U_1391,U_1393))
| U_1389 = U_1393 ) ),
inference(miniscope,[status(thm)],[f_234_2]) ).
cnf(f_234_4,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(U_1387,U_1389,U_1391),U_1393))
| hBOOL(hAPP(U_1391,U_1393))
| U_1389 = U_1393 ),
inference(clausify,[status(thm)],[f_234_3]) ).
cnf(f_234_5,plain,
( U_1390 != U_1394
| hBOOL(hAPP(c_Set_Oinsert(U_1388,U_1390,U_1392),U_1394)) ),
inference(clausify,[status(thm)],[f_234_3]) ).
cnf(f_234_6,plain,
( ~ hBOOL(hAPP(U_1392,U_1394))
| hBOOL(hAPP(c_Set_Oinsert(U_1388,U_1390,U_1392),U_1394)) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_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_235_2,plain,
! [U_1398,U_1397,U_1396,U_1395] : c_Set_Oinsert(U_1395,U_1396,c_Set_Oinsert(U_1395,U_1397,U_1398)) = c_Set_Oinsert(U_1395,U_1397,c_Set_Oinsert(U_1395,U_1396,U_1398)),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
c_Set_Oinsert(U_1395,U_1396,c_Set_Oinsert(U_1395,U_1397,U_1398)) = c_Set_Oinsert(U_1395,U_1397,c_Set_Oinsert(U_1395,U_1396,U_1398)),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_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_236_2,plain,
! [U_1401,U_1400,U_1399] : c_Set_Oinsert(U_1399,U_1400,c_Set_Oinsert(U_1399,U_1400,U_1401)) = c_Set_Oinsert(U_1399,U_1400,U_1401),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
c_Set_Oinsert(U_1399,U_1400,c_Set_Oinsert(U_1399,U_1400,U_1401)) = c_Set_Oinsert(U_1399,U_1400,U_1401),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_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_237_2,plain,
! [U_1405,U_1404,U_1403,U_1402] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1402,tc_HOL_Obool),c_Set_Oinsert(U_1402,U_1403,U_1404),c_Set_Oinsert(U_1402,U_1403,U_1405)) = c_Set_Oinsert(U_1402,U_1403,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1402,tc_HOL_Obool),U_1404,U_1405)),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1402,tc_HOL_Obool),c_Set_Oinsert(U_1402,U_1403,U_1404),c_Set_Oinsert(U_1402,U_1403,U_1405)) = c_Set_Oinsert(U_1402,U_1403,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1402,tc_HOL_Obool),U_1404,U_1405)),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_1408,U_1407,U_1406] : hBOOL(hAPP(hAPP(c_member(U_1406),U_1407),c_Set_Oinsert(U_1406,U_1407,U_1408))),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
hBOOL(hAPP(hAPP(c_member(U_1406),U_1407),c_Set_Oinsert(U_1406,U_1407,U_1408))),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_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_239_2,plain,
! [U_1412,U_1411,U_1410,U_1409] :
( ( hBOOL(hAPP(hAPP(c_member(U_1409),U_1410),c_Set_Oinsert(U_1409,U_1411,U_1412)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_1409),U_1410),U_1412))
& U_1410 != U_1411 ) )
& ( hBOOL(hAPP(hAPP(c_member(U_1409),U_1410),U_1412))
| U_1410 = U_1411
| ~ hBOOL(hAPP(hAPP(c_member(U_1409),U_1410),c_Set_Oinsert(U_1409,U_1411,U_1412))) ) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
( ! [U_1420,U_1418,U_1416,U_1414] :
( hBOOL(hAPP(hAPP(c_member(U_1414),U_1416),c_Set_Oinsert(U_1414,U_1418,U_1420)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_1414),U_1416),U_1420))
& U_1416 != U_1418 ) )
& ! [U_1419,U_1417,U_1415,U_1413] :
( hBOOL(hAPP(hAPP(c_member(U_1413),U_1415),U_1419))
| U_1415 = U_1417
| ~ hBOOL(hAPP(hAPP(c_member(U_1413),U_1415),c_Set_Oinsert(U_1413,U_1417,U_1419))) ) ),
inference(miniscope,[status(thm)],[f_239_2]) ).
cnf(f_239_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1413),U_1415),U_1419))
| U_1415 = U_1417
| ~ hBOOL(hAPP(hAPP(c_member(U_1413),U_1415),c_Set_Oinsert(U_1413,U_1417,U_1419))) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_5,plain,
( U_1416 != U_1418
| hBOOL(hAPP(hAPP(c_member(U_1414),U_1416),c_Set_Oinsert(U_1414,U_1418,U_1420))) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1414),U_1416),U_1420))
| hBOOL(hAPP(hAPP(c_member(U_1414),U_1416),c_Set_Oinsert(U_1414,U_1418,U_1420))) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_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_240_2,plain,
! [U_1424,U_1423,U_1422,U_1421] :
( ( ( c_Set_Oinsert(U_1421,U_1422,U_1423) = c_Set_Oinsert(U_1421,U_1422,U_1424)
| U_1423 != U_1424 )
& ( U_1423 = U_1424
| c_Set_Oinsert(U_1421,U_1422,U_1423) != c_Set_Oinsert(U_1421,U_1422,U_1424) ) )
| hBOOL(hAPP(hAPP(c_member(U_1421),U_1422),U_1424))
| hBOOL(hAPP(hAPP(c_member(U_1421),U_1422),U_1423)) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( U_1423 = U_1424
| c_Set_Oinsert(U_1421,U_1422,U_1423) != c_Set_Oinsert(U_1421,U_1422,U_1424)
| hBOOL(hAPP(hAPP(c_member(U_1421),U_1422),U_1424))
| hBOOL(hAPP(hAPP(c_member(U_1421),U_1422),U_1423)) ),
inference(clausify,[status(thm)],[f_240_2]) ).
cnf(f_240_4,plain,
( c_Set_Oinsert(U_1421,U_1422,U_1423) = c_Set_Oinsert(U_1421,U_1422,U_1424)
| U_1423 != U_1424
| hBOOL(hAPP(hAPP(c_member(U_1421),U_1422),U_1424))
| hBOOL(hAPP(hAPP(c_member(U_1421),U_1422),U_1423)) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_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_241_2,plain,
! [U_1428,U_1427,U_1426,U_1425] :
( hBOOL(hAPP(hAPP(c_member(U_1425),U_1426),c_Set_Oinsert(U_1425,U_1428,U_1427)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1425),U_1426),U_1427)) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_1425),U_1426),c_Set_Oinsert(U_1425,U_1428,U_1427)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1425),U_1426),U_1427)) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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_242_2,plain,
! [U_1431,U_1430,U_1429] :
( c_Set_Oinsert(U_1429,U_1430,U_1431) = U_1431
| ~ hBOOL(hAPP(hAPP(c_member(U_1429),U_1430),U_1431)) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( c_Set_Oinsert(U_1429,U_1430,U_1431) = U_1431
| ~ hBOOL(hAPP(hAPP(c_member(U_1429),U_1430),U_1431)) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_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_243_2,plain,
! [U_1435,U_1434,U_1433,U_1432] :
( ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1432,tc_HOL_Obool),U_1434,c_Set_Oinsert(U_1432,U_1433,U_1435)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1432,tc_HOL_Obool),U_1434,U_1435)
| hBOOL(hAPP(hAPP(c_member(U_1432),U_1433),U_1434)) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1432,tc_HOL_Obool),U_1434,c_Set_Oinsert(U_1432,U_1433,U_1435)) = c_Set_Oinsert(U_1432,U_1433,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1432,tc_HOL_Obool),U_1434,U_1435))
| ~ hBOOL(hAPP(hAPP(c_member(U_1432),U_1433),U_1434)) ) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
( ! [U_1443,U_1441,U_1439,U_1437] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1437,tc_HOL_Obool),U_1441,c_Set_Oinsert(U_1437,U_1439,U_1443)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1437,tc_HOL_Obool),U_1441,U_1443)
| hBOOL(hAPP(hAPP(c_member(U_1437),U_1439),U_1441)) )
& ! [U_1442,U_1440,U_1438,U_1436] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1436,tc_HOL_Obool),U_1440,c_Set_Oinsert(U_1436,U_1438,U_1442)) = c_Set_Oinsert(U_1436,U_1438,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1436,tc_HOL_Obool),U_1440,U_1442))
| ~ hBOOL(hAPP(hAPP(c_member(U_1436),U_1438),U_1440)) ) ),
inference(miniscope,[status(thm)],[f_243_2]) ).
cnf(f_243_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1436,tc_HOL_Obool),U_1440,c_Set_Oinsert(U_1436,U_1438,U_1442)) = c_Set_Oinsert(U_1436,U_1438,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1436,tc_HOL_Obool),U_1440,U_1442))
| ~ hBOOL(hAPP(hAPP(c_member(U_1436),U_1438),U_1440)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1437,tc_HOL_Obool),U_1441,c_Set_Oinsert(U_1437,U_1439,U_1443)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1437,tc_HOL_Obool),U_1441,U_1443)
| hBOOL(hAPP(hAPP(c_member(U_1437),U_1439),U_1441)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_244_2,plain,
! [U_1447,U_1446,U_1445,U_1444] :
( ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1444,tc_HOL_Obool),c_Set_Oinsert(U_1444,U_1445,U_1447),U_1446) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1444,tc_HOL_Obool),U_1447,U_1446)
| hBOOL(hAPP(hAPP(c_member(U_1444),U_1445),U_1446)) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1444,tc_HOL_Obool),c_Set_Oinsert(U_1444,U_1445,U_1447),U_1446) = c_Set_Oinsert(U_1444,U_1445,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1444,tc_HOL_Obool),U_1447,U_1446))
| ~ hBOOL(hAPP(hAPP(c_member(U_1444),U_1445),U_1446)) ) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( ! [U_1455,U_1453,U_1451,U_1449] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1449,tc_HOL_Obool),c_Set_Oinsert(U_1449,U_1451,U_1455),U_1453) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1449,tc_HOL_Obool),U_1455,U_1453)
| hBOOL(hAPP(hAPP(c_member(U_1449),U_1451),U_1453)) )
& ! [U_1454,U_1452,U_1450,U_1448] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1448,tc_HOL_Obool),c_Set_Oinsert(U_1448,U_1450,U_1454),U_1452) = c_Set_Oinsert(U_1448,U_1450,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1448,tc_HOL_Obool),U_1454,U_1452))
| ~ hBOOL(hAPP(hAPP(c_member(U_1448),U_1450),U_1452)) ) ),
inference(miniscope,[status(thm)],[f_244_2]) ).
cnf(f_244_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1448,tc_HOL_Obool),c_Set_Oinsert(U_1448,U_1450,U_1454),U_1452) = c_Set_Oinsert(U_1448,U_1450,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1448,tc_HOL_Obool),U_1454,U_1452))
| ~ hBOOL(hAPP(hAPP(c_member(U_1448),U_1450),U_1452)) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1449,tc_HOL_Obool),c_Set_Oinsert(U_1449,U_1451,U_1455),U_1453) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1449,tc_HOL_Obool),U_1455,U_1453)
| hBOOL(hAPP(hAPP(c_member(U_1449),U_1451),U_1453)) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_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_245_2,plain,
! [U_1459,U_1458,U_1457,U_1456] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1456,tc_HOL_Obool),U_1458,c_Set_Oinsert(U_1456,U_1457,U_1459)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1456,tc_HOL_Obool),U_1458,U_1459)
| hBOOL(hAPP(hAPP(c_member(U_1456),U_1457),U_1458)) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1456,tc_HOL_Obool),U_1458,c_Set_Oinsert(U_1456,U_1457,U_1459)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1456,tc_HOL_Obool),U_1458,U_1459)
| hBOOL(hAPP(hAPP(c_member(U_1456),U_1457),U_1458)) ),
inference(clausify,[status(thm)],[f_245_2]) ).
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_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_246_2,plain,
! [U_1463,U_1462,U_1461,U_1460] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1460,tc_HOL_Obool),c_Set_Oinsert(U_1460,U_1461,U_1463),U_1462) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1460,tc_HOL_Obool),U_1463,U_1462)
| hBOOL(hAPP(hAPP(c_member(U_1460),U_1461),U_1462)) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1460,tc_HOL_Obool),c_Set_Oinsert(U_1460,U_1461,U_1463),U_1462) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1460,tc_HOL_Obool),U_1463,U_1462)
| hBOOL(hAPP(hAPP(c_member(U_1460),U_1461),U_1462)) ),
inference(clausify,[status(thm)],[f_246_2]) ).
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_1467,U_1466,U_1465,U_1464] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1464,tc_HOL_Obool),U_1466,c_Set_Oinsert(U_1464,U_1465,U_1467)) = c_Set_Oinsert(U_1464,U_1465,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1464,tc_HOL_Obool),U_1466,U_1467))
| ~ hBOOL(hAPP(hAPP(c_member(U_1464),U_1465),U_1466)) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1464,tc_HOL_Obool),U_1466,c_Set_Oinsert(U_1464,U_1465,U_1467)) = c_Set_Oinsert(U_1464,U_1465,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1464,tc_HOL_Obool),U_1466,U_1467))
| ~ hBOOL(hAPP(hAPP(c_member(U_1464),U_1465),U_1466)) ),
inference(clausify,[status(thm)],[f_247_2]) ).
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_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_248_2,plain,
! [U_1471,U_1470,U_1469,U_1468] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1468,tc_HOL_Obool),c_Set_Oinsert(U_1468,U_1469,U_1471),U_1470) = c_Set_Oinsert(U_1468,U_1469,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1468,tc_HOL_Obool),U_1471,U_1470))
| ~ hBOOL(hAPP(hAPP(c_member(U_1468),U_1469),U_1470)) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1468,tc_HOL_Obool),c_Set_Oinsert(U_1468,U_1469,U_1471),U_1470) = c_Set_Oinsert(U_1468,U_1469,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1468,tc_HOL_Obool),U_1471,U_1470))
| ~ hBOOL(hAPP(hAPP(c_member(U_1468),U_1469),U_1470)) ),
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_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_249_2,plain,
! [U_1477,U_1476,U_1475,U_1474,U_1473,U_1472] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1472,U_1475)),c_Fun_Ofun__upd(U_1472,U_1475,U_1476,U_1473,c_HOL_Oundefined(U_1475))),c_FuncSet_Oextensional__funcset(U_1472,U_1475,U_1474,U_1477)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1472,U_1475)),U_1476),c_FuncSet_Oextensional__funcset(U_1472,U_1475,c_Set_Oinsert(U_1472,U_1473,U_1474),U_1477)))
| hBOOL(hAPP(hAPP(c_member(U_1472),U_1473),U_1474)) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1472,U_1475)),c_Fun_Ofun__upd(U_1472,U_1475,U_1476,U_1473,c_HOL_Oundefined(U_1475))),c_FuncSet_Oextensional__funcset(U_1472,U_1475,U_1474,U_1477)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1472,U_1475)),U_1476),c_FuncSet_Oextensional__funcset(U_1472,U_1475,c_Set_Oinsert(U_1472,U_1473,U_1474),U_1477)))
| hBOOL(hAPP(hAPP(c_member(U_1472),U_1473),U_1474)) ),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_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_250_2,plain,
! [U_1484,U_1483,U_1482,U_1481,U_1480,U_1479,U_1478] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1481,U_1478)),c_Fun_Ofun__upd(U_1481,U_1478,U_1482,U_1484,U_1479)),c_FuncSet_Oextensional__funcset(U_1481,U_1478,c_Set_Oinsert(U_1481,U_1484,U_1483),U_1480)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1481,U_1478)),U_1482),c_FuncSet_Oextensional__funcset(U_1481,U_1478,U_1483,U_1480)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1478),U_1479),U_1480)) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1481,U_1478)),c_Fun_Ofun__upd(U_1481,U_1478,U_1482,U_1484,U_1479)),c_FuncSet_Oextensional__funcset(U_1481,U_1478,c_Set_Oinsert(U_1481,U_1484,U_1483),U_1480)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1481,U_1478)),U_1482),c_FuncSet_Oextensional__funcset(U_1481,U_1478,U_1483,U_1480)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1478),U_1479),U_1480)) ),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_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_251_2,plain,
! [U_1488,U_1487,U_1486,U_1485] :
( ( c_Wellfounded_Owf(U_1485,c_Set_Oinsert(tc_prod(U_1485,U_1485),hAPP(hAPP(c_Product__Type_OPair(U_1485,U_1485),U_1486),U_1487),U_1488))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1485,U_1485)),hAPP(hAPP(c_Product__Type_OPair(U_1485,U_1485),U_1487),U_1486)),c_Transitive__Closure_Ortrancl(U_1485,U_1488)))
| ~ c_Wellfounded_Owf(U_1485,U_1488) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1485,U_1485)),hAPP(hAPP(c_Product__Type_OPair(U_1485,U_1485),U_1487),U_1486)),c_Transitive__Closure_Ortrancl(U_1485,U_1488)))
& c_Wellfounded_Owf(U_1485,U_1488) )
| ~ c_Wellfounded_Owf(U_1485,c_Set_Oinsert(tc_prod(U_1485,U_1485),hAPP(hAPP(c_Product__Type_OPair(U_1485,U_1485),U_1486),U_1487),U_1488)) ) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_1496,U_1494,U_1492,U_1490] :
( c_Wellfounded_Owf(U_1490,c_Set_Oinsert(tc_prod(U_1490,U_1490),hAPP(hAPP(c_Product__Type_OPair(U_1490,U_1490),U_1492),U_1494),U_1496))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1490,U_1490)),hAPP(hAPP(c_Product__Type_OPair(U_1490,U_1490),U_1494),U_1492)),c_Transitive__Closure_Ortrancl(U_1490,U_1496)))
| ~ c_Wellfounded_Owf(U_1490,U_1496) )
& ! [U_1495,U_1493,U_1491,U_1489] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1489,U_1489)),hAPP(hAPP(c_Product__Type_OPair(U_1489,U_1489),U_1493),U_1491)),c_Transitive__Closure_Ortrancl(U_1489,U_1495)))
& c_Wellfounded_Owf(U_1489,U_1495) )
| ~ c_Wellfounded_Owf(U_1489,c_Set_Oinsert(tc_prod(U_1489,U_1489),hAPP(hAPP(c_Product__Type_OPair(U_1489,U_1489),U_1491),U_1493),U_1495)) ) ),
inference(miniscope,[status(thm)],[f_251_2]) ).
cnf(f_251_4,plain,
( c_Wellfounded_Owf(U_1489,U_1495)
| ~ c_Wellfounded_Owf(U_1489,c_Set_Oinsert(tc_prod(U_1489,U_1489),hAPP(hAPP(c_Product__Type_OPair(U_1489,U_1489),U_1491),U_1493),U_1495)) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1489,U_1489)),hAPP(hAPP(c_Product__Type_OPair(U_1489,U_1489),U_1493),U_1491)),c_Transitive__Closure_Ortrancl(U_1489,U_1495)))
| ~ c_Wellfounded_Owf(U_1489,c_Set_Oinsert(tc_prod(U_1489,U_1489),hAPP(hAPP(c_Product__Type_OPair(U_1489,U_1489),U_1491),U_1493),U_1495)) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_6,plain,
( c_Wellfounded_Owf(U_1490,c_Set_Oinsert(tc_prod(U_1490,U_1490),hAPP(hAPP(c_Product__Type_OPair(U_1490,U_1490),U_1492),U_1494),U_1496))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_1490,U_1490)),hAPP(hAPP(c_Product__Type_OPair(U_1490,U_1490),U_1494),U_1492)),c_Transitive__Closure_Ortrancl(U_1490,U_1496)))
| ~ c_Wellfounded_Owf(U_1490,U_1496) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_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_252_2,plain,
! [U_1500,U_1499,U_1498,U_1497] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1497,hAPP(hAPP(c_COMBC(U_1497,tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_fun(U_1497,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1497,tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_fun(U_1497,tc_HOL_Obool)),U_1497),c_COMBC(U_1497,tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1497,tc_prod(U_1497,U_1497)),tc_fun(U_1497,tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool)),U_1497),hAPP(c_COMBB(tc_prod(U_1497,U_1497),tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool),U_1497),c_member(tc_prod(U_1497,U_1497)))),c_Product__Type_OPair(U_1497,U_1497)))),U_1498)),U_1499),U_1500))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1497,U_1497)),hAPP(hAPP(c_Product__Type_OPair(U_1497,U_1497),U_1499),U_1500)),c_Transitive__Closure_Otrancl(U_1497,U_1498))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1497,U_1497)),hAPP(hAPP(c_Product__Type_OPair(U_1497,U_1497),U_1499),U_1500)),c_Transitive__Closure_Otrancl(U_1497,U_1498)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1497,hAPP(hAPP(c_COMBC(U_1497,tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_fun(U_1497,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1497,tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_fun(U_1497,tc_HOL_Obool)),U_1497),c_COMBC(U_1497,tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1497,tc_prod(U_1497,U_1497)),tc_fun(U_1497,tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool)),U_1497),hAPP(c_COMBB(tc_prod(U_1497,U_1497),tc_fun(tc_fun(tc_prod(U_1497,U_1497),tc_HOL_Obool),tc_HOL_Obool),U_1497),c_member(tc_prod(U_1497,U_1497)))),c_Product__Type_OPair(U_1497,U_1497)))),U_1498)),U_1499),U_1500)) ) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
( ! [U_1508,U_1506,U_1504,U_1502] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1502,hAPP(hAPP(c_COMBC(U_1502,tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_fun(U_1502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1502,tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_fun(U_1502,tc_HOL_Obool)),U_1502),c_COMBC(U_1502,tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1502,tc_prod(U_1502,U_1502)),tc_fun(U_1502,tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool)),U_1502),hAPP(c_COMBB(tc_prod(U_1502,U_1502),tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool),U_1502),c_member(tc_prod(U_1502,U_1502)))),c_Product__Type_OPair(U_1502,U_1502)))),U_1504)),U_1506),U_1508))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1502,U_1502)),hAPP(hAPP(c_Product__Type_OPair(U_1502,U_1502),U_1506),U_1508)),c_Transitive__Closure_Otrancl(U_1502,U_1504))) )
& ! [U_1507,U_1505,U_1503,U_1501] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1501,U_1501)),hAPP(hAPP(c_Product__Type_OPair(U_1501,U_1501),U_1505),U_1507)),c_Transitive__Closure_Otrancl(U_1501,U_1503)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1501,hAPP(hAPP(c_COMBC(U_1501,tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_fun(U_1501,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1501,tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_fun(U_1501,tc_HOL_Obool)),U_1501),c_COMBC(U_1501,tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1501,tc_prod(U_1501,U_1501)),tc_fun(U_1501,tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool)),U_1501),hAPP(c_COMBB(tc_prod(U_1501,U_1501),tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool),U_1501),c_member(tc_prod(U_1501,U_1501)))),c_Product__Type_OPair(U_1501,U_1501)))),U_1503)),U_1505),U_1507)) ) ),
inference(miniscope,[status(thm)],[f_252_2]) ).
cnf(f_252_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1501,U_1501)),hAPP(hAPP(c_Product__Type_OPair(U_1501,U_1501),U_1505),U_1507)),c_Transitive__Closure_Otrancl(U_1501,U_1503)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1501,hAPP(hAPP(c_COMBC(U_1501,tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_fun(U_1501,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1501,tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_fun(U_1501,tc_HOL_Obool)),U_1501),c_COMBC(U_1501,tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1501,tc_prod(U_1501,U_1501)),tc_fun(U_1501,tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool)),U_1501),hAPP(c_COMBB(tc_prod(U_1501,U_1501),tc_fun(tc_fun(tc_prod(U_1501,U_1501),tc_HOL_Obool),tc_HOL_Obool),U_1501),c_member(tc_prod(U_1501,U_1501)))),c_Product__Type_OPair(U_1501,U_1501)))),U_1503)),U_1505),U_1507)) ),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_5,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1502,hAPP(hAPP(c_COMBC(U_1502,tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_fun(U_1502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1502,tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_fun(U_1502,tc_HOL_Obool)),U_1502),c_COMBC(U_1502,tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1502,tc_prod(U_1502,U_1502)),tc_fun(U_1502,tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool)),U_1502),hAPP(c_COMBB(tc_prod(U_1502,U_1502),tc_fun(tc_fun(tc_prod(U_1502,U_1502),tc_HOL_Obool),tc_HOL_Obool),U_1502),c_member(tc_prod(U_1502,U_1502)))),c_Product__Type_OPair(U_1502,U_1502)))),U_1504)),U_1506),U_1508))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1502,U_1502)),hAPP(hAPP(c_Product__Type_OPair(U_1502,U_1502),U_1506),U_1508)),c_Transitive__Closure_Otrancl(U_1502,U_1504))) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_1512,U_1511,U_1510,U_1509] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1512,U_1509),U_1510),U_1511))
| ~ hBOOL(hAPP(hAPP(U_1509,U_1510),U_1511)) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1512,U_1509),U_1510),U_1511))
| ~ hBOOL(hAPP(hAPP(U_1509,U_1510),U_1511)) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_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_254_2,plain,
! [U_1516,U_1515,U_1514,U_1513] :
( c_Wellfounded_Owf(U_1515,hAPP(hAPP(c_Relation_Oinv__image(U_1513,U_1515),U_1514),U_1516))
| ~ c_Wellfounded_Owf(U_1513,U_1514) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
( c_Wellfounded_Owf(U_1515,hAPP(hAPP(c_Relation_Oinv__image(U_1513,U_1515),U_1514),U_1516))
| ~ c_Wellfounded_Owf(U_1513,U_1514) ),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_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_255_2,plain,
! [U_1520,U_1519,U_1518,U_1517] :
( c_Wellfounded_Owf(tc_prod(U_1517,U_1519),c_Wellfounded_Olex__prod(U_1517,U_1519,U_1518,U_1520))
| ~ c_Wellfounded_Owf(U_1519,U_1520)
| ~ c_Wellfounded_Owf(U_1517,U_1518) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( c_Wellfounded_Owf(tc_prod(U_1517,U_1519),c_Wellfounded_Olex__prod(U_1517,U_1519,U_1518,U_1520))
| ~ c_Wellfounded_Owf(U_1519,U_1520)
| ~ c_Wellfounded_Owf(U_1517,U_1518) ),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_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_256_2,plain,
! [U_1523,U_1522,U_1521] :
( c_Wellfounded_Owf(U_1521,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1521,U_1521),tc_HOL_Obool),U_1523,U_1522))
| ~ c_Wellfounded_Owf(U_1521,U_1522) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
( c_Wellfounded_Owf(U_1521,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1521,U_1521),tc_HOL_Obool),U_1523,U_1522))
| ~ c_Wellfounded_Owf(U_1521,U_1522) ),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_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_257_2,plain,
! [U_1526,U_1525,U_1524] :
( c_Wellfounded_Owf(U_1524,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1524,U_1524),tc_HOL_Obool),U_1525,U_1526))
| ~ c_Wellfounded_Owf(U_1524,U_1525) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( c_Wellfounded_Owf(U_1524,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_1524,U_1524),tc_HOL_Obool),U_1525,U_1526))
| ~ c_Wellfounded_Owf(U_1524,U_1525) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_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_258_2,plain,
! [U_1532,U_1531,U_1530,U_1529] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1529,U_1530),U_1531),U_1532))
| ( ! [U_1528] :
( ~ hBOOL(hAPP(hAPP(U_1530,U_1528),U_1532))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1529,U_1530),U_1531),U_1528)) )
& ~ hBOOL(hAPP(hAPP(U_1530,U_1531),U_1532)) ) )
& ( ? [U_1527] :
( hBOOL(hAPP(hAPP(U_1530,U_1527),U_1532))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1529,U_1530),U_1531),U_1527)) )
| hBOOL(hAPP(hAPP(U_1530,U_1531),U_1532))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1529,U_1530),U_1531),U_1532)) ) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_1540,U_1538,U_1536,U_1534] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1534,U_1536),U_1538),U_1540))
| ( ! [U_1528] :
( ~ hBOOL(hAPP(hAPP(U_1536,U_1528),U_1540))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1534,U_1536),U_1538),U_1528)) )
& ~ hBOOL(hAPP(hAPP(U_1536,U_1538),U_1540)) ) )
& ! [U_1539,U_1537,U_1535,U_1533] :
( ? [U_1527] :
( hBOOL(hAPP(hAPP(U_1535,U_1527),U_1539))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1533,U_1535),U_1537),U_1527)) )
| hBOOL(hAPP(hAPP(U_1535,U_1537),U_1539))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1533,U_1535),U_1537),U_1539)) ) ),
inference(miniscope,[status(thm)],[f_258_2]) ).
fof(f_258_4,plain,
( ! [U_1540,U_1538,U_1536,U_1534] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1534,U_1536),U_1538),U_1540))
| ( ! [U_1528] :
( ~ hBOOL(hAPP(hAPP(U_1536,U_1528),U_1540))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1534,U_1536),U_1538),U_1528)) )
& ~ hBOOL(hAPP(hAPP(U_1536,U_1538),U_1540)) ) )
& ! [U_1539,U_1537,U_1535,U_1533] :
( ( hBOOL(hAPP(hAPP(U_1535,sK89(U_1539,U_1537,U_1535,U_1533)),U_1539))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1533,U_1535),U_1537),sK89(U_1539,U_1537,U_1535,U_1533))) )
| hBOOL(hAPP(hAPP(U_1535,U_1537),U_1539))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1533,U_1535),U_1537),U_1539)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_1527,sK89(U_1539,U_1537,U_1535,U_1533))],[f_258_3]) ).
cnf(f_258_5,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1533,U_1535),U_1537),sK89(U_1539,U_1537,U_1535,U_1533)))
| hBOOL(hAPP(hAPP(U_1535,U_1537),U_1539))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1533,U_1535),U_1537),U_1539)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_6,plain,
( hBOOL(hAPP(hAPP(U_1535,sK89(U_1539,U_1537,U_1535,U_1533)),U_1539))
| hBOOL(hAPP(hAPP(U_1535,U_1537),U_1539))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1533,U_1535),U_1537),U_1539)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_7,plain,
( ~ hBOOL(hAPP(hAPP(U_1536,U_1538),U_1540))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1534,U_1536),U_1538),U_1540)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_8,plain,
( ~ hBOOL(hAPP(hAPP(U_1536,U_1528),U_1540))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1534,U_1536),U_1538),U_1528))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1534,U_1536),U_1538),U_1540)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
fof(f_259_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_259_2,plain,
! [U_1546,U_1545,U_1544,U_1543] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1543,U_1544),U_1545),U_1546))
| ( ! [U_1542] :
( ~ hBOOL(hAPP(hAPP(U_1544,U_1542),U_1546))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1543,U_1544),U_1545),U_1542)) )
& ~ hBOOL(hAPP(hAPP(U_1544,U_1545),U_1546)) ) )
& ( ? [U_1541] :
( hBOOL(hAPP(hAPP(U_1544,U_1541),U_1546))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1543,U_1544),U_1545),U_1541)) )
| hBOOL(hAPP(hAPP(U_1544,U_1545),U_1546))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1543,U_1544),U_1545),U_1546)) ) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
( ! [U_1554,U_1552,U_1550,U_1548] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1548,U_1550),U_1552),U_1554))
| ( ! [U_1542] :
( ~ hBOOL(hAPP(hAPP(U_1550,U_1542),U_1554))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1548,U_1550),U_1552),U_1542)) )
& ~ hBOOL(hAPP(hAPP(U_1550,U_1552),U_1554)) ) )
& ! [U_1553,U_1551,U_1549,U_1547] :
( ? [U_1541] :
( hBOOL(hAPP(hAPP(U_1549,U_1541),U_1553))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1547,U_1549),U_1551),U_1541)) )
| hBOOL(hAPP(hAPP(U_1549,U_1551),U_1553))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1547,U_1549),U_1551),U_1553)) ) ),
inference(miniscope,[status(thm)],[f_259_2]) ).
fof(f_259_4,plain,
( ! [U_1554,U_1552,U_1550,U_1548] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1548,U_1550),U_1552),U_1554))
| ( ! [U_1542] :
( ~ hBOOL(hAPP(hAPP(U_1550,U_1542),U_1554))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1548,U_1550),U_1552),U_1542)) )
& ~ hBOOL(hAPP(hAPP(U_1550,U_1552),U_1554)) ) )
& ! [U_1553,U_1551,U_1549,U_1547] :
( ( hBOOL(hAPP(hAPP(U_1549,sK90(U_1553,U_1551,U_1549,U_1547)),U_1553))
& hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1547,U_1549),U_1551),sK90(U_1553,U_1551,U_1549,U_1547))) )
| hBOOL(hAPP(hAPP(U_1549,U_1551),U_1553))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1547,U_1549),U_1551),U_1553)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_1541,sK90(U_1553,U_1551,U_1549,U_1547))],[f_259_3]) ).
cnf(f_259_5,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1547,U_1549),U_1551),sK90(U_1553,U_1551,U_1549,U_1547)))
| hBOOL(hAPP(hAPP(U_1549,U_1551),U_1553))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1547,U_1549),U_1551),U_1553)) ),
inference(clausify,[status(thm)],[f_259_4]) ).
cnf(f_259_6,plain,
( hBOOL(hAPP(hAPP(U_1549,sK90(U_1553,U_1551,U_1549,U_1547)),U_1553))
| hBOOL(hAPP(hAPP(U_1549,U_1551),U_1553))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1547,U_1549),U_1551),U_1553)) ),
inference(clausify,[status(thm)],[f_259_4]) ).
cnf(f_259_7,plain,
( ~ hBOOL(hAPP(hAPP(U_1550,U_1552),U_1554))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1548,U_1550),U_1552),U_1554)) ),
inference(clausify,[status(thm)],[f_259_4]) ).
cnf(f_259_8,plain,
( ~ hBOOL(hAPP(hAPP(U_1550,U_1542),U_1554))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1548,U_1550),U_1552),U_1542))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1548,U_1550),U_1552),U_1554)) ),
inference(clausify,[status(thm)],[f_259_4]) ).
fof(f_260_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_260_2,plain,
! [U_1559,U_1558,U_1557,U_1556,U_1555] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1558,U_1555),U_1556),U_1559))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1558,U_1555),U_1557),U_1559))
| ~ hBOOL(hAPP(hAPP(U_1555,U_1556),U_1557)) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1558,U_1555),U_1556),U_1559))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1558,U_1555),U_1557),U_1559))
| ~ hBOOL(hAPP(hAPP(U_1555,U_1556),U_1557)) ),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_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_261_2,plain,
! [U_1564,U_1563,U_1562,U_1561,U_1560] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1560,U_1561),U_1562),U_1564))
| ~ hBOOL(hAPP(hAPP(U_1561,U_1563),U_1564))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1560,U_1561),U_1562),U_1563)) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1560,U_1561),U_1562),U_1564))
| ~ hBOOL(hAPP(hAPP(U_1561,U_1563),U_1564))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1560,U_1561),U_1562),U_1563)) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_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_262_2,plain,
! [U_1569,U_1568,U_1567,U_1566,U_1565] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1565,U_1566),U_1567),U_1569))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1565,U_1566),U_1568),U_1569))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1565,U_1566),U_1567),U_1568)) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1565,U_1566),U_1567),U_1569))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1565,U_1566),U_1568),U_1569))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1565,U_1566),U_1567),U_1568)) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_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_263_2,plain,
! [U_1571,U_1570] :
( c_Wellfounded_Owf(U_1570,c_Transitive__Closure_Otrancl(U_1570,U_1571))
| ~ c_Wellfounded_Owf(U_1570,U_1571) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( c_Wellfounded_Owf(U_1570,c_Transitive__Closure_Otrancl(U_1570,U_1571))
| ~ c_Wellfounded_Owf(U_1570,U_1571) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_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_264_2,plain,
! [U_1576,U_1575,U_1574,U_1573,U_1572] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1575,U_1572),U_1573),U_1576))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1575,U_1572),U_1574),U_1576))
| ~ hBOOL(hAPP(hAPP(U_1572,U_1573),U_1574)) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1575,U_1572),U_1573),U_1576))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1575,U_1572),U_1574),U_1576))
| ~ hBOOL(hAPP(hAPP(U_1572,U_1573),U_1574)) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_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_265_2,plain,
! [U_1580,U_1579,U_1578,U_1577] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1577,U_1578),U_1579),U_1580))
& U_1579 != U_1580 )
| U_1579 = U_1580
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1577,U_1578),U_1579),U_1580)) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( U_1579 != U_1580
| U_1579 = U_1580
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1577,U_1578),U_1579),U_1580)) ),
inference(clausify,[status(thm)],[f_265_2]) ).
cnf(f_265_4,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1577,U_1578),U_1579),U_1580))
| U_1579 = U_1580
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1577,U_1578),U_1579),U_1580)) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_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_266_2,plain,
! [U_1584,U_1583,U_1582,U_1581] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1581,U_1582),U_1583),U_1584))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1581,U_1582),U_1583),U_1584)) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1581,U_1582),U_1583),U_1584))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1581,U_1582),U_1583),U_1584)) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_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_267_2,plain,
! [U_1589,U_1588,U_1587,U_1586,U_1585] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1585,U_1586),U_1587),U_1589))
| ~ hBOOL(hAPP(hAPP(U_1586,U_1588),U_1589))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1585,U_1586),U_1587),U_1588)) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1585,U_1586),U_1587),U_1589))
| ~ hBOOL(hAPP(hAPP(U_1586,U_1588),U_1589))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1585,U_1586),U_1587),U_1588)) ),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_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_268_2,plain,
! [U_1594,U_1593,U_1592,U_1591,U_1590] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1590,U_1591),U_1592),U_1594))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1590,U_1591),U_1593),U_1594))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1590,U_1591),U_1592),U_1593)) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1590,U_1591),U_1592),U_1594))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1590,U_1591),U_1593),U_1594))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1590,U_1591),U_1592),U_1593)) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_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_269_2,plain,
! [U_1599,U_1598,U_1597,U_1596,U_1595] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1595,U_1596),U_1597),U_1599))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1595,U_1596),U_1598),U_1599))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1595,U_1596),U_1597),U_1598)) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1595,U_1596),U_1597),U_1599))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(U_1595,U_1596),U_1598),U_1599))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(U_1595,U_1596),U_1597),U_1598)) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_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_270_2,plain,
! [U_1601,U_1600] :
( c_Wellfounded_Oacyclic(U_1600,U_1601)
| ~ c_Wellfounded_Owf(U_1600,U_1601) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
( c_Wellfounded_Oacyclic(U_1600,U_1601)
| ~ c_Wellfounded_Owf(U_1600,U_1601) ),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_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_271_2,plain,
! [U_1604,U_1603,U_1602] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1602,U_1602)),hAPP(hAPP(c_Product__Type_OPair(U_1602,U_1602),U_1604),U_1604)),U_1603))
| ~ c_Wellfounded_Owf(U_1602,U_1603) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1602,U_1602)),hAPP(hAPP(c_Product__Type_OPair(U_1602,U_1602),U_1604),U_1604)),U_1603))
| ~ c_Wellfounded_Owf(U_1602,U_1603) ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_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_272_2,plain,
! [U_1608,U_1607,U_1606,U_1605] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1605,U_1605)),hAPP(hAPP(c_Product__Type_OPair(U_1605,U_1605),U_1608),U_1607)),U_1606))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1605,U_1605)),hAPP(hAPP(c_Product__Type_OPair(U_1605,U_1605),U_1607),U_1608)),U_1606))
| ~ c_Wellfounded_Owf(U_1605,U_1606) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1605,U_1605)),hAPP(hAPP(c_Product__Type_OPair(U_1605,U_1605),U_1608),U_1607)),U_1606))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1605,U_1605)),hAPP(hAPP(c_Product__Type_OPair(U_1605,U_1605),U_1607),U_1608)),U_1606))
| ~ c_Wellfounded_Owf(U_1605,U_1606) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_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_273_2,plain,
! [U_1612,U_1611,U_1610,U_1609] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1612),U_1611)),U_1610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1611),U_1612)),U_1610))
| ~ c_Wellfounded_Owf(U_1609,U_1610) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1612),U_1611)),U_1610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1609,U_1609)),hAPP(hAPP(c_Product__Type_OPair(U_1609,U_1609),U_1611),U_1612)),U_1610))
| ~ c_Wellfounded_Owf(U_1609,U_1610) ),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_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_274_2,plain,
! [U_1615,U_1614,U_1613] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1613,U_1613)),hAPP(hAPP(c_Product__Type_OPair(U_1613,U_1613),U_1615),U_1615)),U_1614))
| ~ c_Wellfounded_Owf(U_1613,U_1614) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1613,U_1613)),hAPP(hAPP(c_Product__Type_OPair(U_1613,U_1613),U_1615),U_1615)),U_1614))
| ~ c_Wellfounded_Owf(U_1613,U_1614) ),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_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_275_2,plain,
! [U_1619,U_1618] :
( ( c_Wellfounded_Owf(U_1618,U_1619)
| ? [U_1617] : ~ hBOOL(hAPP(hAPP(c_member(U_1618),U_1617),c_Wellfounded_Oacc(U_1618,U_1619))) )
& ( ! [U_1616] : hBOOL(hAPP(hAPP(c_member(U_1618),U_1616),c_Wellfounded_Oacc(U_1618,U_1619)))
| ~ c_Wellfounded_Owf(U_1618,U_1619) ) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_1623,U_1621] :
( c_Wellfounded_Owf(U_1621,U_1623)
| ? [U_1617] : ~ hBOOL(hAPP(hAPP(c_member(U_1621),U_1617),c_Wellfounded_Oacc(U_1621,U_1623))) )
& ! [U_1622,U_1620] :
( ! [U_1616] : hBOOL(hAPP(hAPP(c_member(U_1620),U_1616),c_Wellfounded_Oacc(U_1620,U_1622)))
| ~ c_Wellfounded_Owf(U_1620,U_1622) ) ),
inference(miniscope,[status(thm)],[f_275_2]) ).
fof(f_275_4,plain,
( ! [U_1623,U_1621] :
( c_Wellfounded_Owf(U_1621,U_1623)
| ~ hBOOL(hAPP(hAPP(c_member(U_1621),sK91(U_1623,U_1621)),c_Wellfounded_Oacc(U_1621,U_1623))) )
& ! [U_1622,U_1620] :
( ! [U_1616] : hBOOL(hAPP(hAPP(c_member(U_1620),U_1616),c_Wellfounded_Oacc(U_1620,U_1622)))
| ~ c_Wellfounded_Owf(U_1620,U_1622) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_1617,sK91(U_1623,U_1621))],[f_275_3]) ).
cnf(f_275_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_1620),U_1616),c_Wellfounded_Oacc(U_1620,U_1622)))
| ~ c_Wellfounded_Owf(U_1620,U_1622) ),
inference(clausify,[status(thm)],[f_275_4]) ).
cnf(f_275_6,plain,
( c_Wellfounded_Owf(U_1621,U_1623)
| ~ hBOOL(hAPP(hAPP(c_member(U_1621),sK91(U_1623,U_1621)),c_Wellfounded_Oacc(U_1621,U_1623))) ),
inference(clausify,[status(thm)],[f_275_4]) ).
fof(f_276_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_276_2,plain,
! [U_1626,U_1625,U_1624] :
( hBOOL(hAPP(hAPP(c_member(U_1624),U_1626),c_Wellfounded_Oacc(U_1624,U_1625)))
| ~ c_Wellfounded_Owf(U_1624,U_1625) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_1624),U_1626),c_Wellfounded_Oacc(U_1624,U_1625)))
| ~ c_Wellfounded_Owf(U_1624,U_1625) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_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_277_2,plain,
! [U_1630,U_1629,U_1628,U_1627] : c_Fun_Ofun__upd(U_1627,U_1628,U_1629,U_1630,hAPP(U_1629,U_1630)) = U_1629,
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
c_Fun_Ofun__upd(U_1627,U_1628,U_1629,U_1630,hAPP(U_1629,U_1630)) = U_1629,
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_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_278_2,plain,
! [U_1632,U_1631] : c_Wellfounded_Owf(U_1631,hAPP(c_Wellfounded_Omeasure(U_1631),U_1632)),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
c_Wellfounded_Owf(U_1631,hAPP(c_Wellfounded_Omeasure(U_1631),U_1632)),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_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_279_2,plain,
! [U_1637,U_1636,U_1635,U_1634,U_1633] :
( ( c_Nitpick_Owfrec_H(U_1633,U_1635,U_1634,U_1636,U_1637) = c_HOL_OThe(U_1635,c_Recdef_Owfrec__rel(U_1633,U_1635,U_1634,hAPP(hAPP(c_COMBC(tc_fun(U_1633,U_1635),tc_fun(U_1633,U_1633),tc_fun(U_1633,U_1635)),hAPP(hAPP(c_COMBB(tc_fun(U_1633,tc_fun(U_1633,U_1635)),tc_fun(tc_fun(U_1633,U_1633),tc_fun(U_1633,U_1635)),tc_fun(U_1633,U_1635)),c_COMBS(U_1633,U_1633,U_1635)),hAPP(hAPP(c_COMBB(tc_fun(U_1633,tc_fun(U_1633,U_1635)),tc_fun(U_1633,tc_fun(U_1633,U_1635)),tc_fun(U_1633,U_1635)),hAPP(c_COMBB(tc_fun(U_1633,U_1635),tc_fun(U_1633,U_1635),U_1633),U_1636)),hAPP(hAPP(c_COMBC(tc_fun(U_1633,U_1635),tc_fun(tc_prod(U_1633,U_1633),tc_HOL_Obool),tc_fun(U_1633,tc_fun(U_1633,U_1635))),c_Recdef_Ocut(U_1633,U_1635)),U_1634)))),c_COMBI(U_1633)),U_1637))
| c_Wellfounded_Owf(U_1633,U_1634) )
& ( c_Nitpick_Owfrec_H(U_1633,U_1635,U_1634,U_1636,U_1637) = c_Nitpick_Owf__wfrec_H(U_1633,U_1635,U_1634,U_1636,U_1637)
| ~ c_Wellfounded_Owf(U_1633,U_1634) ) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
( ! [U_1647,U_1645,U_1643,U_1641,U_1639] :
( c_Nitpick_Owfrec_H(U_1639,U_1643,U_1641,U_1645,U_1647) = c_HOL_OThe(U_1643,c_Recdef_Owfrec__rel(U_1639,U_1643,U_1641,hAPP(hAPP(c_COMBC(tc_fun(U_1639,U_1643),tc_fun(U_1639,U_1639),tc_fun(U_1639,U_1643)),hAPP(hAPP(c_COMBB(tc_fun(U_1639,tc_fun(U_1639,U_1643)),tc_fun(tc_fun(U_1639,U_1639),tc_fun(U_1639,U_1643)),tc_fun(U_1639,U_1643)),c_COMBS(U_1639,U_1639,U_1643)),hAPP(hAPP(c_COMBB(tc_fun(U_1639,tc_fun(U_1639,U_1643)),tc_fun(U_1639,tc_fun(U_1639,U_1643)),tc_fun(U_1639,U_1643)),hAPP(c_COMBB(tc_fun(U_1639,U_1643),tc_fun(U_1639,U_1643),U_1639),U_1645)),hAPP(hAPP(c_COMBC(tc_fun(U_1639,U_1643),tc_fun(tc_prod(U_1639,U_1639),tc_HOL_Obool),tc_fun(U_1639,tc_fun(U_1639,U_1643))),c_Recdef_Ocut(U_1639,U_1643)),U_1641)))),c_COMBI(U_1639)),U_1647))
| c_Wellfounded_Owf(U_1639,U_1641) )
& ! [U_1646,U_1644,U_1642,U_1640,U_1638] :
( c_Nitpick_Owfrec_H(U_1638,U_1642,U_1640,U_1644,U_1646) = c_Nitpick_Owf__wfrec_H(U_1638,U_1642,U_1640,U_1644,U_1646)
| ~ c_Wellfounded_Owf(U_1638,U_1640) ) ),
inference(miniscope,[status(thm)],[f_279_2]) ).
cnf(f_279_4,plain,
( c_Nitpick_Owfrec_H(U_1638,U_1642,U_1640,U_1644,U_1646) = c_Nitpick_Owf__wfrec_H(U_1638,U_1642,U_1640,U_1644,U_1646)
| ~ c_Wellfounded_Owf(U_1638,U_1640) ),
inference(clausify,[status(thm)],[f_279_3]) ).
cnf(f_279_5,plain,
( c_Nitpick_Owfrec_H(U_1639,U_1643,U_1641,U_1645,U_1647) = c_HOL_OThe(U_1643,c_Recdef_Owfrec__rel(U_1639,U_1643,U_1641,hAPP(hAPP(c_COMBC(tc_fun(U_1639,U_1643),tc_fun(U_1639,U_1639),tc_fun(U_1639,U_1643)),hAPP(hAPP(c_COMBB(tc_fun(U_1639,tc_fun(U_1639,U_1643)),tc_fun(tc_fun(U_1639,U_1639),tc_fun(U_1639,U_1643)),tc_fun(U_1639,U_1643)),c_COMBS(U_1639,U_1639,U_1643)),hAPP(hAPP(c_COMBB(tc_fun(U_1639,tc_fun(U_1639,U_1643)),tc_fun(U_1639,tc_fun(U_1639,U_1643)),tc_fun(U_1639,U_1643)),hAPP(c_COMBB(tc_fun(U_1639,U_1643),tc_fun(U_1639,U_1643),U_1639),U_1645)),hAPP(hAPP(c_COMBC(tc_fun(U_1639,U_1643),tc_fun(tc_prod(U_1639,U_1639),tc_HOL_Obool),tc_fun(U_1639,tc_fun(U_1639,U_1643))),c_Recdef_Ocut(U_1639,U_1643)),U_1641)))),c_COMBI(U_1639)),U_1647))
| c_Wellfounded_Owf(U_1639,U_1641) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_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_280_2,plain,
! [U_1653,U_1652,U_1651,U_1650,U_1649,U_1648] :
( hAPP(U_1648,U_1653) = hAPP(hAPP(U_1652,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1649,U_1650),U_1648),U_1651),U_1653)),U_1653)
| ~ c_Wellfounded_Owf(U_1649,U_1651)
| U_1648 != c_Recdef_Owfrec(U_1649,U_1650,U_1651,U_1652) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( hAPP(U_1648,U_1653) = hAPP(hAPP(U_1652,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1649,U_1650),U_1648),U_1651),U_1653)),U_1653)
| ~ c_Wellfounded_Owf(U_1649,U_1651)
| U_1648 != c_Recdef_Owfrec(U_1649,U_1650,U_1651,U_1652) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_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_281_2,plain,
! [U_1658,U_1657,U_1656,U_1655,U_1654] : hAPP(c_Recdef_Owfrec(U_1654,U_1655,U_1656,U_1657),U_1658) = c_HOL_OThe(U_1655,c_Recdef_Owfrec__rel(U_1654,U_1655,U_1656,hAPP(hAPP(c_COMBC(tc_fun(U_1654,U_1655),tc_fun(U_1654,U_1654),tc_fun(U_1654,U_1655)),hAPP(hAPP(c_COMBB(tc_fun(U_1654,tc_fun(U_1654,U_1655)),tc_fun(tc_fun(U_1654,U_1654),tc_fun(U_1654,U_1655)),tc_fun(U_1654,U_1655)),c_COMBS(U_1654,U_1654,U_1655)),hAPP(hAPP(c_COMBB(tc_fun(U_1654,tc_fun(U_1654,U_1655)),tc_fun(U_1654,tc_fun(U_1654,U_1655)),tc_fun(U_1654,U_1655)),hAPP(c_COMBB(tc_fun(U_1654,U_1655),tc_fun(U_1654,U_1655),U_1654),U_1657)),hAPP(hAPP(c_COMBC(tc_fun(U_1654,U_1655),tc_fun(tc_prod(U_1654,U_1654),tc_HOL_Obool),tc_fun(U_1654,tc_fun(U_1654,U_1655))),c_Recdef_Ocut(U_1654,U_1655)),U_1656)))),c_COMBI(U_1654)),U_1658)),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
hAPP(c_Recdef_Owfrec(U_1654,U_1655,U_1656,U_1657),U_1658) = c_HOL_OThe(U_1655,c_Recdef_Owfrec__rel(U_1654,U_1655,U_1656,hAPP(hAPP(c_COMBC(tc_fun(U_1654,U_1655),tc_fun(U_1654,U_1654),tc_fun(U_1654,U_1655)),hAPP(hAPP(c_COMBB(tc_fun(U_1654,tc_fun(U_1654,U_1655)),tc_fun(tc_fun(U_1654,U_1654),tc_fun(U_1654,U_1655)),tc_fun(U_1654,U_1655)),c_COMBS(U_1654,U_1654,U_1655)),hAPP(hAPP(c_COMBB(tc_fun(U_1654,tc_fun(U_1654,U_1655)),tc_fun(U_1654,tc_fun(U_1654,U_1655)),tc_fun(U_1654,U_1655)),hAPP(c_COMBB(tc_fun(U_1654,U_1655),tc_fun(U_1654,U_1655),U_1654),U_1657)),hAPP(hAPP(c_COMBC(tc_fun(U_1654,U_1655),tc_fun(tc_prod(U_1654,U_1654),tc_HOL_Obool),tc_fun(U_1654,tc_fun(U_1654,U_1655))),c_Recdef_Ocut(U_1654,U_1655)),U_1656)))),c_COMBI(U_1654)),U_1658)),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_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_282_2,plain,
! [U_1663,U_1662,U_1661,U_1660,U_1659] :
( ( c_Fun_Ofun__upd(U_1659,U_1660,U_1661,U_1662,U_1663) = U_1661
| hAPP(U_1661,U_1662) != U_1663 )
& ( hAPP(U_1661,U_1662) = U_1663
| c_Fun_Ofun__upd(U_1659,U_1660,U_1661,U_1662,U_1663) != U_1661 ) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
( ! [U_1673,U_1671,U_1669] :
( ! [U_1667,U_1665] : c_Fun_Ofun__upd(U_1665,U_1667,U_1669,U_1671,U_1673) = U_1669
| hAPP(U_1669,U_1671) != U_1673 )
& ! [U_1672,U_1670,U_1668] :
( ! [U_1666,U_1664] : c_Fun_Ofun__upd(U_1664,U_1666,U_1668,U_1670,U_1672) != U_1668
| hAPP(U_1668,U_1670) = U_1672 ) ),
inference(miniscope,[status(thm)],[f_282_2]) ).
cnf(f_282_4,plain,
( c_Fun_Ofun__upd(U_1664,U_1666,U_1668,U_1670,U_1672) != U_1668
| hAPP(U_1668,U_1670) = U_1672 ),
inference(clausify,[status(thm)],[f_282_3]) ).
cnf(f_282_5,plain,
( c_Fun_Ofun__upd(U_1665,U_1667,U_1669,U_1671,U_1673) = U_1669
| hAPP(U_1669,U_1671) != U_1673 ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_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_283_2,plain,
! [U_1679,U_1678,U_1677,U_1676,U_1675,U_1674] : c_Fun_Ofun__upd(U_1674,U_1675,c_Fun_Ofun__upd(U_1674,U_1675,U_1676,U_1677,U_1678),U_1677,U_1679) = c_Fun_Ofun__upd(U_1674,U_1675,U_1676,U_1677,U_1679),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
c_Fun_Ofun__upd(U_1674,U_1675,c_Fun_Ofun__upd(U_1674,U_1675,U_1676,U_1677,U_1678),U_1677,U_1679) = c_Fun_Ofun__upd(U_1674,U_1675,U_1676,U_1677,U_1679),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_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_284_2,plain,
! [U_1684,U_1683,U_1682,U_1681,U_1680] : hAPP(c_Fun_Ofun__upd(U_1680,U_1681,U_1682,U_1683,U_1684),U_1683) = U_1684,
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
hAPP(c_Fun_Ofun__upd(U_1680,U_1681,U_1682,U_1683,U_1684),U_1683) = U_1684,
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_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_285_2,plain,
! [U_1690,U_1689,U_1688,U_1687,U_1686,U_1685] :
( ( hAPP(c_Fun_Ofun__upd(U_1687,U_1688,U_1689,U_1686,U_1690),U_1685) = hAPP(U_1689,U_1685)
| U_1685 = U_1686 )
& ( hAPP(c_Fun_Ofun__upd(U_1687,U_1688,U_1689,U_1686,U_1690),U_1685) = U_1690
| U_1685 != U_1686 ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_1702,U_1700,U_1698,U_1696,U_1694,U_1692] :
( hAPP(c_Fun_Ofun__upd(U_1696,U_1698,U_1700,U_1694,U_1702),U_1692) = hAPP(U_1700,U_1692)
| U_1692 = U_1694 )
& ! [U_1701,U_1699,U_1697,U_1695,U_1693,U_1691] :
( hAPP(c_Fun_Ofun__upd(U_1695,U_1697,U_1699,U_1693,U_1701),U_1691) = U_1701
| U_1691 != U_1693 ) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
cnf(f_285_4,plain,
( hAPP(c_Fun_Ofun__upd(U_1695,U_1697,U_1699,U_1693,U_1701),U_1691) = U_1701
| U_1691 != U_1693 ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_5,plain,
( hAPP(c_Fun_Ofun__upd(U_1696,U_1698,U_1700,U_1694,U_1702),U_1692) = hAPP(U_1700,U_1692)
| U_1692 = U_1694 ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_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_286_2,plain,
! [U_1709,U_1708,U_1707,U_1706,U_1705,U_1704,U_1703] :
( c_Fun_Ofun__upd(U_1705,U_1706,c_Fun_Ofun__upd(U_1705,U_1706,U_1707,U_1703,U_1708),U_1704,U_1709) = c_Fun_Ofun__upd(U_1705,U_1706,c_Fun_Ofun__upd(U_1705,U_1706,U_1707,U_1704,U_1709),U_1703,U_1708)
| U_1703 = U_1704 ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( c_Fun_Ofun__upd(U_1705,U_1706,c_Fun_Ofun__upd(U_1705,U_1706,U_1707,U_1703,U_1708),U_1704,U_1709) = c_Fun_Ofun__upd(U_1705,U_1706,c_Fun_Ofun__upd(U_1705,U_1706,U_1707,U_1704,U_1709),U_1703,U_1708)
| U_1703 = U_1704 ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_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_287_2,plain,
! [U_1715,U_1714,U_1713,U_1712,U_1711,U_1710] :
( hAPP(c_Fun_Ofun__upd(U_1712,U_1713,U_1714,U_1711,U_1715),U_1710) = hAPP(U_1714,U_1710)
| U_1710 = U_1711 ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( hAPP(c_Fun_Ofun__upd(U_1712,U_1713,U_1714,U_1711,U_1715),U_1710) = hAPP(U_1714,U_1710)
| U_1710 = U_1711 ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_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_288_2,plain,
! [U_1720,U_1719,U_1718,U_1717,U_1716] :
( c_Fun_Ofun__upd(U_1719,U_1720,U_1716,U_1717,U_1718) = U_1716
| hAPP(U_1716,U_1717) != U_1718 ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( c_Fun_Ofun__upd(U_1719,U_1720,U_1716,U_1717,U_1718) = U_1716
| hAPP(U_1716,U_1717) != U_1718 ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_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_289_2,plain,
! [U_1726,U_1725,U_1724,U_1723,U_1722,U_1721] :
( ( hAPP(c_Fun_Ofun__upd(U_1723,U_1724,U_1725,U_1722,U_1726),U_1721) = hAPP(U_1725,U_1721)
| U_1721 = U_1722 )
& ( hAPP(c_Fun_Ofun__upd(U_1723,U_1724,U_1725,U_1722,U_1726),U_1721) = U_1726
| U_1721 != U_1722 ) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
( ! [U_1738,U_1736,U_1734,U_1732,U_1730,U_1728] :
( hAPP(c_Fun_Ofun__upd(U_1732,U_1734,U_1736,U_1730,U_1738),U_1728) = hAPP(U_1736,U_1728)
| U_1728 = U_1730 )
& ! [U_1737,U_1735,U_1733,U_1731,U_1729,U_1727] :
( hAPP(c_Fun_Ofun__upd(U_1731,U_1733,U_1735,U_1729,U_1737),U_1727) = U_1737
| U_1727 != U_1729 ) ),
inference(miniscope,[status(thm)],[f_289_2]) ).
cnf(f_289_4,plain,
( hAPP(c_Fun_Ofun__upd(U_1731,U_1733,U_1735,U_1729,U_1737),U_1727) = U_1737
| U_1727 != U_1729 ),
inference(clausify,[status(thm)],[f_289_3]) ).
cnf(f_289_5,plain,
( hAPP(c_Fun_Ofun__upd(U_1732,U_1734,U_1736,U_1730,U_1738),U_1728) = hAPP(U_1736,U_1728)
| U_1728 = U_1730 ),
inference(clausify,[status(thm)],[f_289_3]) ).
fof(f_290_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_290_2,plain,
! [U_1743,U_1742,U_1741,U_1740] :
( ! [U_1739] : hAPP(c_Recdef_Owfrec(U_1742,U_1743,U_1740,U_1741),U_1739) = hAPP(hAPP(U_1741,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1742,U_1743),c_Recdef_Owfrec(U_1742,U_1743,U_1740,U_1741)),U_1740),U_1739)),U_1739)
| ~ c_Wellfounded_Owf(U_1742,U_1740) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( hAPP(c_Recdef_Owfrec(U_1742,U_1743,U_1740,U_1741),U_1739) = hAPP(hAPP(U_1741,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1742,U_1743),c_Recdef_Owfrec(U_1742,U_1743,U_1740,U_1741)),U_1740),U_1739)),U_1739)
| ~ c_Wellfounded_Owf(U_1742,U_1740) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_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_291_2,plain,
! [U_1748,U_1747,U_1746,U_1745,U_1744] :
( hAPP(c_Recdef_Owfrec(U_1744,U_1746,U_1745,U_1747),U_1748) = hAPP(hAPP(U_1747,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1744,U_1746),c_Recdef_Owfrec(U_1744,U_1746,U_1745,U_1747)),U_1745),U_1748)),U_1748)
| ~ c_Wellfounded_Owf(U_1744,U_1745) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( hAPP(c_Recdef_Owfrec(U_1744,U_1746,U_1745,U_1747),U_1748) = hAPP(hAPP(U_1747,hAPP(hAPP(hAPP(c_Recdef_Ocut(U_1744,U_1746),c_Recdef_Owfrec(U_1744,U_1746,U_1745,U_1747)),U_1745),U_1748)),U_1748)
| ~ c_Wellfounded_Owf(U_1744,U_1745) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_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_292_2,plain,
! [U_1753,U_1752,U_1751,U_1750] :
( c_Wellfounded_Owf(tc_prod(U_1753,U_1751),c_Recdef_Osame__fst(U_1753,U_1751,U_1750,U_1752))
| ? [U_1749] :
( ~ c_Wellfounded_Owf(U_1751,hAPP(U_1752,U_1749))
& hBOOL(hAPP(U_1750,U_1749)) ) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1753,U_1752,U_1751,U_1750] :
( c_Wellfounded_Owf(tc_prod(U_1753,U_1751),c_Recdef_Osame__fst(U_1753,U_1751,U_1750,U_1752))
| ( ~ c_Wellfounded_Owf(U_1751,hAPP(U_1752,sK92(U_1753,U_1752,U_1751,U_1750)))
& hBOOL(hAPP(U_1750,sK92(U_1753,U_1752,U_1751,U_1750))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_1749,sK92(U_1753,U_1752,U_1751,U_1750))],[f_292_2]) ).
cnf(f_292_4,plain,
( hBOOL(hAPP(U_1750,sK92(U_1753,U_1752,U_1751,U_1750)))
| c_Wellfounded_Owf(tc_prod(U_1753,U_1751),c_Recdef_Osame__fst(U_1753,U_1751,U_1750,U_1752)) ),
inference(clausify,[status(thm)],[f_292_3]) ).
cnf(f_292_5,plain,
( ~ c_Wellfounded_Owf(U_1751,hAPP(U_1752,sK92(U_1753,U_1752,U_1751,U_1750)))
| c_Wellfounded_Owf(tc_prod(U_1753,U_1751),c_Recdef_Osame__fst(U_1753,U_1751,U_1750,U_1752)) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_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_293_2,plain,
! [U_1755,U_1754] : c_HOL_OThe(U_1754,hAPP(c_fequal,U_1755)) = U_1755,
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
c_HOL_OThe(U_1754,hAPP(c_fequal,U_1755)) = U_1755,
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_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_294_2,plain,
! [U_1757,U_1756] : c_HOL_OThe(U_1756,hAPP(hAPP(c_COMBC(U_1756,U_1756,tc_HOL_Obool),c_fequal),U_1757)) = U_1757,
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
c_HOL_OThe(U_1756,hAPP(hAPP(c_COMBC(U_1756,U_1756,tc_HOL_Obool),c_fequal),U_1757)) = U_1757,
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_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_295_2,plain,
! [U_1764,U_1763,U_1762,U_1761,U_1760] :
( ? [U_1759] :
( ! [U_1758] :
( U_1758 = U_1759
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1760,U_1761,U_1762,U_1763,U_1764),U_1758)) )
& hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1760,U_1761,U_1762,U_1763,U_1764),U_1759)) )
| ~ c_Wellfounded_Owf(U_1760,U_1762)
| ~ c_Recdef_Oadm__wf(U_1760,U_1761,U_1762,U_1763) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1764,U_1763,U_1762,U_1761,U_1760] :
( ( ! [U_1758] :
( U_1758 = sK93(U_1764,U_1763,U_1762,U_1761,U_1760)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1760,U_1761,U_1762,U_1763,U_1764),U_1758)) )
& hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1760,U_1761,U_1762,U_1763,U_1764),sK93(U_1764,U_1763,U_1762,U_1761,U_1760))) )
| ~ c_Wellfounded_Owf(U_1760,U_1762)
| ~ c_Recdef_Oadm__wf(U_1760,U_1761,U_1762,U_1763) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_1759,sK93(U_1764,U_1763,U_1762,U_1761,U_1760))],[f_295_2]) ).
cnf(f_295_4,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1760,U_1761,U_1762,U_1763,U_1764),sK93(U_1764,U_1763,U_1762,U_1761,U_1760)))
| ~ c_Wellfounded_Owf(U_1760,U_1762)
| ~ c_Recdef_Oadm__wf(U_1760,U_1761,U_1762,U_1763) ),
inference(clausify,[status(thm)],[f_295_3]) ).
cnf(f_295_5,plain,
( U_1758 = sK93(U_1764,U_1763,U_1762,U_1761,U_1760)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(U_1760,U_1761,U_1762,U_1763,U_1764),U_1758))
| ~ c_Wellfounded_Owf(U_1760,U_1762)
| ~ c_Recdef_Oadm__wf(U_1760,U_1761,U_1762,U_1763) ),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_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_296_2,plain,
! [U_1766,U_1765] :
( ( c_Wellfounded_OwfP(U_1765,hAPP(hAPP(c_COMBC(U_1765,tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_fun(U_1765,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1765,tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_fun(U_1765,tc_HOL_Obool)),U_1765),c_COMBC(U_1765,tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1765,tc_prod(U_1765,U_1765)),tc_fun(U_1765,tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool)),U_1765),hAPP(c_COMBB(tc_prod(U_1765,U_1765),tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool),U_1765),c_member(tc_prod(U_1765,U_1765)))),c_Product__Type_OPair(U_1765,U_1765)))),U_1766))
| ~ c_Wellfounded_Owf(U_1765,U_1766) )
& ( c_Wellfounded_Owf(U_1765,U_1766)
| ~ c_Wellfounded_OwfP(U_1765,hAPP(hAPP(c_COMBC(U_1765,tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_fun(U_1765,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1765,tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_fun(U_1765,tc_HOL_Obool)),U_1765),c_COMBC(U_1765,tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1765,tc_prod(U_1765,U_1765)),tc_fun(U_1765,tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool)),U_1765),hAPP(c_COMBB(tc_prod(U_1765,U_1765),tc_fun(tc_fun(tc_prod(U_1765,U_1765),tc_HOL_Obool),tc_HOL_Obool),U_1765),c_member(tc_prod(U_1765,U_1765)))),c_Product__Type_OPair(U_1765,U_1765)))),U_1766)) ) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
( ! [U_1770,U_1768] :
( c_Wellfounded_OwfP(U_1768,hAPP(hAPP(c_COMBC(U_1768,tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_fun(U_1768,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1768,tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_fun(U_1768,tc_HOL_Obool)),U_1768),c_COMBC(U_1768,tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1768,tc_prod(U_1768,U_1768)),tc_fun(U_1768,tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool)),U_1768),hAPP(c_COMBB(tc_prod(U_1768,U_1768),tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool),U_1768),c_member(tc_prod(U_1768,U_1768)))),c_Product__Type_OPair(U_1768,U_1768)))),U_1770))
| ~ c_Wellfounded_Owf(U_1768,U_1770) )
& ! [U_1769,U_1767] :
( c_Wellfounded_Owf(U_1767,U_1769)
| ~ c_Wellfounded_OwfP(U_1767,hAPP(hAPP(c_COMBC(U_1767,tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_fun(U_1767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1767,tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_fun(U_1767,tc_HOL_Obool)),U_1767),c_COMBC(U_1767,tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1767,tc_prod(U_1767,U_1767)),tc_fun(U_1767,tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool)),U_1767),hAPP(c_COMBB(tc_prod(U_1767,U_1767),tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool),U_1767),c_member(tc_prod(U_1767,U_1767)))),c_Product__Type_OPair(U_1767,U_1767)))),U_1769)) ) ),
inference(miniscope,[status(thm)],[f_296_2]) ).
cnf(f_296_4,plain,
( c_Wellfounded_Owf(U_1767,U_1769)
| ~ c_Wellfounded_OwfP(U_1767,hAPP(hAPP(c_COMBC(U_1767,tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_fun(U_1767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1767,tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_fun(U_1767,tc_HOL_Obool)),U_1767),c_COMBC(U_1767,tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1767,tc_prod(U_1767,U_1767)),tc_fun(U_1767,tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool)),U_1767),hAPP(c_COMBB(tc_prod(U_1767,U_1767),tc_fun(tc_fun(tc_prod(U_1767,U_1767),tc_HOL_Obool),tc_HOL_Obool),U_1767),c_member(tc_prod(U_1767,U_1767)))),c_Product__Type_OPair(U_1767,U_1767)))),U_1769)) ),
inference(clausify,[status(thm)],[f_296_3]) ).
cnf(f_296_5,plain,
( c_Wellfounded_OwfP(U_1768,hAPP(hAPP(c_COMBC(U_1768,tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_fun(U_1768,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1768,tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_fun(U_1768,tc_HOL_Obool)),U_1768),c_COMBC(U_1768,tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_1768,tc_prod(U_1768,U_1768)),tc_fun(U_1768,tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool)),U_1768),hAPP(c_COMBB(tc_prod(U_1768,U_1768),tc_fun(tc_fun(tc_prod(U_1768,U_1768),tc_HOL_Obool),tc_HOL_Obool),U_1768),c_member(tc_prod(U_1768,U_1768)))),c_Product__Type_OPair(U_1768,U_1768)))),U_1770))
| ~ c_Wellfounded_Owf(U_1768,U_1770) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_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_297_2,plain,
! [U_1780,U_1779] :
( ( c_Wellfounded_Owf(U_1779,U_1780)
| ? [U_1778] :
( ! [U_1777] :
( ? [U_1776] :
( hBOOL(hAPP(hAPP(c_member(U_1779),U_1776),U_1778))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1779,U_1779)),hAPP(hAPP(c_Product__Type_OPair(U_1779,U_1779),U_1776),U_1777)),U_1780)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1779),U_1777),U_1778)) )
& ? [U_1775] : hBOOL(hAPP(hAPP(c_member(U_1779),U_1775),U_1778)) ) )
& ( ! [U_1774] :
( ? [U_1773] :
( ! [U_1772] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1779),U_1772),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1779,U_1779)),hAPP(hAPP(c_Product__Type_OPair(U_1779,U_1779),U_1772),U_1773)),U_1780)) )
& hBOOL(hAPP(hAPP(c_member(U_1779),U_1773),U_1774)) )
| ! [U_1771] : ~ hBOOL(hAPP(hAPP(c_member(U_1779),U_1771),U_1774)) )
| ~ c_Wellfounded_Owf(U_1779,U_1780) ) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
( ! [U_1784,U_1782] :
( c_Wellfounded_Owf(U_1782,U_1784)
| ? [U_1778] :
( ! [U_1777] :
( ? [U_1776] :
( hBOOL(hAPP(hAPP(c_member(U_1782),U_1776),U_1778))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1782,U_1782)),hAPP(hAPP(c_Product__Type_OPair(U_1782,U_1782),U_1776),U_1777)),U_1784)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1782),U_1777),U_1778)) )
& ? [U_1775] : hBOOL(hAPP(hAPP(c_member(U_1782),U_1775),U_1778)) ) )
& ! [U_1783,U_1781] :
( ! [U_1774] :
( ? [U_1773] :
( ! [U_1772] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1772),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1781,U_1781)),hAPP(hAPP(c_Product__Type_OPair(U_1781,U_1781),U_1772),U_1773)),U_1783)) )
& hBOOL(hAPP(hAPP(c_member(U_1781),U_1773),U_1774)) )
| ! [U_1771] : ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1771),U_1774)) )
| ~ c_Wellfounded_Owf(U_1781,U_1783) ) ),
inference(miniscope,[status(thm)],[f_297_2]) ).
fof(f_297_4,plain,
( ! [U_1784,U_1782] :
( c_Wellfounded_Owf(U_1782,U_1784)
| ? [U_1778] :
( ! [U_1777] :
( ? [U_1776] :
( hBOOL(hAPP(hAPP(c_member(U_1782),U_1776),U_1778))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1782,U_1782)),hAPP(hAPP(c_Product__Type_OPair(U_1782,U_1782),U_1776),U_1777)),U_1784)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1782),U_1777),U_1778)) )
& ? [U_1775] : hBOOL(hAPP(hAPP(c_member(U_1782),U_1775),U_1778)) ) )
& ! [U_1783,U_1781] :
( ! [U_1774] :
( ( ! [U_1772] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1772),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1781,U_1781)),hAPP(hAPP(c_Product__Type_OPair(U_1781,U_1781),U_1772),sK94(U_1783,U_1781,U_1774))),U_1783)) )
& hBOOL(hAPP(hAPP(c_member(U_1781),sK94(U_1783,U_1781,U_1774)),U_1774)) )
| ! [U_1771] : ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1771),U_1774)) )
| ~ c_Wellfounded_Owf(U_1781,U_1783) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_1773,sK94(U_1783,U_1781,U_1774))],[f_297_3]) ).
fof(f_297_5,plain,
( ! [U_1784,U_1782] :
( c_Wellfounded_Owf(U_1782,U_1784)
| ( ! [U_1777] :
( ? [U_1776] :
( hBOOL(hAPP(hAPP(c_member(U_1782),U_1776),sK95(U_1784,U_1782)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1782,U_1782)),hAPP(hAPP(c_Product__Type_OPair(U_1782,U_1782),U_1776),U_1777)),U_1784)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1782),U_1777),sK95(U_1784,U_1782))) )
& ? [U_1775] : hBOOL(hAPP(hAPP(c_member(U_1782),U_1775),sK95(U_1784,U_1782))) ) )
& ! [U_1783,U_1781] :
( ! [U_1774] :
( ( ! [U_1772] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1772),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1781,U_1781)),hAPP(hAPP(c_Product__Type_OPair(U_1781,U_1781),U_1772),sK94(U_1783,U_1781,U_1774))),U_1783)) )
& hBOOL(hAPP(hAPP(c_member(U_1781),sK94(U_1783,U_1781,U_1774)),U_1774)) )
| ! [U_1771] : ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1771),U_1774)) )
| ~ c_Wellfounded_Owf(U_1781,U_1783) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_1778,sK95(U_1784,U_1782))],[f_297_4]) ).
fof(f_297_6,plain,
( ! [U_1784,U_1782] :
( c_Wellfounded_Owf(U_1782,U_1784)
| ( ! [U_1777] :
( ? [U_1776] :
( hBOOL(hAPP(hAPP(c_member(U_1782),U_1776),sK95(U_1784,U_1782)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1782,U_1782)),hAPP(hAPP(c_Product__Type_OPair(U_1782,U_1782),U_1776),U_1777)),U_1784)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1782),U_1777),sK95(U_1784,U_1782))) )
& hBOOL(hAPP(hAPP(c_member(U_1782),sK96(U_1784,U_1782)),sK95(U_1784,U_1782))) ) )
& ! [U_1783,U_1781] :
( ! [U_1774] :
( ( ! [U_1772] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1772),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1781,U_1781)),hAPP(hAPP(c_Product__Type_OPair(U_1781,U_1781),U_1772),sK94(U_1783,U_1781,U_1774))),U_1783)) )
& hBOOL(hAPP(hAPP(c_member(U_1781),sK94(U_1783,U_1781,U_1774)),U_1774)) )
| ! [U_1771] : ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1771),U_1774)) )
| ~ c_Wellfounded_Owf(U_1781,U_1783) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_1775,sK96(U_1784,U_1782))],[f_297_5]) ).
fof(f_297_7,plain,
( ! [U_1784,U_1782] :
( c_Wellfounded_Owf(U_1782,U_1784)
| ( ! [U_1777] :
( ( hBOOL(hAPP(hAPP(c_member(U_1782),sK97(U_1784,U_1782,U_1777)),sK95(U_1784,U_1782)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1782,U_1782)),hAPP(hAPP(c_Product__Type_OPair(U_1782,U_1782),sK97(U_1784,U_1782,U_1777)),U_1777)),U_1784)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1782),U_1777),sK95(U_1784,U_1782))) )
& hBOOL(hAPP(hAPP(c_member(U_1782),sK96(U_1784,U_1782)),sK95(U_1784,U_1782))) ) )
& ! [U_1783,U_1781] :
( ! [U_1774] :
( ( ! [U_1772] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1772),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1781,U_1781)),hAPP(hAPP(c_Product__Type_OPair(U_1781,U_1781),U_1772),sK94(U_1783,U_1781,U_1774))),U_1783)) )
& hBOOL(hAPP(hAPP(c_member(U_1781),sK94(U_1783,U_1781,U_1774)),U_1774)) )
| ! [U_1771] : ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1771),U_1774)) )
| ~ c_Wellfounded_Owf(U_1781,U_1783) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_1776,sK97(U_1784,U_1782,U_1777))],[f_297_6]) ).
cnf(f_297_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1781),sK94(U_1783,U_1781,U_1774)),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1771),U_1774))
| ~ c_Wellfounded_Owf(U_1781,U_1783) ),
inference(clausify,[status(thm)],[f_297_7]) ).
cnf(f_297_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1772),U_1774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1781,U_1781)),hAPP(hAPP(c_Product__Type_OPair(U_1781,U_1781),U_1772),sK94(U_1783,U_1781,U_1774))),U_1783))
| ~ hBOOL(hAPP(hAPP(c_member(U_1781),U_1771),U_1774))
| ~ c_Wellfounded_Owf(U_1781,U_1783) ),
inference(clausify,[status(thm)],[f_297_7]) ).
cnf(f_297_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_1782),sK96(U_1784,U_1782)),sK95(U_1784,U_1782)))
| c_Wellfounded_Owf(U_1782,U_1784) ),
inference(clausify,[status(thm)],[f_297_7]) ).
cnf(f_297_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1782,U_1782)),hAPP(hAPP(c_Product__Type_OPair(U_1782,U_1782),sK97(U_1784,U_1782,U_1777)),U_1777)),U_1784))
| ~ hBOOL(hAPP(hAPP(c_member(U_1782),U_1777),sK95(U_1784,U_1782)))
| c_Wellfounded_Owf(U_1782,U_1784) ),
inference(clausify,[status(thm)],[f_297_7]) ).
cnf(f_297_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_1782),sK97(U_1784,U_1782,U_1777)),sK95(U_1784,U_1782)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1782),U_1777),sK95(U_1784,U_1782)))
| c_Wellfounded_Owf(U_1782,U_1784) ),
inference(clausify,[status(thm)],[f_297_7]) ).
fof(f_298_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_298_2,plain,
! [U_1785] : c_Wellfounded_OwfP(U_1785,c_COMBK(tc_fun(U_1785,tc_HOL_Obool),U_1785,c_COMBK(tc_HOL_Obool,U_1785,c_fFalse))),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
c_Wellfounded_OwfP(U_1785,c_COMBK(tc_fun(U_1785,tc_HOL_Obool),U_1785,c_COMBK(tc_HOL_Obool,U_1785,c_fFalse))),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_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_299_2,plain,
! [U_1788,U_1787,U_1786] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1786,U_1787),U_1788))
| ~ c_Wellfounded_OwfP(U_1786,U_1787) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1786,U_1787),U_1788))
| ~ c_Wellfounded_OwfP(U_1786,U_1787) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_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_300_2,plain,
! [U_1792,U_1791] :
( ( c_Wellfounded_OwfP(U_1791,U_1792)
| ? [U_1790] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1791,U_1792),U_1790)) )
& ( ! [U_1789] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_1791,U_1792),U_1789))
| ~ c_Wellfounded_OwfP(U_1791,U_1792) ) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
( ! [U_1796,U_1794] :
( c_Wellfounded_OwfP(U_1794,U_1796)
| ? [U_1790] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1794,U_1796),U_1790)) )
& ! [U_1795,U_1793] :
( ! [U_1789] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_1793,U_1795),U_1789))
| ~ c_Wellfounded_OwfP(U_1793,U_1795) ) ),
inference(miniscope,[status(thm)],[f_300_2]) ).
fof(f_300_4,plain,
( ! [U_1796,U_1794] :
( c_Wellfounded_OwfP(U_1794,U_1796)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1794,U_1796),sK98(U_1796,U_1794))) )
& ! [U_1795,U_1793] :
( ! [U_1789] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_1793,U_1795),U_1789))
| ~ c_Wellfounded_OwfP(U_1793,U_1795) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_1790,sK98(U_1796,U_1794))],[f_300_3]) ).
cnf(f_300_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_1793,U_1795),U_1789))
| ~ c_Wellfounded_OwfP(U_1793,U_1795) ),
inference(clausify,[status(thm)],[f_300_4]) ).
cnf(f_300_6,plain,
( c_Wellfounded_OwfP(U_1794,U_1796)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_1794,U_1796),sK98(U_1796,U_1794))) ),
inference(clausify,[status(thm)],[f_300_4]) ).
fof(f_301_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_301_2,plain,
! [U_1798,U_1797] :
( c_Wellfounded_OwfP(U_1797,c_Transitive__Closure_Otranclp(U_1797,U_1798))
| ~ c_Wellfounded_OwfP(U_1797,U_1798) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
( c_Wellfounded_OwfP(U_1797,c_Transitive__Closure_Otranclp(U_1797,U_1798))
| ~ c_Wellfounded_OwfP(U_1797,U_1798) ),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_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_302_2,plain,
! [U_1800,U_1799] :
( c_Wellfounded_OwfP(U_1799,c_FunDef_Oin__rel(U_1799,U_1799,U_1800))
| ~ c_Wellfounded_Owf(U_1799,U_1800) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( c_Wellfounded_OwfP(U_1799,c_FunDef_Oin__rel(U_1799,U_1799,U_1800))
| ~ c_Wellfounded_Owf(U_1799,U_1800) ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_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_303_2,plain,
! [U_1805,U_1804,U_1803,U_1802,U_1801] : c_Fun_Othe__inv__into(U_1801,U_1802,U_1803,U_1804,U_1805) = c_HOL_OThe(U_1801,hAPP(hAPP(c_COMBS(U_1801,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_1801),c_fconj),hAPP(hAPP(c_COMBC(U_1801,tc_fun(U_1801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1801)),U_1803))),hAPP(hAPP(c_COMBC(U_1801,U_1802,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_1802,tc_fun(U_1802,tc_HOL_Obool),U_1801),c_fequal),U_1804)),U_1805))),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
c_Fun_Othe__inv__into(U_1801,U_1802,U_1803,U_1804,U_1805) = c_HOL_OThe(U_1801,hAPP(hAPP(c_COMBS(U_1801,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_1801),c_fconj),hAPP(hAPP(c_COMBC(U_1801,tc_fun(U_1801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1801)),U_1803))),hAPP(hAPP(c_COMBC(U_1801,U_1802,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_1802,tc_fun(U_1802,tc_HOL_Obool),U_1801),c_fequal),U_1804)),U_1805))),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_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_304_2,plain,
! [U_1808,U_1807] :
( c_Wellfounded_Owf(U_1807,U_1808)
| ? [U_1806] : ~ hBOOL(hAPP(hAPP(c_member(U_1807),U_1806),c_Wellfounded_Oacc(U_1807,U_1808))) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1808,U_1807] :
( c_Wellfounded_Owf(U_1807,U_1808)
| ~ hBOOL(hAPP(hAPP(c_member(U_1807),sK99(U_1808,U_1807)),c_Wellfounded_Oacc(U_1807,U_1808))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_1806,sK99(U_1808,U_1807))],[f_304_2]) ).
cnf(f_304_4,plain,
( c_Wellfounded_Owf(U_1807,U_1808)
| ~ hBOOL(hAPP(hAPP(c_member(U_1807),sK99(U_1808,U_1807)),c_Wellfounded_Oacc(U_1807,U_1808))) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_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_305_2,plain,
! [U_1812,U_1811,U_1810,U_1809] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1809,U_1809)),hAPP(hAPP(c_Product__Type_OPair(U_1809,U_1809),U_1810),U_1811)),hAPP(c_Wellfounded_Omeasure(U_1809),U_1812)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1812,U_1810),hAPP(U_1812,U_1811)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1812,U_1810),hAPP(U_1812,U_1811))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1809,U_1809)),hAPP(hAPP(c_Product__Type_OPair(U_1809,U_1809),U_1810),U_1811)),hAPP(c_Wellfounded_Omeasure(U_1809),U_1812))) ) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
( ! [U_1820,U_1818,U_1816] :
( ! [U_1814] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_1814,U_1814)),hAPP(hAPP(c_Product__Type_OPair(U_1814,U_1814),U_1816),U_1818)),hAPP(c_Wellfounded_Omeasure(U_1814),U_1820)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1820,U_1816),hAPP(U_1820,U_1818)) )
& ! [U_1819,U_1817,U_1815] :
( ! [U_1813] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1813,U_1813)),hAPP(hAPP(c_Product__Type_OPair(U_1813,U_1813),U_1815),U_1817)),hAPP(c_Wellfounded_Omeasure(U_1813),U_1819)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1819,U_1815),hAPP(U_1819,U_1817)) ) ),
inference(miniscope,[status(thm)],[f_305_2]) ).
cnf(f_305_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1813,U_1813)),hAPP(hAPP(c_Product__Type_OPair(U_1813,U_1813),U_1815),U_1817)),hAPP(c_Wellfounded_Omeasure(U_1813),U_1819)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1819,U_1815),hAPP(U_1819,U_1817)) ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1814,U_1814)),hAPP(hAPP(c_Product__Type_OPair(U_1814,U_1814),U_1816),U_1818)),hAPP(c_Wellfounded_Omeasure(U_1814),U_1820)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1820,U_1816),hAPP(U_1820,U_1818)) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_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_306_2,plain,
! [U_1824,U_1823,U_1822,U_1821] :
( c_Orderings_Oord__class_Oless(U_1821,c_Lattices_Osemilattice__inf__class_Oinf(U_1821,U_1824,U_1822),U_1823)
| ~ c_Orderings_Oord__class_Oless(U_1821,U_1822,U_1823)
| ~ class_Lattices_Osemilattice__inf(U_1821) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( c_Orderings_Oord__class_Oless(U_1821,c_Lattices_Osemilattice__inf__class_Oinf(U_1821,U_1824,U_1822),U_1823)
| ~ c_Orderings_Oord__class_Oless(U_1821,U_1822,U_1823)
| ~ class_Lattices_Osemilattice__inf(U_1821) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_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_307_2,plain,
! [U_1828,U_1827,U_1826,U_1825] :
( c_Orderings_Oord__class_Oless(U_1825,c_Lattices_Osemilattice__inf__class_Oinf(U_1825,U_1826,U_1828),U_1827)
| ~ c_Orderings_Oord__class_Oless(U_1825,U_1826,U_1827)
| ~ class_Lattices_Osemilattice__inf(U_1825) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( c_Orderings_Oord__class_Oless(U_1825,c_Lattices_Osemilattice__inf__class_Oinf(U_1825,U_1826,U_1828),U_1827)
| ~ c_Orderings_Oord__class_Oless(U_1825,U_1826,U_1827)
| ~ class_Lattices_Osemilattice__inf(U_1825) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_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_308_2,plain,
! [U_1833,U_1832,U_1831,U_1830,U_1829] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1832,U_1832)),hAPP(hAPP(c_Product__Type_OPair(U_1832,U_1832),U_1830),U_1831)),c_Wellfounded_Omlex__prod(U_1832,U_1829,U_1833)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1829,U_1830),hAPP(U_1829,U_1831)) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1832,U_1832)),hAPP(hAPP(c_Product__Type_OPair(U_1832,U_1832),U_1830),U_1831)),c_Wellfounded_Omlex__prod(U_1832,U_1829,U_1833)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1829,U_1830),hAPP(U_1829,U_1831)) ),
inference(clausify,[status(thm)],[f_308_2]) ).
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_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_309_2,plain,
! [U_1839,U_1838,U_1837,U_1836,U_1835,U_1834] :
( ( c_Fun_Ooverride__on(U_1834,U_1837,U_1838,U_1839,U_1836,U_1835) = hAPP(U_1838,U_1835)
| hBOOL(hAPP(hAPP(c_member(U_1834),U_1835),U_1836)) )
& ( c_Fun_Ooverride__on(U_1834,U_1837,U_1838,U_1839,U_1836,U_1835) = hAPP(U_1839,U_1835)
| ~ hBOOL(hAPP(hAPP(c_member(U_1834),U_1835),U_1836)) ) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
( ! [U_1851,U_1849,U_1847,U_1845,U_1843,U_1841] :
( c_Fun_Ooverride__on(U_1841,U_1847,U_1849,U_1851,U_1845,U_1843) = hAPP(U_1849,U_1843)
| hBOOL(hAPP(hAPP(c_member(U_1841),U_1843),U_1845)) )
& ! [U_1850,U_1848,U_1846,U_1844,U_1842,U_1840] :
( c_Fun_Ooverride__on(U_1840,U_1846,U_1848,U_1850,U_1844,U_1842) = hAPP(U_1850,U_1842)
| ~ hBOOL(hAPP(hAPP(c_member(U_1840),U_1842),U_1844)) ) ),
inference(miniscope,[status(thm)],[f_309_2]) ).
cnf(f_309_4,plain,
( c_Fun_Ooverride__on(U_1840,U_1846,U_1848,U_1850,U_1844,U_1842) = hAPP(U_1850,U_1842)
| ~ hBOOL(hAPP(hAPP(c_member(U_1840),U_1842),U_1844)) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_5,plain,
( c_Fun_Ooverride__on(U_1841,U_1847,U_1849,U_1851,U_1845,U_1843) = hAPP(U_1849,U_1843)
| hBOOL(hAPP(hAPP(c_member(U_1841),U_1843),U_1845)) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_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_310_2,plain,
! [U_1852] : c_Wellfounded_Omeasure(U_1852) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_1852),c_Wellfounded_Oless__than),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
c_Wellfounded_Omeasure(U_1852) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_1852),c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).
cnf(f_311_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_311_1]) ).
fof(f_312_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_312_2,plain,
! [U_1856,U_1855,U_1854,U_1853] :
( hBOOL(hAPP(hAPP(c_member(U_1853),U_1856),U_1855))
| ~ hBOOL(hAPP(hAPP(c_member(U_1853),U_1856),U_1854))
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1853,tc_HOL_Obool),U_1854,U_1855) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
cnf(f_312_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_1853),U_1856),U_1855))
| ~ hBOOL(hAPP(hAPP(c_member(U_1853),U_1856),U_1854))
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1853,tc_HOL_Obool),U_1854,U_1855) ),
inference(clausify,[status(thm)],[f_312_2]) ).
fof(f_313_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_313_2,plain,
! [U_1859,U_1858,U_1857] : c_Wellfounded_Omlex__prod(U_1857,U_1858,U_1859) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_1857),U_1857),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_1857,c_Wellfounded_Oless__than,U_1859)),hAPP(hAPP(c_COMBS(U_1857,U_1857,tc_prod(tc_Nat_Onat,U_1857)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_1857,tc_prod(tc_Nat_Onat,U_1857)),U_1857),c_Product__Type_OPair(tc_Nat_Onat,U_1857)),U_1858)),c_COMBI(U_1857))),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
c_Wellfounded_Omlex__prod(U_1857,U_1858,U_1859) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_1857),U_1857),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_1857,c_Wellfounded_Oless__than,U_1859)),hAPP(hAPP(c_COMBS(U_1857,U_1857,tc_prod(tc_Nat_Onat,U_1857)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_1857,tc_prod(tc_Nat_Onat,U_1857)),U_1857),c_Product__Type_OPair(tc_Nat_Onat,U_1857)),U_1858)),c_COMBI(U_1857))),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_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_314_2,plain,
! [U_1861,U_1860] :
( ( 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_1860),U_1861)),c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1860,U_1861) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1860,U_1861)
| ~ 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_1860),U_1861)),c_Wellfounded_Oless__than)) ) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
( ! [U_1865,U_1863] :
( 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_1863),U_1865)),c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1863,U_1865) )
& ! [U_1864,U_1862] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1862,U_1864)
| ~ 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_1862),U_1864)),c_Wellfounded_Oless__than)) ) ),
inference(miniscope,[status(thm)],[f_314_2]) ).
cnf(f_314_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1862,U_1864)
| ~ 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_1862),U_1864)),c_Wellfounded_Oless__than)) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1863),U_1865)),c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1863,U_1865) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_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_315_2,plain,
! [U_1871,U_1870,U_1869,U_1868,U_1867,U_1866] :
( c_Fun_Ooverride__on(U_1866,U_1869,U_1870,U_1871,U_1868,U_1867) = hAPP(U_1870,U_1867)
| hBOOL(hAPP(hAPP(c_member(U_1866),U_1867),U_1868)) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
( c_Fun_Ooverride__on(U_1866,U_1869,U_1870,U_1871,U_1868,U_1867) = hAPP(U_1870,U_1867)
| hBOOL(hAPP(hAPP(c_member(U_1866),U_1867),U_1868)) ),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_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_316_2,plain,
! [U_1877,U_1876,U_1875,U_1874,U_1873,U_1872] :
( c_Fun_Ooverride__on(U_1872,U_1875,U_1876,U_1877,U_1874,U_1873) = hAPP(U_1877,U_1873)
| ~ hBOOL(hAPP(hAPP(c_member(U_1872),U_1873),U_1874)) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( c_Fun_Ooverride__on(U_1872,U_1875,U_1876,U_1877,U_1874,U_1873) = hAPP(U_1877,U_1873)
| ~ hBOOL(hAPP(hAPP(c_member(U_1872),U_1873),U_1874)) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_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_317_2,plain,
! [U_1880,U_1879,U_1878] :
( c_Wellfounded_Owf(U_1878,c_Wellfounded_Omlex__prod(U_1878,U_1880,U_1879))
| ~ c_Wellfounded_Owf(U_1878,U_1879) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( c_Wellfounded_Owf(U_1878,c_Wellfounded_Omlex__prod(U_1878,U_1880,U_1879))
| ~ c_Wellfounded_Owf(U_1878,U_1879) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_1,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(fof_nnf,[status(thm)],[fact_less__than__def]) ).
cnf(f_318_2,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_318_1]) ).
fof(f_319_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_319_2,plain,
! [U_1885,U_1884,U_1883,U_1882,U_1881] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1884,U_1884)),hAPP(hAPP(c_Product__Type_OPair(U_1884,U_1884),U_1882),U_1883)),c_Wellfounded_Omlex__prod(U_1884,U_1881,U_1885)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1884,U_1884)),hAPP(hAPP(c_Product__Type_OPair(U_1884,U_1884),U_1882),U_1883)),U_1885))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(U_1881,U_1882),hAPP(U_1881,U_1883)) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
cnf(f_319_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1884,U_1884)),hAPP(hAPP(c_Product__Type_OPair(U_1884,U_1884),U_1882),U_1883)),c_Wellfounded_Omlex__prod(U_1884,U_1881,U_1885)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1884,U_1884)),hAPP(hAPP(c_Product__Type_OPair(U_1884,U_1884),U_1882),U_1883)),U_1885))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(U_1881,U_1882),hAPP(U_1881,U_1883)) ),
inference(clausify,[status(thm)],[f_319_2]) ).
fof(f_320_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_320_2,plain,
! [U_1887,U_1886] :
( c_Relation_Oantisym(U_1886,c_Transitive__Closure_Ortrancl(U_1886,U_1887))
| ~ c_Wellfounded_Oacyclic(U_1886,U_1887) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( c_Relation_Oantisym(U_1886,c_Transitive__Closure_Ortrancl(U_1886,U_1887))
| ~ c_Wellfounded_Oacyclic(U_1886,U_1887) ),
inference(clausify,[status(thm)],[f_320_2]) ).
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_1889,U_1888] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1888,U_1889)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1888,U_1889) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1888,U_1889)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1888,U_1889) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_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_322_2,plain,
! [U_1893,U_1892,U_1891,U_1890] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1890,tc_HOL_Obool),U_1891,U_1893)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1890,tc_HOL_Obool),U_1892,U_1893)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1890,tc_HOL_Obool),U_1891,U_1892) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_1890,tc_HOL_Obool),U_1891,U_1893)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1890,tc_HOL_Obool),U_1892,U_1893)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1890,tc_HOL_Obool),U_1891,U_1892) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).
cnf(f_323_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_323_1]) ).
fof(f_324_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_324_2,plain,
! [U_1895,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_1894),U_1895)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1894,U_1895) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1894,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_1894),U_1895)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
( ! [U_1899,U_1897] :
( 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_1897),U_1899)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1897,U_1899) )
& ! [U_1898,U_1896] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1896,U_1898)
| ~ 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_1896),U_1898)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(miniscope,[status(thm)],[f_324_2]) ).
cnf(f_324_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1896,U_1898)
| ~ 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_1896),U_1898)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1897),U_1899)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1897,U_1899) ),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_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_325_2,plain,
! [U_1903,U_1902,U_1901,U_1900] :
( ( c_Orderings_Oord__class_Oless__eq(U_1900,U_1901,U_1903)
& c_Orderings_Oord__class_Oless__eq(U_1900,U_1901,U_1902) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1900,U_1901,c_Lattices_Osemilattice__inf__class_Oinf(U_1900,U_1902,U_1903))
| ~ class_Lattices_Osemilattice__inf(U_1900) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1900,U_1901,U_1902)
| ~ c_Orderings_Oord__class_Oless__eq(U_1900,U_1901,c_Lattices_Osemilattice__inf__class_Oinf(U_1900,U_1902,U_1903))
| ~ class_Lattices_Osemilattice__inf(U_1900) ),
inference(clausify,[status(thm)],[f_325_2]) ).
cnf(f_325_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1900,U_1901,U_1903)
| ~ c_Orderings_Oord__class_Oless__eq(U_1900,U_1901,c_Lattices_Osemilattice__inf__class_Oinf(U_1900,U_1902,U_1903))
| ~ class_Lattices_Osemilattice__inf(U_1900) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_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_326_2,plain,
! [U_1908,U_1907,U_1906,U_1905,U_1904] :
( c_Orderings_Oord__class_Oless__eq(U_1904,c_Lattices_Osemilattice__inf__class_Oinf(U_1904,U_1905,U_1907),c_Lattices_Osemilattice__inf__class_Oinf(U_1904,U_1906,U_1908))
| ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1907,U_1908)
| ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1905,U_1906)
| ~ class_Lattices_Osemilattice__inf(U_1904) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1904,c_Lattices_Osemilattice__inf__class_Oinf(U_1904,U_1905,U_1907),c_Lattices_Osemilattice__inf__class_Oinf(U_1904,U_1906,U_1908))
| ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1907,U_1908)
| ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1905,U_1906)
| ~ class_Lattices_Osemilattice__inf(U_1904) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_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_327_2,plain,
! [U_1912,U_1911,U_1910,U_1909] :
( c_Orderings_Oord__class_Oless__eq(U_1909,U_1910,c_Lattices_Osemilattice__inf__class_Oinf(U_1909,U_1911,U_1912))
| ~ c_Orderings_Oord__class_Oless__eq(U_1909,U_1910,U_1912)
| ~ c_Orderings_Oord__class_Oless__eq(U_1909,U_1910,U_1911)
| ~ class_Lattices_Osemilattice__inf(U_1909) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1909,U_1910,c_Lattices_Osemilattice__inf__class_Oinf(U_1909,U_1911,U_1912))
| ~ c_Orderings_Oord__class_Oless__eq(U_1909,U_1910,U_1912)
| ~ c_Orderings_Oord__class_Oless__eq(U_1909,U_1910,U_1911)
| ~ class_Lattices_Osemilattice__inf(U_1909) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_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_328_2,plain,
! [U_1916,U_1915,U_1914,U_1913] :
( c_Orderings_Oord__class_Oless__eq(U_1913,U_1914,c_Lattices_Osemilattice__inf__class_Oinf(U_1913,U_1915,U_1916))
| ~ c_Orderings_Oord__class_Oless__eq(U_1913,U_1914,U_1916)
| ~ c_Orderings_Oord__class_Oless__eq(U_1913,U_1914,U_1915)
| ~ class_Lattices_Osemilattice__inf(U_1913) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1913,U_1914,c_Lattices_Osemilattice__inf__class_Oinf(U_1913,U_1915,U_1916))
| ~ c_Orderings_Oord__class_Oless__eq(U_1913,U_1914,U_1916)
| ~ c_Orderings_Oord__class_Oless__eq(U_1913,U_1914,U_1915)
| ~ class_Lattices_Osemilattice__inf(U_1913) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_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_329_2,plain,
! [U_1919,U_1918,U_1917] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1917,U_1919,U_1918) = U_1918
| ~ c_Orderings_Oord__class_Oless__eq(U_1917,U_1918,U_1919)
| ~ class_Lattices_Osemilattice__inf(U_1917) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1917,U_1919,U_1918) = U_1918
| ~ c_Orderings_Oord__class_Oless__eq(U_1917,U_1918,U_1919)
| ~ class_Lattices_Osemilattice__inf(U_1917) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_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_330_2,plain,
! [U_1922,U_1921,U_1920] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_1920,U_1921,U_1922) = U_1921
| ~ c_Orderings_Oord__class_Oless__eq(U_1920,U_1921,U_1922)
| ~ class_Lattices_Osemilattice__inf(U_1920) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1920,U_1921,U_1922) = U_1921
| ~ c_Orderings_Oord__class_Oless__eq(U_1920,U_1921,U_1922)
| ~ class_Lattices_Osemilattice__inf(U_1920) ),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_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_331_2,plain,
! [U_1926,U_1925,U_1924,U_1923] :
( c_Orderings_Oord__class_Oless__eq(U_1923,c_Lattices_Osemilattice__inf__class_Oinf(U_1923,U_1926,U_1924),U_1925)
| ~ c_Orderings_Oord__class_Oless__eq(U_1923,U_1924,U_1925)
| ~ class_Lattices_Osemilattice__inf(U_1923) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1923,c_Lattices_Osemilattice__inf__class_Oinf(U_1923,U_1926,U_1924),U_1925)
| ~ c_Orderings_Oord__class_Oless__eq(U_1923,U_1924,U_1925)
| ~ class_Lattices_Osemilattice__inf(U_1923) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_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_332_2,plain,
! [U_1930,U_1929,U_1928,U_1927] :
( c_Orderings_Oord__class_Oless__eq(U_1927,c_Lattices_Osemilattice__inf__class_Oinf(U_1927,U_1928,U_1930),U_1929)
| ~ c_Orderings_Oord__class_Oless__eq(U_1927,U_1928,U_1929)
| ~ class_Lattices_Osemilattice__inf(U_1927) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1927,c_Lattices_Osemilattice__inf__class_Oinf(U_1927,U_1928,U_1930),U_1929)
| ~ c_Orderings_Oord__class_Oless__eq(U_1927,U_1928,U_1929)
| ~ class_Lattices_Osemilattice__inf(U_1927) ),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_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_333_2,plain,
! [U_1934,U_1933,U_1932,U_1931] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,c_Lattices_Osemilattice__inf__class_Oinf(U_1931,U_1933,U_1934))
| ~ c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1934)
| ~ c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1933) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1934)
& c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1933) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,c_Lattices_Osemilattice__inf__class_Oinf(U_1931,U_1933,U_1934)) ) )
| ~ class_Lattices_Osemilattice__inf(U_1931) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1933)
| ~ c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,c_Lattices_Osemilattice__inf__class_Oinf(U_1931,U_1933,U_1934))
| ~ class_Lattices_Osemilattice__inf(U_1931) ),
inference(clausify,[status(thm)],[f_333_2]) ).
cnf(f_333_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1934)
| ~ c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,c_Lattices_Osemilattice__inf__class_Oinf(U_1931,U_1933,U_1934))
| ~ class_Lattices_Osemilattice__inf(U_1931) ),
inference(clausify,[status(thm)],[f_333_2]) ).
cnf(f_333_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,c_Lattices_Osemilattice__inf__class_Oinf(U_1931,U_1933,U_1934))
| ~ c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1934)
| ~ c_Orderings_Oord__class_Oless__eq(U_1931,U_1932,U_1933)
| ~ class_Lattices_Osemilattice__inf(U_1931) ),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_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_334_2,plain,
! [U_1937,U_1936,U_1935] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1935,U_1936,U_1937)
| c_Lattices_Osemilattice__inf__class_Oinf(U_1935,U_1936,U_1937) != U_1936 )
& ( c_Lattices_Osemilattice__inf__class_Oinf(U_1935,U_1936,U_1937) = U_1936
| ~ c_Orderings_Oord__class_Oless__eq(U_1935,U_1936,U_1937) ) )
| ~ class_Lattices_Osemilattice__inf(U_1935) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
cnf(f_334_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_1935,U_1936,U_1937) = U_1936
| ~ c_Orderings_Oord__class_Oless__eq(U_1935,U_1936,U_1937)
| ~ class_Lattices_Osemilattice__inf(U_1935) ),
inference(clausify,[status(thm)],[f_334_2]) ).
cnf(f_334_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1935,U_1936,U_1937)
| c_Lattices_Osemilattice__inf__class_Oinf(U_1935,U_1936,U_1937) != U_1936
| ~ class_Lattices_Osemilattice__inf(U_1935) ),
inference(clausify,[status(thm)],[f_334_2]) ).
fof(f_335_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_335_2,plain,
! [U_1940,U_1939,U_1938] :
( c_Orderings_Oord__class_Oless__eq(U_1938,c_Lattices_Osemilattice__inf__class_Oinf(U_1938,U_1939,U_1940),U_1940)
| ~ class_Lattices_Osemilattice__inf(U_1938) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1938,c_Lattices_Osemilattice__inf__class_Oinf(U_1938,U_1939,U_1940),U_1940)
| ~ class_Lattices_Osemilattice__inf(U_1938) ),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_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_336_2,plain,
! [U_1943,U_1942,U_1941] :
( c_Orderings_Oord__class_Oless__eq(U_1941,c_Lattices_Osemilattice__inf__class_Oinf(U_1941,U_1942,U_1943),U_1943)
| ~ class_Lattices_Olattice(U_1941) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1941,c_Lattices_Osemilattice__inf__class_Oinf(U_1941,U_1942,U_1943),U_1943)
| ~ class_Lattices_Olattice(U_1941) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_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_337_2,plain,
! [U_1946,U_1945,U_1944] :
( c_Orderings_Oord__class_Oless__eq(U_1944,c_Lattices_Osemilattice__inf__class_Oinf(U_1944,U_1945,U_1946),U_1945)
| ~ class_Lattices_Osemilattice__inf(U_1944) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1944,c_Lattices_Osemilattice__inf__class_Oinf(U_1944,U_1945,U_1946),U_1945)
| ~ class_Lattices_Osemilattice__inf(U_1944) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_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_338_2,plain,
! [U_1949,U_1948,U_1947] :
( c_Orderings_Oord__class_Oless__eq(U_1947,c_Lattices_Osemilattice__inf__class_Oinf(U_1947,U_1948,U_1949),U_1948)
| ~ class_Lattices_Olattice(U_1947) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1947,c_Lattices_Osemilattice__inf__class_Oinf(U_1947,U_1948,U_1949),U_1948)
| ~ class_Lattices_Olattice(U_1947) ),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_1,plain,
! [T_a] : c_Relation_Oantisym(T_a,c_Relation_OId(T_a)),
inference(fof_nnf,[status(thm)],[fact_antisym__Id]) ).
fof(f_339_2,plain,
! [U_1950] : c_Relation_Oantisym(U_1950,c_Relation_OId(U_1950)),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
c_Relation_Oantisym(U_1950,c_Relation_OId(U_1950)),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_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_340_2,plain,
! [U_1952,U_1951] : c_Relation_Oantisym(U_1951,c_Relation_OId__on(U_1951,U_1952)),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
c_Relation_Oantisym(U_1951,c_Relation_OId__on(U_1951,U_1952)),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_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_341_2,plain,
! [U_1954,U_1953] :
( ( 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_1953),U_1954)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1953,U_1954) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1953,U_1954)
| ~ 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_1953),U_1954)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
( ! [U_1958,U_1956] :
( 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_1956),U_1958)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1956,U_1958) )
& ! [U_1957,U_1955] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1955,U_1957)
| ~ 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_1955),U_1957)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(miniscope,[status(thm)],[f_341_2]) ).
cnf(f_341_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1955,U_1957)
| ~ 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_1955),U_1957)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(clausify,[status(thm)],[f_341_3]) ).
cnf(f_341_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_1956),U_1958)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1956,U_1958) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_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_342_2,plain,
! [U_1964,U_1963] :
( ( c_Relation_Oantisym(U_1963,U_1964)
| ? [U_1962,U_1961] :
( U_1962 != U_1961
& 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))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1962),U_1961)),U_1964)) ) )
& ( ! [U_1960,U_1959] :
( U_1960 = U_1959
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1963,U_1963)),hAPP(hAPP(c_Product__Type_OPair(U_1963,U_1963),U_1959),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_1960),U_1959)),U_1964)) )
| ~ c_Relation_Oantisym(U_1963,U_1964) ) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
( ! [U_1968,U_1966] :
( c_Relation_Oantisym(U_1966,U_1968)
| ? [U_1962,U_1961] :
( U_1962 != U_1961
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),U_1961),U_1962)),U_1968))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),U_1962),U_1961)),U_1968)) ) )
& ! [U_1967,U_1965] :
( ! [U_1960,U_1959] :
( U_1960 = U_1959
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1959),U_1960)),U_1967))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1960),U_1959)),U_1967)) )
| ~ c_Relation_Oantisym(U_1965,U_1967) ) ),
inference(miniscope,[status(thm)],[f_342_2]) ).
fof(f_342_4,plain,
( ! [U_1968,U_1966] :
( c_Relation_Oantisym(U_1966,U_1968)
| ? [U_1961] :
( sK100(U_1968,U_1966) != U_1961
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),U_1961),sK100(U_1968,U_1966))),U_1968))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),sK100(U_1968,U_1966)),U_1961)),U_1968)) ) )
& ! [U_1967,U_1965] :
( ! [U_1960,U_1959] :
( U_1960 = U_1959
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1959),U_1960)),U_1967))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1960),U_1959)),U_1967)) )
| ~ c_Relation_Oantisym(U_1965,U_1967) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_1962,sK100(U_1968,U_1966))],[f_342_3]) ).
fof(f_342_5,plain,
( ! [U_1968,U_1966] :
( c_Relation_Oantisym(U_1966,U_1968)
| ( sK100(U_1968,U_1966) != sK101(U_1968,U_1966)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),sK101(U_1968,U_1966)),sK100(U_1968,U_1966))),U_1968))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),sK100(U_1968,U_1966)),sK101(U_1968,U_1966))),U_1968)) ) )
& ! [U_1967,U_1965] :
( ! [U_1960,U_1959] :
( U_1960 = U_1959
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1959),U_1960)),U_1967))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1960),U_1959)),U_1967)) )
| ~ c_Relation_Oantisym(U_1965,U_1967) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_1961,sK101(U_1968,U_1966))],[f_342_4]) ).
cnf(f_342_6,plain,
( U_1960 = U_1959
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1959),U_1960)),U_1967))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1965,U_1965)),hAPP(hAPP(c_Product__Type_OPair(U_1965,U_1965),U_1960),U_1959)),U_1967))
| ~ c_Relation_Oantisym(U_1965,U_1967) ),
inference(clausify,[status(thm)],[f_342_5]) ).
cnf(f_342_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),sK100(U_1968,U_1966)),sK101(U_1968,U_1966))),U_1968))
| c_Relation_Oantisym(U_1966,U_1968) ),
inference(clausify,[status(thm)],[f_342_5]) ).
cnf(f_342_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_1966,U_1966)),hAPP(hAPP(c_Product__Type_OPair(U_1966,U_1966),sK101(U_1968,U_1966)),sK100(U_1968,U_1966))),U_1968))
| c_Relation_Oantisym(U_1966,U_1968) ),
inference(clausify,[status(thm)],[f_342_5]) ).
cnf(f_342_9,plain,
( sK100(U_1968,U_1966) != sK101(U_1968,U_1966)
| c_Relation_Oantisym(U_1966,U_1968) ),
inference(clausify,[status(thm)],[f_342_5]) ).
fof(f_343_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_343_2,plain,
! [U_1972,U_1971,U_1970,U_1969] :
( U_1971 = U_1972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1969,U_1969)),hAPP(hAPP(c_Product__Type_OPair(U_1969,U_1969),U_1972),U_1971)),U_1970))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1969,U_1969)),hAPP(hAPP(c_Product__Type_OPair(U_1969,U_1969),U_1971),U_1972)),U_1970))
| ~ c_Relation_Oantisym(U_1969,U_1970) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
( U_1971 = U_1972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1969,U_1969)),hAPP(hAPP(c_Product__Type_OPair(U_1969,U_1969),U_1972),U_1971)),U_1970))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_1969,U_1969)),hAPP(hAPP(c_Product__Type_OPair(U_1969,U_1969),U_1971),U_1972)),U_1970))
| ~ c_Relation_Oantisym(U_1969,U_1970) ),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_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_344_2,plain,
! [U_1974,U_1973] :
( c_Orderings_Oord__class_Oless__eq(U_1973,U_1974,U_1974)
| ~ class_Orderings_Opreorder(U_1973) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1973,U_1974,U_1974)
| ~ class_Orderings_Opreorder(U_1973) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_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_345_2,plain,
! [U_1976,U_1975] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1975,U_1976)
| ( U_1975 != U_1976
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1975,U_1976) ) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1975,U_1976)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1975,U_1976) ),
inference(clausify,[status(thm)],[f_345_2]) ).
cnf(f_345_4,plain,
( U_1975 != U_1976
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1975,U_1976) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_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_346_2,plain,
! [U_1978,U_1977] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1977,U_1978)
| U_1977 = U_1978
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1977,U_1978) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1977,U_1978)
| U_1977 = U_1978
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1977,U_1978) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_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_347_2,plain,
! [U_1982,U_1981,U_1980,U_1979] :
( hBOOL(hAPP(hAPP(c_member(U_1979),U_1982),U_1981))
| ~ hBOOL(hAPP(hAPP(c_member(U_1979),U_1982),U_1980))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1979,tc_HOL_Obool),U_1980,U_1981) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_1979),U_1982),U_1981))
| ~ hBOOL(hAPP(hAPP(c_member(U_1979),U_1982),U_1980))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1979,tc_HOL_Obool),U_1980,U_1981) ),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_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_348_2,plain,
! [U_1985,U_1984,U_1983] :
( ( c_Orderings_Oord__class_Oless(tc_fun(U_1983,tc_HOL_Obool),U_1984,U_1985)
| U_1984 = U_1985
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1983,tc_HOL_Obool),U_1984,U_1985) )
& ( ( U_1984 != U_1985
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_1983,tc_HOL_Obool),U_1984,U_1985) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1983,tc_HOL_Obool),U_1984,U_1985) ) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
( ! [U_1991,U_1989,U_1987] :
( c_Orderings_Oord__class_Oless(tc_fun(U_1987,tc_HOL_Obool),U_1989,U_1991)
| U_1989 = U_1991
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1987,tc_HOL_Obool),U_1989,U_1991) )
& ! [U_1990,U_1988,U_1986] :
( ( U_1988 != U_1990
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_1986,tc_HOL_Obool),U_1988,U_1990) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1986,tc_HOL_Obool),U_1988,U_1990) ) ),
inference(miniscope,[status(thm)],[f_348_2]) ).
cnf(f_348_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1986,tc_HOL_Obool),U_1988,U_1990)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1986,tc_HOL_Obool),U_1988,U_1990) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_5,plain,
( U_1988 != U_1990
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1986,tc_HOL_Obool),U_1988,U_1990) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_6,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_1987,tc_HOL_Obool),U_1989,U_1991)
| U_1989 = U_1991
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1987,tc_HOL_Obool),U_1989,U_1991) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_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_349_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_349_1]) ).
fof(f_349_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_349_2]) ).
cnf(f_349_4,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_349_3]) ).
cnf(f_349_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000) ),
inference(clausify,[status(thm)],[f_349_3]) ).
cnf(f_349_6,plain,
( U_1998 != U_2000
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_1996,tc_HOL_Obool),U_1998,U_2000) ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_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_350_2,plain,
! [U_2003,U_2002,U_2001] :
( 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_350_1]) ).
cnf(f_350_3,plain,
( 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(clausify,[status(thm)],[f_350_2]) ).
fof(f_351_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_351_2,plain,
! [U_2007,U_2006,U_2005,U_2004] :
( c_Orderings_Oord__class_Oless(tc_fun(U_2004,tc_HOL_Obool),U_2005,U_2007)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2007)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2004,tc_HOL_Obool),U_2005,U_2006) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
cnf(f_351_3,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_2004,tc_HOL_Obool),U_2005,U_2007)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2004,tc_HOL_Obool),U_2006,U_2007)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2004,tc_HOL_Obool),U_2005,U_2006) ),
inference(clausify,[status(thm)],[f_351_2]) ).
fof(f_352_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_352_2,plain,
! [U_2011,U_2010,U_2009,U_2008] :
( c_Orderings_Oord__class_Oless(tc_fun(U_2008,tc_HOL_Obool),U_2009,U_2011)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2008,tc_HOL_Obool),U_2010,U_2011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2008,tc_HOL_Obool),U_2009,U_2010) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_2008,tc_HOL_Obool),U_2009,U_2011)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2008,tc_HOL_Obool),U_2010,U_2011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2008,tc_HOL_Obool),U_2009,U_2010) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_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_353_2,plain,
! [U_2015,U_2014,U_2013,U_2012] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_2013,U_2012),U_2014,U_2015)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2015,U_2014)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2014,U_2015) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2015,U_2014)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2014,U_2015) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2013,U_2012),U_2014,U_2015) ) )
| ~ class_Orderings_Oord(U_2012) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2014,U_2015)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2013,U_2012),U_2014,U_2015)
| ~ class_Orderings_Oord(U_2012) ),
inference(clausify,[status(thm)],[f_353_2]) ).
cnf(f_353_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2015,U_2014)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2013,U_2012),U_2014,U_2015)
| ~ class_Orderings_Oord(U_2012) ),
inference(clausify,[status(thm)],[f_353_2]) ).
cnf(f_353_5,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_2013,U_2012),U_2014,U_2015)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2015,U_2014)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2013,U_2012),U_2014,U_2015)
| ~ class_Orderings_Oord(U_2012) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_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_354_2,plain,
! [U_2018,U_2017,U_2016] :
( c_Wellfounded_OwfP(U_2016,U_2018)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2016,tc_fun(U_2016,tc_HOL_Obool)),U_2018,U_2017)
| ~ c_Wellfounded_OwfP(U_2016,U_2017) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( c_Wellfounded_OwfP(U_2016,U_2018)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2016,tc_fun(U_2016,tc_HOL_Obool)),U_2018,U_2017)
| ~ c_Wellfounded_OwfP(U_2016,U_2017) ),
inference(clausify,[status(thm)],[f_354_2]) ).
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_2021,U_2020,U_2019] :
( c_Wellfounded_Owf(U_2019,U_2021)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2019,U_2019),tc_HOL_Obool),U_2021,U_2020)
| ~ c_Wellfounded_Owf(U_2019,U_2020) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( c_Wellfounded_Owf(U_2019,U_2021)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2019,U_2019),tc_HOL_Obool),U_2021,U_2020)
| ~ c_Wellfounded_Owf(U_2019,U_2020) ),
inference(clausify,[status(thm)],[f_355_2]) ).
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_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_356_2,plain,
! [U_2025,U_2024,U_2023,U_2022] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2022,tc_fun(U_2023,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2022,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),U_2022),c_COMBC(U_2023,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_prod(U_2022,U_2023)),tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),U_2022),hAPP(c_COMBB(tc_prod(U_2022,U_2023),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool),U_2023),c_member(tc_prod(U_2022,U_2023)))),c_Product__Type_OPair(U_2022,U_2023)))),U_2024),hAPP(hAPP(c_COMBC(U_2022,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),U_2022),c_COMBC(U_2023,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_prod(U_2022,U_2023)),tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),U_2022),hAPP(c_COMBB(tc_prod(U_2022,U_2023),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool),U_2023),c_member(tc_prod(U_2022,U_2023)))),c_Product__Type_OPair(U_2022,U_2023)))),U_2025))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),U_2024,U_2025) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),U_2024,U_2025)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2022,tc_fun(U_2023,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2022,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),U_2022),c_COMBC(U_2023,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_prod(U_2022,U_2023)),tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),U_2022),hAPP(c_COMBB(tc_prod(U_2022,U_2023),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool),U_2023),c_member(tc_prod(U_2022,U_2023)))),c_Product__Type_OPair(U_2022,U_2023)))),U_2024),hAPP(hAPP(c_COMBC(U_2022,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_fun(U_2023,tc_HOL_Obool)),U_2022),c_COMBC(U_2023,tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2023,tc_prod(U_2022,U_2023)),tc_fun(U_2023,tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool)),U_2022),hAPP(c_COMBB(tc_prod(U_2022,U_2023),tc_fun(tc_fun(tc_prod(U_2022,U_2023),tc_HOL_Obool),tc_HOL_Obool),U_2023),c_member(tc_prod(U_2022,U_2023)))),c_Product__Type_OPair(U_2022,U_2023)))),U_2025)) ) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
( ! [U_2033,U_2031,U_2029,U_2027] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2027,tc_fun(U_2029,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2027,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),U_2027),c_COMBC(U_2029,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_prod(U_2027,U_2029)),tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),U_2027),hAPP(c_COMBB(tc_prod(U_2027,U_2029),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool),U_2029),c_member(tc_prod(U_2027,U_2029)))),c_Product__Type_OPair(U_2027,U_2029)))),U_2031),hAPP(hAPP(c_COMBC(U_2027,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),U_2027),c_COMBC(U_2029,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_prod(U_2027,U_2029)),tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),U_2027),hAPP(c_COMBB(tc_prod(U_2027,U_2029),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool),U_2029),c_member(tc_prod(U_2027,U_2029)))),c_Product__Type_OPair(U_2027,U_2029)))),U_2033))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),U_2031,U_2033) )
& ! [U_2032,U_2030,U_2028,U_2026] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),U_2030,U_2032)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2026,tc_fun(U_2028,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2026,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),U_2026),c_COMBC(U_2028,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_prod(U_2026,U_2028)),tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),U_2026),hAPP(c_COMBB(tc_prod(U_2026,U_2028),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool),U_2028),c_member(tc_prod(U_2026,U_2028)))),c_Product__Type_OPair(U_2026,U_2028)))),U_2030),hAPP(hAPP(c_COMBC(U_2026,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),U_2026),c_COMBC(U_2028,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_prod(U_2026,U_2028)),tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),U_2026),hAPP(c_COMBB(tc_prod(U_2026,U_2028),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool),U_2028),c_member(tc_prod(U_2026,U_2028)))),c_Product__Type_OPair(U_2026,U_2028)))),U_2032)) ) ),
inference(miniscope,[status(thm)],[f_356_2]) ).
cnf(f_356_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),U_2030,U_2032)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2026,tc_fun(U_2028,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2026,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),U_2026),c_COMBC(U_2028,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_prod(U_2026,U_2028)),tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),U_2026),hAPP(c_COMBB(tc_prod(U_2026,U_2028),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool),U_2028),c_member(tc_prod(U_2026,U_2028)))),c_Product__Type_OPair(U_2026,U_2028)))),U_2030),hAPP(hAPP(c_COMBC(U_2026,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_fun(U_2028,tc_HOL_Obool)),U_2026),c_COMBC(U_2028,tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2028,tc_prod(U_2026,U_2028)),tc_fun(U_2028,tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool)),U_2026),hAPP(c_COMBB(tc_prod(U_2026,U_2028),tc_fun(tc_fun(tc_prod(U_2026,U_2028),tc_HOL_Obool),tc_HOL_Obool),U_2028),c_member(tc_prod(U_2026,U_2028)))),c_Product__Type_OPair(U_2026,U_2028)))),U_2032)) ),
inference(clausify,[status(thm)],[f_356_3]) ).
cnf(f_356_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2027,tc_fun(U_2029,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_2027,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),U_2027),c_COMBC(U_2029,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_prod(U_2027,U_2029)),tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),U_2027),hAPP(c_COMBB(tc_prod(U_2027,U_2029),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool),U_2029),c_member(tc_prod(U_2027,U_2029)))),c_Product__Type_OPair(U_2027,U_2029)))),U_2031),hAPP(hAPP(c_COMBC(U_2027,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_fun(U_2029,tc_HOL_Obool)),U_2027),c_COMBC(U_2029,tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2029,tc_prod(U_2027,U_2029)),tc_fun(U_2029,tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool)),U_2027),hAPP(c_COMBB(tc_prod(U_2027,U_2029),tc_fun(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),tc_HOL_Obool),U_2029),c_member(tc_prod(U_2027,U_2029)))),c_Product__Type_OPair(U_2027,U_2029)))),U_2033))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2027,U_2029),tc_HOL_Obool),U_2031,U_2033) ),
inference(clausify,[status(thm)],[f_356_3]) ).
fof(f_357_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_357_2,plain,
! [U_2037,U_2036,U_2035,U_2034] :
( hBOOL(hAPP(hAPP(c_member(U_2034),U_2037),U_2036))
| ~ hBOOL(hAPP(hAPP(c_member(U_2034),U_2037),U_2035))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2034,tc_HOL_Obool),U_2035,U_2036) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2034),U_2037),U_2036))
| ~ hBOOL(hAPP(hAPP(c_member(U_2034),U_2037),U_2035))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2034,tc_HOL_Obool),U_2035,U_2036) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_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_358_2,plain,
! [U_2041,U_2040,U_2039,U_2038] :
( hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),U_2041))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2038,tc_HOL_Obool),U_2040,U_2041)
| ~ hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),U_2040)) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
cnf(f_358_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),U_2041))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2038,tc_HOL_Obool),U_2040,U_2041)
| ~ hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),U_2040)) ),
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_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_359_2,plain,
! [U_2045,U_2044,U_2043,U_2042] :
( hBOOL(hAPP(hAPP(c_member(U_2042),U_2045),U_2044))
| ~ hBOOL(hAPP(hAPP(c_member(U_2042),U_2045),U_2043))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2042,tc_HOL_Obool),U_2043,U_2044) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
cnf(f_359_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2042),U_2045),U_2044))
| ~ hBOOL(hAPP(hAPP(c_member(U_2042),U_2045),U_2043))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2042,tc_HOL_Obool),U_2043,U_2044) ),
inference(clausify,[status(thm)],[f_359_2]) ).
fof(f_360_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_360_2,plain,
! [U_2050,U_2049,U_2048,U_2047,U_2046] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2046,U_2049),tc_HOL_Obool),c_FuncSet_OPi(U_2046,U_2049,U_2048,U_2050),c_FuncSet_OPi(U_2046,U_2049,U_2047,U_2050))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2046,tc_HOL_Obool),U_2047,U_2048) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
cnf(f_360_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2046,U_2049),tc_HOL_Obool),c_FuncSet_OPi(U_2046,U_2049,U_2048,U_2050),c_FuncSet_OPi(U_2046,U_2049,U_2047,U_2050))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2046,tc_HOL_Obool),U_2047,U_2048) ),
inference(clausify,[status(thm)],[f_360_2]) ).
fof(f_361_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_361_2,plain,
! [U_2053,U_2052,U_2051] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2051,tc_HOL_Obool),c_Wellfounded_Oacc(U_2051,U_2053),c_Wellfounded_Oacc(U_2051,U_2052))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2051,U_2051),tc_HOL_Obool),U_2052,U_2053) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
cnf(f_361_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2051,tc_HOL_Obool),c_Wellfounded_Oacc(U_2051,U_2053),c_Wellfounded_Oacc(U_2051,U_2052))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2051,U_2051),tc_HOL_Obool),U_2052,U_2053) ),
inference(clausify,[status(thm)],[f_361_2]) ).
fof(f_362_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_362_2,plain,
! [U_2056,U_2055,U_2054] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2054,tc_HOL_Obool),c_Wellfounded_Oaccp(U_2054,U_2056),c_Wellfounded_Oaccp(U_2054,U_2055))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2054,tc_fun(U_2054,tc_HOL_Obool)),U_2055,U_2056) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
cnf(f_362_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2054,tc_HOL_Obool),c_Wellfounded_Oaccp(U_2054,U_2056),c_Wellfounded_Oaccp(U_2054,U_2055))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2054,tc_fun(U_2054,tc_HOL_Obool)),U_2055,U_2056) ),
inference(clausify,[status(thm)],[f_362_2]) ).
fof(f_363_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_363_2,plain,
! [U_2059,U_2058,U_2057] :
( c_Relation_Oantisym(U_2057,U_2058)
| ~ c_Relation_Oantisym(U_2057,U_2059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2057,U_2057),tc_HOL_Obool),U_2058,U_2059) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
( c_Relation_Oantisym(U_2057,U_2058)
| ~ c_Relation_Oantisym(U_2057,U_2059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2057,U_2057),tc_HOL_Obool),U_2058,U_2059) ),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_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_364_2,plain,
! [U_2063,U_2062,U_2061,U_2060] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2060,tc_HOL_Obool),c_Relation_ODomain(U_2060,U_2061,U_2062),c_Relation_ODomain(U_2060,U_2061,U_2063))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2060,U_2061),tc_HOL_Obool),U_2062,U_2063) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
cnf(f_364_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2060,tc_HOL_Obool),c_Relation_ODomain(U_2060,U_2061,U_2062),c_Relation_ODomain(U_2060,U_2061,U_2063))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2060,U_2061),tc_HOL_Obool),U_2062,U_2063) ),
inference(clausify,[status(thm)],[f_364_2]) ).
fof(f_365_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_365_2,plain,
! [U_2066,U_2065,U_2064] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2064,U_2065),c_Transitive__Closure_Ortrancl(U_2064,U_2066))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2065,c_Transitive__Closure_Ortrancl(U_2064,U_2066)) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
cnf(f_365_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2064,U_2065),c_Transitive__Closure_Ortrancl(U_2064,U_2066))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2064,U_2064),tc_HOL_Obool),U_2065,c_Transitive__Closure_Ortrancl(U_2064,U_2066)) ),
inference(clausify,[status(thm)],[f_365_2]) ).
fof(f_366_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_366_2,plain,
! [U_2069,U_2068,U_2067] :
( c_Transitive__Closure_Ortrancl(U_2067,U_2069) = c_Transitive__Closure_Ortrancl(U_2067,U_2068)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),U_2069,c_Transitive__Closure_Ortrancl(U_2067,U_2068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),U_2068,U_2069) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
cnf(f_366_3,plain,
( c_Transitive__Closure_Ortrancl(U_2067,U_2069) = c_Transitive__Closure_Ortrancl(U_2067,U_2068)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),U_2069,c_Transitive__Closure_Ortrancl(U_2067,U_2068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2067,U_2067),tc_HOL_Obool),U_2068,U_2069) ),
inference(clausify,[status(thm)],[f_366_2]) ).
fof(f_367_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_367_2,plain,
! [U_2072,U_2071,U_2070] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2070,U_2070),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2070,U_2071),c_Transitive__Closure_Ortrancl(U_2070,U_2072))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2070,U_2070),tc_HOL_Obool),U_2071,U_2072) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
cnf(f_367_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2070,U_2070),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(U_2070,U_2071),c_Transitive__Closure_Ortrancl(U_2070,U_2072))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2070,U_2070),tc_HOL_Obool),U_2071,U_2072) ),
inference(clausify,[status(thm)],[f_367_2]) ).
fof(f_368_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_368_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_368_1]) ).
cnf(f_368_3,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_368_2]) ).
fof(f_369_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_369_2,plain,
! [U_2078,U_2077,U_2076] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2076,tc_fun(U_2076,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(U_2076,U_2077),c_Transitive__Closure_Ortranclp(U_2076,U_2078))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2076,tc_fun(U_2076,tc_HOL_Obool)),U_2077,U_2078) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2076,tc_fun(U_2076,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(U_2076,U_2077),c_Transitive__Closure_Ortranclp(U_2076,U_2078))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2076,tc_fun(U_2076,tc_HOL_Obool)),U_2077,U_2078) ),
inference(clausify,[status(thm)],[f_369_2]) ).
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_2083,U_2082,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_2082),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2079,tc_HOL_Obool),U_2081,U_2083))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool),U_2082,U_2083)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool),U_2080,U_2081) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,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_2082),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2079,tc_HOL_Obool),U_2081,U_2083))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool),U_2082,U_2083)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool),U_2080,U_2081) ),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_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_371_2,plain,
! [U_2087,U_2086,U_2085,U_2084] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool),U_2085,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2084,tc_HOL_Obool),U_2086,U_2087))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool),U_2085,U_2087)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool),U_2085,U_2086) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool),U_2085,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2084,tc_HOL_Obool),U_2086,U_2087))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool),U_2085,U_2087)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool),U_2085,U_2086) ),
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_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_372_2,plain,
! [U_2090,U_2089,U_2088] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2088,tc_HOL_Obool),U_2090,U_2089) = U_2089
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2090) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2088,tc_HOL_Obool),U_2090,U_2089) = U_2089
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2088,tc_HOL_Obool),U_2089,U_2090) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_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_373_2,plain,
! [U_2093,U_2092,U_2091] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2091,tc_HOL_Obool),U_2092,U_2093) = U_2092
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2091,tc_HOL_Obool),U_2092,U_2093) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2091,tc_HOL_Obool),U_2092,U_2093) = U_2092
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2091,tc_HOL_Obool),U_2092,U_2093) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_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_374_2,plain,
! [U_2096,U_2095,U_2094] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2094,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2094,tc_HOL_Obool),U_2095,U_2096),U_2096),
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2094,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2094,tc_HOL_Obool),U_2095,U_2096),U_2096),
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_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_375_2,plain,
! [U_2099,U_2098,U_2097] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2097,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2097,tc_HOL_Obool),U_2098,U_2099),U_2098),
inference(variable_rename,[status(thm)],[f_375_1]) ).
cnf(f_375_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2097,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2097,tc_HOL_Obool),U_2098,U_2099),U_2098),
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_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_376_2,plain,
! [U_2102,U_2101,U_2100] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2100,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2100,tc_fun(U_2100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2100)),U_2101),hAPP(hAPP(c_COMBC(U_2100,tc_fun(U_2100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2100)),U_2102))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2100,tc_HOL_Obool),U_2101,U_2102) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2100,tc_HOL_Obool),U_2101,U_2102)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2100,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2100,tc_fun(U_2100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2100)),U_2101),hAPP(hAPP(c_COMBC(U_2100,tc_fun(U_2100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2100)),U_2102)) ) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
( ! [U_2108,U_2106,U_2104] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2104,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2104,tc_fun(U_2104,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2104)),U_2106),hAPP(hAPP(c_COMBC(U_2104,tc_fun(U_2104,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2104)),U_2108))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2104,tc_HOL_Obool),U_2106,U_2108) )
& ! [U_2107,U_2105,U_2103] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2103,tc_HOL_Obool),U_2105,U_2107)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2103,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2103,tc_fun(U_2103,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2103)),U_2105),hAPP(hAPP(c_COMBC(U_2103,tc_fun(U_2103,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2103)),U_2107)) ) ),
inference(miniscope,[status(thm)],[f_376_2]) ).
cnf(f_376_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2103,tc_HOL_Obool),U_2105,U_2107)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2103,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2103,tc_fun(U_2103,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2103)),U_2105),hAPP(hAPP(c_COMBC(U_2103,tc_fun(U_2103,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2103)),U_2107)) ),
inference(clausify,[status(thm)],[f_376_3]) ).
cnf(f_376_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2104,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_2104,tc_fun(U_2104,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2104)),U_2106),hAPP(hAPP(c_COMBC(U_2104,tc_fun(U_2104,tc_HOL_Obool),tc_HOL_Obool),c_member(U_2104)),U_2108))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2104,tc_HOL_Obool),U_2106,U_2108) ),
inference(clausify,[status(thm)],[f_376_3]) ).
fof(f_377_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_377_2,plain,
! [U_2112,U_2111,U_2110,U_2109] :
( c_Relation_Osingle__valued(U_2109,U_2110,U_2111)
| ~ c_Relation_Osingle__valued(U_2109,U_2110,U_2112)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2109,U_2110),tc_HOL_Obool),U_2111,U_2112) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
( c_Relation_Osingle__valued(U_2109,U_2110,U_2111)
| ~ c_Relation_Osingle__valued(U_2109,U_2110,U_2112)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2109,U_2110),tc_HOL_Obool),U_2111,U_2112) ),
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_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_378_2,plain,
! [U_2115,U_2114,U_2113] :
( c_Wellfounded_Oacyclic(U_2113,U_2115)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2113,U_2113),tc_HOL_Obool),U_2115,U_2114)
| ~ c_Wellfounded_Oacyclic(U_2113,U_2114) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
( c_Wellfounded_Oacyclic(U_2113,U_2115)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2113,U_2113),tc_HOL_Obool),U_2115,U_2114)
| ~ c_Wellfounded_Oacyclic(U_2113,U_2114) ),
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_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_379_2,plain,
! [U_2118,U_2117,U_2116] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2116,tc_HOL_Obool),U_2117,c_Set_Oinsert(U_2116,U_2118,U_2117)),
inference(variable_rename,[status(thm)],[f_379_1]) ).
cnf(f_379_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2116,tc_HOL_Obool),U_2117,c_Set_Oinsert(U_2116,U_2118,U_2117)),
inference(clausify,[status(thm)],[f_379_2]) ).
fof(f_380_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_380_2,plain,
! [U_2122,U_2121,U_2120,U_2119] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2119,tc_HOL_Obool),U_2120,c_Set_Oinsert(U_2119,U_2122,U_2121))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2119,tc_HOL_Obool),U_2120,U_2121) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2119,tc_HOL_Obool),U_2120,c_Set_Oinsert(U_2119,U_2122,U_2121))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2119,tc_HOL_Obool),U_2120,U_2121) ),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_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_381_2,plain,
! [U_2126,U_2125,U_2124,U_2123] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2123,tc_HOL_Obool),c_Set_Oinsert(U_2123,U_2126,U_2124),c_Set_Oinsert(U_2123,U_2126,U_2125))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2123,tc_HOL_Obool),U_2124,U_2125) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2123,tc_HOL_Obool),c_Set_Oinsert(U_2123,U_2126,U_2124),c_Set_Oinsert(U_2123,U_2126,U_2125))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2123,tc_HOL_Obool),U_2124,U_2125) ),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_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_382_2,plain,
! [U_2130,U_2129,U_2128,U_2127] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2127,tc_HOL_Obool),c_Set_Oinsert(U_2127,U_2128,U_2129),U_2130)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2127,tc_HOL_Obool),U_2129,U_2130)
| ~ hBOOL(hAPP(hAPP(c_member(U_2127),U_2128),U_2130)) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2127,tc_HOL_Obool),U_2129,U_2130)
& hBOOL(hAPP(hAPP(c_member(U_2127),U_2128),U_2130)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2127,tc_HOL_Obool),c_Set_Oinsert(U_2127,U_2128,U_2129),U_2130) ) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
( ! [U_2138,U_2136,U_2134,U_2132] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2132,tc_HOL_Obool),c_Set_Oinsert(U_2132,U_2134,U_2136),U_2138)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2132,tc_HOL_Obool),U_2136,U_2138)
| ~ hBOOL(hAPP(hAPP(c_member(U_2132),U_2134),U_2138)) )
& ! [U_2137,U_2135,U_2133,U_2131] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2131,tc_HOL_Obool),U_2135,U_2137)
& hBOOL(hAPP(hAPP(c_member(U_2131),U_2133),U_2137)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2131,tc_HOL_Obool),c_Set_Oinsert(U_2131,U_2133,U_2135),U_2137) ) ),
inference(miniscope,[status(thm)],[f_382_2]) ).
cnf(f_382_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2131),U_2133),U_2137))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2131,tc_HOL_Obool),c_Set_Oinsert(U_2131,U_2133,U_2135),U_2137) ),
inference(clausify,[status(thm)],[f_382_3]) ).
cnf(f_382_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2131,tc_HOL_Obool),U_2135,U_2137)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2131,tc_HOL_Obool),c_Set_Oinsert(U_2131,U_2133,U_2135),U_2137) ),
inference(clausify,[status(thm)],[f_382_3]) ).
cnf(f_382_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2132,tc_HOL_Obool),c_Set_Oinsert(U_2132,U_2134,U_2136),U_2138)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2132,tc_HOL_Obool),U_2136,U_2138)
| ~ hBOOL(hAPP(hAPP(c_member(U_2132),U_2134),U_2138)) ),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_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_383_2,plain,
! [U_2142,U_2141,U_2140,U_2139] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,c_Set_Oinsert(U_2139,U_2140,U_2142))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,U_2142) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,U_2142)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,c_Set_Oinsert(U_2139,U_2140,U_2142)) ) )
| hBOOL(hAPP(hAPP(c_member(U_2139),U_2140),U_2141)) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
cnf(f_383_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,U_2142)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,c_Set_Oinsert(U_2139,U_2140,U_2142))
| hBOOL(hAPP(hAPP(c_member(U_2139),U_2140),U_2141)) ),
inference(clausify,[status(thm)],[f_383_2]) ).
cnf(f_383_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,c_Set_Oinsert(U_2139,U_2140,U_2142))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2139,tc_HOL_Obool),U_2141,U_2142)
| hBOOL(hAPP(hAPP(c_member(U_2139),U_2140),U_2141)) ),
inference(clausify,[status(thm)],[f_383_2]) ).
fof(f_384_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_384_2,plain,
! [U_2146,U_2145,U_2144,U_2143] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2143,U_2143)),U_2144),c_Transitive__Closure_Otrancl(U_2143,U_2146)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2143,U_2143),tc_HOL_Obool),U_2145,U_2146)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2143,U_2143)),U_2144),c_Transitive__Closure_Otrancl(U_2143,U_2145))) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2143,U_2143)),U_2144),c_Transitive__Closure_Otrancl(U_2143,U_2146)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2143,U_2143),tc_HOL_Obool),U_2145,U_2146)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2143,U_2143)),U_2144),c_Transitive__Closure_Otrancl(U_2143,U_2145))) ),
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_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_385_2,plain,
! [U_2151,U_2150,U_2149,U_2148,U_2147] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2147,U_2148)),U_2149),c_FuncSet_Oextensional(U_2147,U_2148,U_2151)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2147,tc_HOL_Obool),U_2150,U_2151)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2147,U_2148)),U_2149),c_FuncSet_Oextensional(U_2147,U_2148,U_2150))) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
cnf(f_385_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2147,U_2148)),U_2149),c_FuncSet_Oextensional(U_2147,U_2148,U_2151)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2147,tc_HOL_Obool),U_2150,U_2151)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2147,U_2148)),U_2149),c_FuncSet_Oextensional(U_2147,U_2148,U_2150))) ),
inference(clausify,[status(thm)],[f_385_2]) ).
fof(f_386_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_386_2,plain,
! [U_2157,U_2156,U_2155,U_2154] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2155,U_2154),U_2156,U_2157)
| ? [U_2153] : ~ c_Orderings_Oord__class_Oless__eq(U_2154,hAPP(U_2156,U_2153),hAPP(U_2157,U_2153)) )
& ( ! [U_2152] : c_Orderings_Oord__class_Oless__eq(U_2154,hAPP(U_2156,U_2152),hAPP(U_2157,U_2152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2155,U_2154),U_2156,U_2157) ) )
| ~ class_Orderings_Oord(U_2154) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
! [U_2157,U_2156,U_2155,U_2154] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2155,U_2154),U_2156,U_2157)
| ~ c_Orderings_Oord__class_Oless__eq(U_2154,hAPP(U_2156,sK102(U_2157,U_2156,U_2155,U_2154)),hAPP(U_2157,sK102(U_2157,U_2156,U_2155,U_2154))) )
& ( ! [U_2152] : c_Orderings_Oord__class_Oless__eq(U_2154,hAPP(U_2156,U_2152),hAPP(U_2157,U_2152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2155,U_2154),U_2156,U_2157) ) )
| ~ class_Orderings_Oord(U_2154) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_2153,sK102(U_2157,U_2156,U_2155,U_2154))],[f_386_2]) ).
cnf(f_386_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2154,hAPP(U_2156,U_2152),hAPP(U_2157,U_2152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2155,U_2154),U_2156,U_2157)
| ~ class_Orderings_Oord(U_2154) ),
inference(clausify,[status(thm)],[f_386_3]) ).
cnf(f_386_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2155,U_2154),U_2156,U_2157)
| ~ c_Orderings_Oord__class_Oless__eq(U_2154,hAPP(U_2156,sK102(U_2157,U_2156,U_2155,U_2154)),hAPP(U_2157,sK102(U_2157,U_2156,U_2155,U_2154)))
| ~ class_Orderings_Oord(U_2154) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_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_387_2,plain,
! [U_2160,U_2159,U_2158] :
( c_Orderings_Oord__class_Oless__eq(U_2158,U_2160,U_2159)
| c_Orderings_Oord__class_Oless__eq(U_2158,U_2159,U_2160)
| ~ class_Orderings_Olinorder(U_2158) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2158,U_2160,U_2159)
| c_Orderings_Oord__class_Oless__eq(U_2158,U_2159,U_2160)
| ~ class_Orderings_Olinorder(U_2158) ),
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_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_388_2,plain,
! [U_2163,U_2162,U_2161] :
( ( ( U_2162 = U_2163
| ~ c_Orderings_Oord__class_Oless__eq(U_2161,U_2163,U_2162)
| ~ c_Orderings_Oord__class_Oless__eq(U_2161,U_2162,U_2163) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_2161,U_2163,U_2162)
& c_Orderings_Oord__class_Oless__eq(U_2161,U_2162,U_2163) )
| U_2162 != U_2163 ) )
| ~ class_Orderings_Oorder(U_2161) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2161,U_2162,U_2163)
| U_2162 != U_2163
| ~ class_Orderings_Oorder(U_2161) ),
inference(clausify,[status(thm)],[f_388_2]) ).
cnf(f_388_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2161,U_2163,U_2162)
| U_2162 != U_2163
| ~ class_Orderings_Oorder(U_2161) ),
inference(clausify,[status(thm)],[f_388_2]) ).
cnf(f_388_5,plain,
( U_2162 = U_2163
| ~ c_Orderings_Oord__class_Oless__eq(U_2161,U_2163,U_2162)
| ~ c_Orderings_Oord__class_Oless__eq(U_2161,U_2162,U_2163)
| ~ class_Orderings_Oorder(U_2161) ),
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_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_389_2,plain,
! [U_2166,U_2165,U_2164] :
( c_Orderings_Oord__class_Oless__eq(U_2164,U_2165,U_2166)
| U_2165 != U_2166
| ~ class_Orderings_Opreorder(U_2164) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2164,U_2165,U_2166)
| U_2165 != U_2166
| ~ class_Orderings_Opreorder(U_2164) ),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_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_390_2,plain,
! [U_2171,U_2170,U_2169,U_2168,U_2167] :
( c_Orderings_Oord__class_Oless__eq(U_2167,hAPP(U_2169,U_2171),hAPP(U_2170,U_2171))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2168,U_2167),U_2169,U_2170)
| ~ class_Orderings_Oord(U_2167) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
cnf(f_390_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2167,hAPP(U_2169,U_2171),hAPP(U_2170,U_2171))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2168,U_2167),U_2169,U_2170)
| ~ class_Orderings_Oord(U_2167) ),
inference(clausify,[status(thm)],[f_390_2]) ).
fof(f_391_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_391_2,plain,
! [U_2174,U_2173,U_2172] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2172,U_2174,U_2173)
| U_2174 != U_2173 )
& ( U_2174 = U_2173
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2174,U_2173) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2173,U_2174)
| ~ class_Orderings_Oorder(U_2172) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( U_2174 = U_2173
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2174,U_2173)
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2173,U_2174)
| ~ class_Orderings_Oorder(U_2172) ),
inference(clausify,[status(thm)],[f_391_2]) ).
cnf(f_391_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2172,U_2174,U_2173)
| U_2174 != U_2173
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2173,U_2174)
| ~ class_Orderings_Oorder(U_2172) ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_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_392_2,plain,
! [U_2178,U_2177,U_2176,U_2175] :
( c_Orderings_Oord__class_Oless__eq(U_2175,U_2176,U_2178)
| ~ c_Orderings_Oord__class_Oless__eq(U_2175,U_2177,U_2178)
| U_2176 != U_2177
| ~ class_Orderings_Oord(U_2175) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2175,U_2176,U_2178)
| ~ c_Orderings_Oord__class_Oless__eq(U_2175,U_2177,U_2178)
| U_2176 != U_2177
| ~ class_Orderings_Oord(U_2175) ),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_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_393_2,plain,
! [U_2182,U_2181,U_2180,U_2179] :
( c_Orderings_Oord__class_Oless__eq(U_2179,U_2182,U_2180)
| ~ c_Orderings_Oord__class_Oless__eq(U_2179,U_2182,U_2181)
| U_2180 != U_2181
| ~ class_Orderings_Oorder(U_2179) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2179,U_2182,U_2180)
| ~ c_Orderings_Oord__class_Oless__eq(U_2179,U_2182,U_2181)
| U_2180 != U_2181
| ~ class_Orderings_Oorder(U_2179) ),
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_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_394_2,plain,
! [U_2186,U_2185,U_2184,U_2183] :
( c_Orderings_Oord__class_Oless__eq(U_2183,U_2184,U_2186)
| U_2185 != U_2186
| ~ c_Orderings_Oord__class_Oless__eq(U_2183,U_2184,U_2185)
| ~ class_Orderings_Oord(U_2183) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
cnf(f_394_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2183,U_2184,U_2186)
| U_2185 != U_2186
| ~ c_Orderings_Oord__class_Oless__eq(U_2183,U_2184,U_2185)
| ~ class_Orderings_Oord(U_2183) ),
inference(clausify,[status(thm)],[f_394_2]) ).
fof(f_395_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_395_2,plain,
! [U_2190,U_2189,U_2188,U_2187] :
( c_Orderings_Oord__class_Oless__eq(U_2187,U_2190,U_2189)
| U_2188 != U_2190
| ~ c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189)
| ~ class_Orderings_Oorder(U_2187) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2187,U_2190,U_2189)
| U_2188 != U_2190
| ~ c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189)
| ~ class_Orderings_Oorder(U_2187) ),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_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_396_2,plain,
! [U_2193,U_2192,U_2191] :
( U_2192 = U_2193
| ~ c_Orderings_Oord__class_Oless__eq(U_2191,U_2193,U_2192)
| ~ c_Orderings_Oord__class_Oless__eq(U_2191,U_2192,U_2193)
| ~ class_Orderings_Oorder(U_2191) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( U_2192 = U_2193
| ~ c_Orderings_Oord__class_Oless__eq(U_2191,U_2193,U_2192)
| ~ c_Orderings_Oord__class_Oless__eq(U_2191,U_2192,U_2193)
| ~ class_Orderings_Oorder(U_2191) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_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_397_2,plain,
! [U_2197,U_2196,U_2195,U_2194] :
( c_Orderings_Oord__class_Oless__eq(U_2194,U_2195,U_2197)
| ~ c_Orderings_Oord__class_Oless__eq(U_2194,U_2196,U_2197)
| ~ c_Orderings_Oord__class_Oless__eq(U_2194,U_2195,U_2196)
| ~ class_Orderings_Opreorder(U_2194) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2194,U_2195,U_2197)
| ~ c_Orderings_Oord__class_Oless__eq(U_2194,U_2196,U_2197)
| ~ c_Orderings_Oord__class_Oless__eq(U_2194,U_2195,U_2196)
| ~ class_Orderings_Opreorder(U_2194) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_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_398_2,plain,
! [U_2200,U_2199,U_2198] :
( U_2200 = U_2199
| ~ c_Orderings_Oord__class_Oless__eq(U_2198,U_2200,U_2199)
| ~ c_Orderings_Oord__class_Oless__eq(U_2198,U_2199,U_2200)
| ~ class_Orderings_Oorder(U_2198) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
( U_2200 = U_2199
| ~ c_Orderings_Oord__class_Oless__eq(U_2198,U_2200,U_2199)
| ~ c_Orderings_Oord__class_Oless__eq(U_2198,U_2199,U_2200)
| ~ class_Orderings_Oorder(U_2198) ),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_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_399_2,plain,
! [U_2204,U_2203,U_2202,U_2201] :
( c_Orderings_Oord__class_Oless__eq(U_2201,U_2204,U_2203)
| ~ c_Orderings_Oord__class_Oless__eq(U_2201,U_2204,U_2202)
| ~ c_Orderings_Oord__class_Oless__eq(U_2201,U_2202,U_2203)
| ~ class_Orderings_Oorder(U_2201) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
cnf(f_399_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2201,U_2204,U_2203)
| ~ c_Orderings_Oord__class_Oless__eq(U_2201,U_2204,U_2202)
| ~ c_Orderings_Oord__class_Oless__eq(U_2201,U_2202,U_2203)
| ~ class_Orderings_Oorder(U_2201) ),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_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_400_2,plain,
! [U_2209,U_2208,U_2207,U_2206,U_2205] :
( c_Orderings_Oord__class_Oless__eq(U_2205,hAPP(U_2207,U_2209),hAPP(U_2208,U_2209))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2206,U_2205),U_2207,U_2208)
| ~ class_Orderings_Oord(U_2205) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2205,hAPP(U_2207,U_2209),hAPP(U_2208,U_2209))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2206,U_2205),U_2207,U_2208)
| ~ class_Orderings_Oord(U_2205) ),
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_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_401_2,plain,
! [U_2212,U_2211,U_2210] :
( c_Orderings_Oord__class_Oless__eq(U_2210,U_2212,U_2211)
| c_Orderings_Oord__class_Oless__eq(U_2210,U_2211,U_2212)
| ~ class_Orderings_Olinorder(U_2210) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2210,U_2212,U_2211)
| c_Orderings_Oord__class_Oless__eq(U_2210,U_2211,U_2212)
| ~ class_Orderings_Olinorder(U_2210) ),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_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_402_2,plain,
! [U_2214,U_2213] :
( ~ c_Orderings_Oord__class_Oless(U_2213,U_2214,U_2214)
| ~ class_Orderings_Opreorder(U_2213) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
cnf(f_402_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2213,U_2214,U_2214)
| ~ class_Orderings_Opreorder(U_2213) ),
inference(clausify,[status(thm)],[f_402_2]) ).
fof(f_403_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_403_2,plain,
! [U_2217,U_2216,U_2215] :
( ( ( U_2216 != U_2217
| ( ~ c_Orderings_Oord__class_Oless(U_2215,U_2217,U_2216)
& ~ c_Orderings_Oord__class_Oless(U_2215,U_2216,U_2217) ) )
& ( c_Orderings_Oord__class_Oless(U_2215,U_2217,U_2216)
| c_Orderings_Oord__class_Oless(U_2215,U_2216,U_2217)
| U_2216 = U_2217 ) )
| ~ class_Orderings_Olinorder(U_2215) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
( c_Orderings_Oord__class_Oless(U_2215,U_2217,U_2216)
| c_Orderings_Oord__class_Oless(U_2215,U_2216,U_2217)
| U_2216 = U_2217
| ~ class_Orderings_Olinorder(U_2215) ),
inference(clausify,[status(thm)],[f_403_2]) ).
cnf(f_403_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2215,U_2216,U_2217)
| U_2216 != U_2217
| ~ class_Orderings_Olinorder(U_2215) ),
inference(clausify,[status(thm)],[f_403_2]) ).
cnf(f_403_5,plain,
( ~ c_Orderings_Oord__class_Oless(U_2215,U_2217,U_2216)
| U_2216 != U_2217
| ~ class_Orderings_Olinorder(U_2215) ),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_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_404_2,plain,
! [U_2220,U_2219,U_2218] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2218,U_2219,U_2220)
| ( U_2219 != U_2220
& ~ c_Orderings_Oord__class_Oless(U_2218,U_2220,U_2219) ) )
& ( U_2219 = U_2220
| c_Orderings_Oord__class_Oless(U_2218,U_2220,U_2219)
| c_Orderings_Oord__class_Oless(U_2218,U_2219,U_2220) ) )
| ~ class_Orderings_Olinorder(U_2218) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
cnf(f_404_3,plain,
( U_2219 = U_2220
| c_Orderings_Oord__class_Oless(U_2218,U_2220,U_2219)
| c_Orderings_Oord__class_Oless(U_2218,U_2219,U_2220)
| ~ class_Orderings_Olinorder(U_2218) ),
inference(clausify,[status(thm)],[f_404_2]) ).
cnf(f_404_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2218,U_2220,U_2219)
| ~ c_Orderings_Oord__class_Oless(U_2218,U_2219,U_2220)
| ~ class_Orderings_Olinorder(U_2218) ),
inference(clausify,[status(thm)],[f_404_2]) ).
cnf(f_404_5,plain,
( U_2219 != U_2220
| ~ c_Orderings_Oord__class_Oless(U_2218,U_2219,U_2220)
| ~ class_Orderings_Olinorder(U_2218) ),
inference(clausify,[status(thm)],[f_404_2]) ).
fof(f_405_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_405_2,plain,
! [U_2223,U_2222,U_2221] :
( c_Orderings_Oord__class_Oless(U_2221,U_2223,U_2222)
| U_2222 = U_2223
| c_Orderings_Oord__class_Oless(U_2221,U_2222,U_2223)
| ~ class_Orderings_Olinorder(U_2221) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
( c_Orderings_Oord__class_Oless(U_2221,U_2223,U_2222)
| U_2222 = U_2223
| c_Orderings_Oord__class_Oless(U_2221,U_2222,U_2223)
| ~ class_Orderings_Olinorder(U_2221) ),
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_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_406_2,plain,
! [U_2226,U_2225,U_2224] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2224,U_2226,U_2225)
| U_2226 != U_2225 )
& ( U_2226 = U_2225
| c_Orderings_Oord__class_Oless(U_2224,U_2226,U_2225) ) )
| c_Orderings_Oord__class_Oless(U_2224,U_2225,U_2226)
| ~ class_Orderings_Olinorder(U_2224) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
( U_2226 = U_2225
| c_Orderings_Oord__class_Oless(U_2224,U_2226,U_2225)
| c_Orderings_Oord__class_Oless(U_2224,U_2225,U_2226)
| ~ class_Orderings_Olinorder(U_2224) ),
inference(clausify,[status(thm)],[f_406_2]) ).
cnf(f_406_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2224,U_2226,U_2225)
| U_2226 != U_2225
| c_Orderings_Oord__class_Oless(U_2224,U_2225,U_2226)
| ~ class_Orderings_Olinorder(U_2224) ),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_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_407_2,plain,
! [U_2229,U_2228,U_2227] :
( c_Orderings_Oord__class_Oless(U_2227,U_2229,U_2228)
| c_Orderings_Oord__class_Oless(U_2227,U_2228,U_2229)
| U_2228 = U_2229
| ~ class_Orderings_Olinorder(U_2227) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
cnf(f_407_3,plain,
( c_Orderings_Oord__class_Oless(U_2227,U_2229,U_2228)
| c_Orderings_Oord__class_Oless(U_2227,U_2228,U_2229)
| U_2228 = U_2229
| ~ class_Orderings_Olinorder(U_2227) ),
inference(clausify,[status(thm)],[f_407_2]) ).
fof(f_408_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_408_2,plain,
! [U_2232,U_2231,U_2230] :
( U_2231 != U_2232
| ~ c_Orderings_Oord__class_Oless(U_2230,U_2231,U_2232)
| ~ class_Orderings_Oorder(U_2230) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
cnf(f_408_3,plain,
( U_2231 != U_2232
| ~ c_Orderings_Oord__class_Oless(U_2230,U_2231,U_2232)
| ~ class_Orderings_Oorder(U_2230) ),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_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_409_2,plain,
! [U_2235,U_2234,U_2233] :
( ~ c_Orderings_Oord__class_Oless(U_2233,U_2235,U_2234)
| ~ c_Orderings_Oord__class_Oless(U_2233,U_2234,U_2235)
| ~ class_Orderings_Opreorder(U_2233) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2233,U_2235,U_2234)
| ~ c_Orderings_Oord__class_Oless(U_2233,U_2234,U_2235)
| ~ class_Orderings_Opreorder(U_2233) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_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_410_2,plain,
! [U_2238,U_2237,U_2236] :
( ~ c_Orderings_Oord__class_Oless(U_2236,U_2238,U_2237)
| ~ c_Orderings_Oord__class_Oless(U_2236,U_2237,U_2238)
| ~ class_Orderings_Opreorder(U_2236) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
cnf(f_410_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2236,U_2238,U_2237)
| ~ c_Orderings_Oord__class_Oless(U_2236,U_2237,U_2238)
| ~ class_Orderings_Opreorder(U_2236) ),
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_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_411_2,plain,
! [U_2241,U_2240,U_2239] :
( U_2240 != U_2241
| ~ c_Orderings_Oord__class_Oless(U_2239,U_2240,U_2241)
| ~ class_Orderings_Oorder(U_2239) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( U_2240 != U_2241
| ~ c_Orderings_Oord__class_Oless(U_2239,U_2240,U_2241)
| ~ class_Orderings_Oorder(U_2239) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_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_412_2,plain,
! [U_2244,U_2243,U_2242] :
( U_2244 != U_2243
| ~ c_Orderings_Oord__class_Oless(U_2242,U_2243,U_2244)
| ~ class_Orderings_Oorder(U_2242) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( U_2244 != U_2243
| ~ c_Orderings_Oord__class_Oless(U_2242,U_2243,U_2244)
| ~ class_Orderings_Oorder(U_2242) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_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_413_2,plain,
! [U_2247,U_2246,U_2245] :
( ~ c_Orderings_Oord__class_Oless(U_2245,U_2247,U_2246)
| ~ c_Orderings_Oord__class_Oless(U_2245,U_2246,U_2247)
| ~ class_Orderings_Opreorder(U_2245) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
cnf(f_413_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2245,U_2247,U_2246)
| ~ c_Orderings_Oord__class_Oless(U_2245,U_2246,U_2247)
| ~ class_Orderings_Opreorder(U_2245) ),
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_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_414_2,plain,
! [U_2250,U_2249,U_2248] :
( ~ c_Orderings_Oord__class_Oless(U_2248,U_2250,U_2249)
| ~ c_Orderings_Oord__class_Oless(U_2248,U_2249,U_2250)
| ~ class_Orderings_Oorder(U_2248) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2248,U_2250,U_2249)
| ~ c_Orderings_Oord__class_Oless(U_2248,U_2249,U_2250)
| ~ class_Orderings_Oorder(U_2248) ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_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_415_2,plain,
! [U_2254,U_2253,U_2252,U_2251] :
( c_Orderings_Oord__class_Oless(U_2251,U_2252,U_2254)
| ~ c_Orderings_Oord__class_Oless(U_2251,U_2253,U_2254)
| U_2252 != U_2253
| ~ class_Orderings_Oord(U_2251) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( c_Orderings_Oord__class_Oless(U_2251,U_2252,U_2254)
| ~ c_Orderings_Oord__class_Oless(U_2251,U_2253,U_2254)
| U_2252 != U_2253
| ~ class_Orderings_Oord(U_2251) ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_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_416_2,plain,
! [U_2258,U_2257,U_2256,U_2255] :
( c_Orderings_Oord__class_Oless(U_2255,U_2258,U_2256)
| ~ c_Orderings_Oord__class_Oless(U_2255,U_2258,U_2257)
| U_2256 != U_2257
| ~ class_Orderings_Oorder(U_2255) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
( c_Orderings_Oord__class_Oless(U_2255,U_2258,U_2256)
| ~ c_Orderings_Oord__class_Oless(U_2255,U_2258,U_2257)
| U_2256 != U_2257
| ~ class_Orderings_Oorder(U_2255) ),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_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_417_2,plain,
! [U_2262,U_2261,U_2260,U_2259] :
( c_Orderings_Oord__class_Oless(U_2259,U_2260,U_2262)
| U_2261 != U_2262
| ~ c_Orderings_Oord__class_Oless(U_2259,U_2260,U_2261)
| ~ class_Orderings_Oord(U_2259) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
cnf(f_417_3,plain,
( c_Orderings_Oord__class_Oless(U_2259,U_2260,U_2262)
| U_2261 != U_2262
| ~ c_Orderings_Oord__class_Oless(U_2259,U_2260,U_2261)
| ~ class_Orderings_Oord(U_2259) ),
inference(clausify,[status(thm)],[f_417_2]) ).
fof(f_418_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_418_2,plain,
! [U_2266,U_2265,U_2264,U_2263] :
( c_Orderings_Oord__class_Oless(U_2263,U_2266,U_2265)
| U_2264 != U_2266
| ~ c_Orderings_Oord__class_Oless(U_2263,U_2264,U_2265)
| ~ class_Orderings_Oorder(U_2263) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
cnf(f_418_3,plain,
( c_Orderings_Oord__class_Oless(U_2263,U_2266,U_2265)
| U_2264 != U_2266
| ~ c_Orderings_Oord__class_Oless(U_2263,U_2264,U_2265)
| ~ class_Orderings_Oorder(U_2263) ),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_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_419_2,plain,
! [U_2270,U_2269,U_2268,U_2267] :
( c_Orderings_Oord__class_Oless(U_2267,U_2268,U_2270)
| ~ c_Orderings_Oord__class_Oless(U_2267,U_2269,U_2270)
| ~ c_Orderings_Oord__class_Oless(U_2267,U_2268,U_2269)
| ~ class_Orderings_Opreorder(U_2267) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( c_Orderings_Oord__class_Oless(U_2267,U_2268,U_2270)
| ~ c_Orderings_Oord__class_Oless(U_2267,U_2269,U_2270)
| ~ c_Orderings_Oord__class_Oless(U_2267,U_2268,U_2269)
| ~ class_Orderings_Opreorder(U_2267) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_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_420_2,plain,
! [U_2274,U_2273,U_2272,U_2271] :
( c_Orderings_Oord__class_Oless(U_2271,U_2274,U_2273)
| ~ c_Orderings_Oord__class_Oless(U_2271,U_2274,U_2272)
| ~ c_Orderings_Oord__class_Oless(U_2271,U_2272,U_2273)
| ~ class_Orderings_Oorder(U_2271) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
( c_Orderings_Oord__class_Oless(U_2271,U_2274,U_2273)
| ~ c_Orderings_Oord__class_Oless(U_2271,U_2274,U_2272)
| ~ c_Orderings_Oord__class_Oless(U_2271,U_2272,U_2273)
| ~ class_Orderings_Oorder(U_2271) ),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_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_421_2,plain,
! [U_2277,U_2276,U_2275] :
( ~ c_Orderings_Oord__class_Oless(U_2275,U_2277,U_2276)
| ~ c_Orderings_Oord__class_Oless(U_2275,U_2276,U_2277)
| ~ class_Orderings_Opreorder(U_2275) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2275,U_2277,U_2276)
| ~ c_Orderings_Oord__class_Oless(U_2275,U_2276,U_2277)
| ~ class_Orderings_Opreorder(U_2275) ),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_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_422_2,plain,
! [U_2280,U_2279,U_2278] :
( c_Orderings_Oord__class_Oless(U_2278,U_2280,U_2279)
| U_2279 = U_2280
| c_Orderings_Oord__class_Oless(U_2278,U_2279,U_2280)
| ~ class_Orderings_Olinorder(U_2278) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
( c_Orderings_Oord__class_Oless(U_2278,U_2280,U_2279)
| U_2279 = U_2280
| c_Orderings_Oord__class_Oless(U_2278,U_2279,U_2280)
| ~ class_Orderings_Olinorder(U_2278) ),
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_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_423_2,plain,
! [U_2281] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2281,U_2281),
inference(variable_rename,[status(thm)],[f_423_1]) ).
cnf(f_423_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2281,U_2281),
inference(clausify,[status(thm)],[f_423_2]) ).
fof(f_424_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_424_2,plain,
! [U_2283,U_2282] :
( ( U_2282 != U_2283
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2283,U_2282)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2282,U_2283) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2283,U_2282)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2282,U_2283)
| U_2282 = U_2283 ) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
( ! [U_2287,U_2285] :
( U_2285 != U_2287
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2287,U_2285)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2285,U_2287) ) )
& ! [U_2286,U_2284] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2286,U_2284)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2284,U_2286)
| U_2284 = U_2286 ) ),
inference(miniscope,[status(thm)],[f_424_2]) ).
cnf(f_424_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2286,U_2284)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2284,U_2286)
| U_2284 = U_2286 ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2285,U_2287)
| U_2285 != U_2287 ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2287,U_2285)
| U_2285 != U_2287 ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_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_425_2,plain,
! [U_2289,U_2288] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2289,U_2288)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2288,U_2289)
| U_2288 = U_2289 ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2289,U_2288)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2288,U_2289)
| U_2288 = U_2289 ),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_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_426_2,plain,
! [U_2290] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2290,U_2290),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2290,U_2290),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_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_427_2,plain,
! [U_2292,U_2291] :
( U_2292 != U_2291
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2291,U_2292) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
cnf(f_427_3,plain,
( U_2292 != U_2291
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_427_2]) ).
fof(f_428_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_428_2,plain,
! [U_2294,U_2293] :
( U_2293 != U_2294
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2293,U_2294) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
cnf(f_428_3,plain,
( U_2293 != U_2294
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2293,U_2294) ),
inference(clausify,[status(thm)],[f_428_2]) ).
fof(f_429_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_429_2,plain,
! [U_2297,U_2296,U_2295] :
( hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| ( ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2296,U_2295) )
| ( ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
& U_2295 = U_2296 )
| ( ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2295,U_2296) ) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2296,U_2295)
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| U_2295 = U_2296
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2295,U_2296) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_4,plain,
( ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| U_2295 = U_2296
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2295,U_2296) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2296,U_2295)
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2295,U_2296) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_6,plain,
( ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2295,U_2296) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2296,U_2295)
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| U_2295 = U_2296
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_8,plain,
( ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| U_2295 = U_2296
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2296,U_2295)
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_10,plain,
( ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295))
| ~ hBOOL(hAPP(hAPP(U_2297,U_2296),U_2295)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_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_430_2,plain,
! [U_2298] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2298,U_2298),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2298,U_2298),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_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_431_2,plain,
! [U_2300,U_2299] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2300,U_2299)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2299,U_2300) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2300,U_2299)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2299,U_2300) ),
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_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_432_2,plain,
! [U_2302,U_2301] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2301,U_2302)
| U_2301 != U_2302 ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2301,U_2302)
| U_2301 != U_2302 ),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_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_433_2,plain,
! [U_2305,U_2304,U_2303] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2303,U_2305)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2304,U_2305)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2303,U_2304) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2303,U_2305)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2304,U_2305)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2303,U_2304) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_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_434_2,plain,
! [U_2307,U_2306] :
( U_2306 = U_2307
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2307,U_2306)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2306,U_2307) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
cnf(f_434_3,plain,
( U_2306 = U_2307
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2307,U_2306)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2306,U_2307) ),
inference(clausify,[status(thm)],[f_434_2]) ).
fof(f_435_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_435_2,plain,
! [U_2311,U_2310,U_2309,U_2308] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2308,tc_HOL_Obool),c_Relation_ODomain(U_2308,U_2309,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2308,U_2309),tc_HOL_Obool),U_2310,U_2311)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2308,tc_HOL_Obool),c_Relation_ODomain(U_2308,U_2309,U_2310),c_Relation_ODomain(U_2308,U_2309,U_2311))),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2308,tc_HOL_Obool),c_Relation_ODomain(U_2308,U_2309,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2308,U_2309),tc_HOL_Obool),U_2310,U_2311)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2308,tc_HOL_Obool),c_Relation_ODomain(U_2308,U_2309,U_2310),c_Relation_ODomain(U_2308,U_2309,U_2311))),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_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_436_2,plain,
! [U_2315,U_2314,U_2313,U_2312] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2312,tc_HOL_Obool),c_Relation_ORange(U_2313,U_2312,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2313,U_2312),tc_HOL_Obool),U_2314,U_2315)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2312,tc_HOL_Obool),c_Relation_ORange(U_2313,U_2312,U_2314),c_Relation_ORange(U_2313,U_2312,U_2315))),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2312,tc_HOL_Obool),c_Relation_ORange(U_2313,U_2312,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_2313,U_2312),tc_HOL_Obool),U_2314,U_2315)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2312,tc_HOL_Obool),c_Relation_ORange(U_2313,U_2312,U_2314),c_Relation_ORange(U_2313,U_2312,U_2315))),
inference(clausify,[status(thm)],[f_436_2]) ).
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_2318,U_2317,U_2316] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2316,U_2317,U_2318)
| ~ c_Orderings_Oord__class_Oless__eq(U_2316,U_2318,U_2317) )
& ( c_Orderings_Oord__class_Oless__eq(U_2316,U_2318,U_2317)
| c_Orderings_Oord__class_Oless(U_2316,U_2317,U_2318) ) )
| ~ class_Orderings_Olinorder(U_2316) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2316,U_2318,U_2317)
| c_Orderings_Oord__class_Oless(U_2316,U_2317,U_2318)
| ~ class_Orderings_Olinorder(U_2316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2316,U_2317,U_2318)
| ~ c_Orderings_Oord__class_Oless__eq(U_2316,U_2318,U_2317)
| ~ class_Orderings_Olinorder(U_2316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
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_2321,U_2320,U_2319] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2319,U_2320,U_2321)
| ~ c_Orderings_Oord__class_Oless(U_2319,U_2321,U_2320) )
& ( c_Orderings_Oord__class_Oless(U_2319,U_2321,U_2320)
| c_Orderings_Oord__class_Oless__eq(U_2319,U_2320,U_2321) ) )
| ~ class_Orderings_Olinorder(U_2319) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( c_Orderings_Oord__class_Oless(U_2319,U_2321,U_2320)
| c_Orderings_Oord__class_Oless__eq(U_2319,U_2320,U_2321)
| ~ class_Orderings_Olinorder(U_2319) ),
inference(clausify,[status(thm)],[f_438_2]) ).
cnf(f_438_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2319,U_2320,U_2321)
| ~ c_Orderings_Oord__class_Oless(U_2319,U_2321,U_2320)
| ~ class_Orderings_Olinorder(U_2319) ),
inference(clausify,[status(thm)],[f_438_2]) ).
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_2324,U_2323,U_2322] :
( c_Orderings_Oord__class_Oless(U_2322,U_2324,U_2323)
| c_Orderings_Oord__class_Oless__eq(U_2322,U_2323,U_2324)
| ~ class_Orderings_Olinorder(U_2322) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( c_Orderings_Oord__class_Oless(U_2322,U_2324,U_2323)
| c_Orderings_Oord__class_Oless__eq(U_2322,U_2323,U_2324)
| ~ class_Orderings_Olinorder(U_2322) ),
inference(clausify,[status(thm)],[f_439_2]) ).
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_2327,U_2326,U_2325] :
( ( ( c_Orderings_Oord__class_Oless(U_2325,U_2326,U_2327)
| U_2326 = U_2327
| ~ c_Orderings_Oord__class_Oless__eq(U_2325,U_2326,U_2327) )
& ( ( U_2326 != U_2327
& c_Orderings_Oord__class_Oless__eq(U_2325,U_2326,U_2327) )
| ~ c_Orderings_Oord__class_Oless(U_2325,U_2326,U_2327) ) )
| ~ class_Orderings_Oorder(U_2325) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2325,U_2326,U_2327)
| ~ c_Orderings_Oord__class_Oless(U_2325,U_2326,U_2327)
| ~ class_Orderings_Oorder(U_2325) ),
inference(clausify,[status(thm)],[f_440_2]) ).
cnf(f_440_4,plain,
( U_2326 != U_2327
| ~ c_Orderings_Oord__class_Oless(U_2325,U_2326,U_2327)
| ~ class_Orderings_Oorder(U_2325) ),
inference(clausify,[status(thm)],[f_440_2]) ).
cnf(f_440_5,plain,
( c_Orderings_Oord__class_Oless(U_2325,U_2326,U_2327)
| U_2326 = U_2327
| ~ c_Orderings_Oord__class_Oless__eq(U_2325,U_2326,U_2327)
| ~ class_Orderings_Oorder(U_2325) ),
inference(clausify,[status(thm)],[f_440_2]) ).
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_2330,U_2329,U_2328] :
( ( ( c_Orderings_Oord__class_Oless(U_2328,U_2329,U_2330)
| c_Orderings_Oord__class_Oless__eq(U_2328,U_2330,U_2329)
| ~ c_Orderings_Oord__class_Oless__eq(U_2328,U_2329,U_2330) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2328,U_2330,U_2329)
& c_Orderings_Oord__class_Oless__eq(U_2328,U_2329,U_2330) )
| ~ c_Orderings_Oord__class_Oless(U_2328,U_2329,U_2330) ) )
| ~ class_Orderings_Opreorder(U_2328) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
cnf(f_441_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2328,U_2329,U_2330)
| ~ c_Orderings_Oord__class_Oless(U_2328,U_2329,U_2330)
| ~ class_Orderings_Opreorder(U_2328) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2328,U_2330,U_2329)
| ~ c_Orderings_Oord__class_Oless(U_2328,U_2329,U_2330)
| ~ class_Orderings_Opreorder(U_2328) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_5,plain,
( c_Orderings_Oord__class_Oless(U_2328,U_2329,U_2330)
| c_Orderings_Oord__class_Oless__eq(U_2328,U_2330,U_2329)
| ~ c_Orderings_Oord__class_Oless__eq(U_2328,U_2329,U_2330)
| ~ class_Orderings_Opreorder(U_2328) ),
inference(clausify,[status(thm)],[f_441_2]) ).
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_2333,U_2332,U_2331] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2331,U_2332,U_2333)
| ( U_2332 != U_2333
& ~ c_Orderings_Oord__class_Oless(U_2331,U_2332,U_2333) ) )
& ( U_2332 = U_2333
| c_Orderings_Oord__class_Oless(U_2331,U_2332,U_2333)
| ~ c_Orderings_Oord__class_Oless__eq(U_2331,U_2332,U_2333) ) )
| ~ class_Orderings_Oorder(U_2331) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
cnf(f_442_3,plain,
( U_2332 = U_2333
| c_Orderings_Oord__class_Oless(U_2331,U_2332,U_2333)
| ~ c_Orderings_Oord__class_Oless__eq(U_2331,U_2332,U_2333)
| ~ class_Orderings_Oorder(U_2331) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2331,U_2332,U_2333)
| c_Orderings_Oord__class_Oless__eq(U_2331,U_2332,U_2333)
| ~ class_Orderings_Oorder(U_2331) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_5,plain,
( U_2332 != U_2333
| c_Orderings_Oord__class_Oless__eq(U_2331,U_2332,U_2333)
| ~ class_Orderings_Oorder(U_2331) ),
inference(clausify,[status(thm)],[f_442_2]) ).
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_2336,U_2335,U_2334] :
( c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2335)
| c_Orderings_Oord__class_Oless(U_2334,U_2335,U_2336)
| ~ class_Orderings_Olinorder(U_2334) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
cnf(f_443_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2335)
| c_Orderings_Oord__class_Oless(U_2334,U_2335,U_2336)
| ~ class_Orderings_Olinorder(U_2334) ),
inference(clausify,[status(thm)],[f_443_2]) ).
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_2339,U_2338,U_2337] :
( c_Orderings_Oord__class_Oless(U_2337,U_2339,U_2338)
| c_Orderings_Oord__class_Oless__eq(U_2337,U_2338,U_2339)
| ~ class_Orderings_Olinorder(U_2337) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( c_Orderings_Oord__class_Oless(U_2337,U_2339,U_2338)
| c_Orderings_Oord__class_Oless__eq(U_2337,U_2338,U_2339)
| ~ class_Orderings_Olinorder(U_2337) ),
inference(clausify,[status(thm)],[f_444_2]) ).
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_2342,U_2341,U_2340] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2340,U_2341,U_2342)
| U_2341 != U_2342 )
& ( U_2341 = U_2342
| ~ c_Orderings_Oord__class_Oless__eq(U_2340,U_2341,U_2342) ) )
| c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ class_Orderings_Olinorder(U_2340) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
( U_2341 = U_2342
| ~ c_Orderings_Oord__class_Oless__eq(U_2340,U_2341,U_2342)
| c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ class_Orderings_Olinorder(U_2340) ),
inference(clausify,[status(thm)],[f_445_2]) ).
cnf(f_445_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2340,U_2341,U_2342)
| U_2341 != U_2342
| c_Orderings_Oord__class_Oless(U_2340,U_2341,U_2342)
| ~ class_Orderings_Olinorder(U_2340) ),
inference(clausify,[status(thm)],[f_445_2]) ).
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_2345,U_2344,U_2343] :
( c_Orderings_Oord__class_Oless(U_2343,U_2344,U_2345)
| ~ c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345)
| U_2344 = U_2345
| ~ class_Orderings_Oorder(U_2343) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( c_Orderings_Oord__class_Oless(U_2343,U_2344,U_2345)
| ~ c_Orderings_Oord__class_Oless__eq(U_2343,U_2344,U_2345)
| U_2344 = U_2345
| ~ class_Orderings_Oorder(U_2343) ),
inference(clausify,[status(thm)],[f_446_2]) ).
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_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_2348,U_2347)
| U_2347 = U_2348
| ~ class_Orderings_Oorder(U_2346) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( c_Orderings_Oord__class_Oless(U_2346,U_2348,U_2347)
| ~ c_Orderings_Oord__class_Oless__eq(U_2346,U_2348,U_2347)
| U_2347 = U_2348
| ~ class_Orderings_Oorder(U_2346) ),
inference(clausify,[status(thm)],[f_447_2]) ).
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_2351,U_2350,U_2349] :
( ~ c_Orderings_Oord__class_Oless(U_2349,U_2351,U_2350)
| ~ c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351)
| ~ class_Orderings_Olinorder(U_2349) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
cnf(f_448_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2349,U_2351,U_2350)
| ~ c_Orderings_Oord__class_Oless__eq(U_2349,U_2350,U_2351)
| ~ class_Orderings_Olinorder(U_2349) ),
inference(clausify,[status(thm)],[f_448_2]) ).
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_2354,U_2353,U_2352] :
( 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_449_1]) ).
cnf(f_449_3,plain,
( 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(clausify,[status(thm)],[f_449_2]) ).
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_2357,U_2356,U_2355] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357)
| 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_Olinorder(U_2355) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,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)
| ~ class_Orderings_Olinorder(U_2355) ),
inference(clausify,[status(thm)],[f_450_2]) ).
cnf(f_450_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2355,U_2356,U_2357)
| U_2356 != U_2357
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,U_2356,U_2357)
| ~ class_Orderings_Olinorder(U_2355) ),
inference(clausify,[status(thm)],[f_450_2]) ).
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_2360,U_2359,U_2358] :
( U_2359 = U_2360
| c_Orderings_Oord__class_Oless(U_2358,U_2359,U_2360)
| ~ c_Orderings_Oord__class_Oless__eq(U_2358,U_2359,U_2360)
| ~ class_Orderings_Oorder(U_2358) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
( U_2359 = U_2360
| c_Orderings_Oord__class_Oless(U_2358,U_2359,U_2360)
| ~ c_Orderings_Oord__class_Oless__eq(U_2358,U_2359,U_2360)
| ~ class_Orderings_Oorder(U_2358) ),
inference(clausify,[status(thm)],[f_451_2]) ).
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_2363,U_2362,U_2361] :
( c_Orderings_Oord__class_Oless(U_2361,U_2362,U_2363)
| U_2362 = U_2363
| ~ c_Orderings_Oord__class_Oless__eq(U_2361,U_2362,U_2363)
| ~ class_Orderings_Oorder(U_2361) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,plain,
( c_Orderings_Oord__class_Oless(U_2361,U_2362,U_2363)
| U_2362 = U_2363
| ~ c_Orderings_Oord__class_Oless__eq(U_2361,U_2362,U_2363)
| ~ class_Orderings_Oorder(U_2361) ),
inference(clausify,[status(thm)],[f_452_2]) ).
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_2366,U_2365,U_2364] :
( c_Orderings_Oord__class_Oless(U_2364,U_2365,U_2366)
| U_2366 = U_2365
| ~ c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366)
| ~ class_Orderings_Oorder(U_2364) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
( c_Orderings_Oord__class_Oless(U_2364,U_2365,U_2366)
| U_2366 = U_2365
| ~ c_Orderings_Oord__class_Oless__eq(U_2364,U_2365,U_2366)
| ~ class_Orderings_Oorder(U_2364) ),
inference(clausify,[status(thm)],[f_453_2]) ).
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_2370,U_2369,U_2368,U_2367] :
( c_Orderings_Oord__class_Oless(U_2367,U_2368,U_2370)
| ~ c_Orderings_Oord__class_Oless__eq(U_2367,U_2369,U_2370)
| ~ c_Orderings_Oord__class_Oless(U_2367,U_2368,U_2369)
| ~ class_Orderings_Opreorder(U_2367) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
( c_Orderings_Oord__class_Oless(U_2367,U_2368,U_2370)
| ~ c_Orderings_Oord__class_Oless__eq(U_2367,U_2369,U_2370)
| ~ c_Orderings_Oord__class_Oless(U_2367,U_2368,U_2369)
| ~ class_Orderings_Opreorder(U_2367) ),
inference(clausify,[status(thm)],[f_454_2]) ).
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_2374,U_2373,U_2372,U_2371] :
( c_Orderings_Oord__class_Oless(U_2371,U_2374,U_2373)
| ~ c_Orderings_Oord__class_Oless__eq(U_2371,U_2374,U_2372)
| ~ c_Orderings_Oord__class_Oless(U_2371,U_2372,U_2373)
| ~ class_Orderings_Oorder(U_2371) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
cnf(f_455_3,plain,
( c_Orderings_Oord__class_Oless(U_2371,U_2374,U_2373)
| ~ c_Orderings_Oord__class_Oless__eq(U_2371,U_2374,U_2372)
| ~ c_Orderings_Oord__class_Oless(U_2371,U_2372,U_2373)
| ~ class_Orderings_Oorder(U_2371) ),
inference(clausify,[status(thm)],[f_455_2]) ).
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_2378,U_2377,U_2376,U_2375] :
( c_Orderings_Oord__class_Oless(U_2375,U_2376,U_2378)
| ~ c_Orderings_Oord__class_Oless(U_2375,U_2377,U_2378)
| ~ c_Orderings_Oord__class_Oless__eq(U_2375,U_2376,U_2377)
| ~ class_Orderings_Opreorder(U_2375) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
cnf(f_456_3,plain,
( c_Orderings_Oord__class_Oless(U_2375,U_2376,U_2378)
| ~ c_Orderings_Oord__class_Oless(U_2375,U_2377,U_2378)
| ~ c_Orderings_Oord__class_Oless__eq(U_2375,U_2376,U_2377)
| ~ class_Orderings_Opreorder(U_2375) ),
inference(clausify,[status(thm)],[f_456_2]) ).
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_2382,U_2381,U_2380,U_2379] :
( c_Orderings_Oord__class_Oless(U_2379,U_2382,U_2381)
| ~ c_Orderings_Oord__class_Oless(U_2379,U_2382,U_2380)
| ~ c_Orderings_Oord__class_Oless__eq(U_2379,U_2380,U_2381)
| ~ class_Orderings_Oorder(U_2379) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
cnf(f_457_3,plain,
( c_Orderings_Oord__class_Oless(U_2379,U_2382,U_2381)
| ~ c_Orderings_Oord__class_Oless(U_2379,U_2382,U_2380)
| ~ c_Orderings_Oord__class_Oless__eq(U_2379,U_2380,U_2381)
| ~ class_Orderings_Oorder(U_2379) ),
inference(clausify,[status(thm)],[f_457_2]) ).
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_2384,U_2383] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2383,U_2384)
| U_2383 = U_2384
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2383,U_2384) )
& ( ( U_2383 != U_2384
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2383,U_2384) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2383,U_2384) ) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
( ! [U_2388,U_2386] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2386,U_2388)
| U_2386 = U_2388
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2386,U_2388) )
& ! [U_2387,U_2385] :
( ( U_2385 != U_2387
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2385,U_2387) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2385,U_2387) ) ),
inference(miniscope,[status(thm)],[f_458_2]) ).
cnf(f_458_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2385,U_2387)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2385,U_2387) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_5,plain,
( U_2385 != U_2387
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2385,U_2387) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2386,U_2388)
| U_2386 = U_2388
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2386,U_2388) ),
inference(clausify,[status(thm)],[f_458_3]) ).
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_2390,U_2389] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2389,U_2390)
| ( U_2389 != U_2390
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2389,U_2390) ) )
& ( U_2389 = U_2390
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2389,U_2390)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2389,U_2390) ) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
( ! [U_2394,U_2392] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2392,U_2394)
| ( U_2392 != U_2394
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,U_2394) ) )
& ! [U_2393,U_2391] :
( U_2391 = U_2393
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2391,U_2393)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2391,U_2393) ) ),
inference(miniscope,[status(thm)],[f_459_2]) ).
cnf(f_459_4,plain,
( U_2391 = U_2393
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2391,U_2393)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2391,U_2393) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,U_2394)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2392,U_2394) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_6,plain,
( U_2392 != U_2394
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2392,U_2394) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_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_460_2,plain,
! [U_2396,U_2395] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2395,U_2396)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2395,U_2396) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2395,U_2396)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2395,U_2396) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_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_461_2,plain,
! [U_2400,U_2399,U_2398,U_2397] :
( 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_2397),U_2399)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2398),U_2400))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2399,U_2400)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2397,U_2398) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2397),U_2399)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2398),U_2400))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2399,U_2400)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2397,U_2398) ),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_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_462_2,plain,
! [U_2404,U_2403,U_2402,U_2401] :
( 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_2401),U_2403)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2402),U_2404))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2403,U_2404)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2401,U_2402) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
cnf(f_462_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2401),U_2403)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2402),U_2404))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2403,U_2404)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2401,U_2402) ),
inference(clausify,[status(thm)],[f_462_2]) ).
fof(f_463_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_463_2,plain,
! [U_2408,U_2407,U_2406,U_2405] :
( 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_2405),U_2407)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2406),U_2408))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2405,U_2406) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2405),U_2407)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2406),U_2408))),c_FunDef_Opair__leq))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2405,U_2406) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_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_464_2,plain,
! [U_2411,U_2410,U_2409] :
( U_2410 = U_2411
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2409,tc_HOL_Obool),U_2411,U_2410)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2409,tc_HOL_Obool),U_2410,U_2411) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
( U_2410 = U_2411
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2409,tc_HOL_Obool),U_2411,U_2410)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2409,tc_HOL_Obool),U_2410,U_2411) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_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_465_2,plain,
! [U_2413,U_2412] : c_Orderings_Oord__class_Oless__eq(tc_fun(U_2412,tc_HOL_Obool),U_2413,U_2413),
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(U_2412,tc_HOL_Obool),U_2413,U_2413),
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_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_466_2,plain,
! [U_2416,U_2415,U_2414] :
( ( U_2414 = U_2415
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool),U_2415,U_2414)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool),U_2414,U_2415) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool),U_2415,U_2414)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool),U_2414,U_2415) )
| U_2414 != U_2415 ) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
( ! [U_2422,U_2420,U_2418] :
( U_2418 = U_2420
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2422,tc_HOL_Obool),U_2420,U_2418)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2422,tc_HOL_Obool),U_2418,U_2420) )
& ! [U_2421,U_2419,U_2417] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool),U_2419,U_2417)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool),U_2417,U_2419) )
| U_2417 != U_2419 ) ),
inference(miniscope,[status(thm)],[f_466_2]) ).
cnf(f_466_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool),U_2417,U_2419)
| U_2417 != U_2419 ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool),U_2419,U_2417)
| U_2417 != U_2419 ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_6,plain,
( U_2418 = U_2420
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2422,tc_HOL_Obool),U_2420,U_2418)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2422,tc_HOL_Obool),U_2418,U_2420) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_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_467_2,plain,
! [U_2425,U_2424,U_2423] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2425,tc_HOL_Obool),U_2423,U_2424)
| U_2423 != U_2424 ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2425,tc_HOL_Obool),U_2423,U_2424)
| U_2423 != U_2424 ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_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_468_2,plain,
! [U_2428,U_2427,U_2426] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2428,tc_HOL_Obool),U_2427,U_2426)
| U_2426 != U_2427 ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2428,tc_HOL_Obool),U_2427,U_2426)
| U_2426 != U_2427 ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_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_469_2,plain,
! [U_2432,U_2431,U_2430,U_2429] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2429,tc_HOL_Obool),U_2430,U_2432)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2429,tc_HOL_Obool),U_2431,U_2432)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2429,tc_HOL_Obool),U_2430,U_2431) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2429,tc_HOL_Obool),U_2430,U_2432)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2429,tc_HOL_Obool),U_2431,U_2432)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2429,tc_HOL_Obool),U_2430,U_2431) ),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_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_470_2,plain,
! [U_2435,U_2434,U_2433] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2435,tc_HOL_Obool),U_2434,U_2433)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2435,tc_HOL_Obool),U_2433,U_2434) )
| U_2433 != U_2434 ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2435,tc_HOL_Obool),U_2433,U_2434)
| U_2433 != U_2434 ),
inference(clausify,[status(thm)],[f_470_2]) ).
cnf(f_470_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2435,tc_HOL_Obool),U_2434,U_2433)
| U_2433 != U_2434 ),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_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_471_2,plain,
! [U_2439,U_2438,U_2437,U_2436] :
( hBOOL(hAPP(U_2439,U_2437))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2438,tc_HOL_Obool),U_2436,U_2439)
| ~ hBOOL(hAPP(U_2436,U_2437)) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
( hBOOL(hAPP(U_2439,U_2437))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2438,tc_HOL_Obool),U_2436,U_2439)
| ~ hBOOL(hAPP(U_2436,U_2437)) ),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_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_472_2,plain,
! [U_2443,U_2442,U_2441,U_2440] :
( hBOOL(hAPP(U_2442,U_2443))
| ~ hBOOL(hAPP(U_2441,U_2443))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2440,tc_HOL_Obool),U_2441,U_2442) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
! [U_2443,U_2442,U_2441] :
( ! [U_2440] : ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2440,tc_HOL_Obool),U_2441,U_2442)
| hBOOL(hAPP(U_2442,U_2443))
| ~ hBOOL(hAPP(U_2441,U_2443)) ),
inference(miniscope,[status(thm)],[f_472_2]) ).
cnf(f_472_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2440,tc_HOL_Obool),U_2441,U_2442)
| hBOOL(hAPP(U_2442,U_2443))
| ~ hBOOL(hAPP(U_2441,U_2443)) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_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_473_2,plain,
! [U_2449,U_2448,U_2447,U_2446,U_2445,U_2444] :
( hBOOL(hAPP(hAPP(U_2447,U_2448),U_2449))
| ~ hBOOL(hAPP(hAPP(U_2446,U_2448),U_2449))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2444,tc_fun(U_2445,tc_HOL_Obool)),U_2446,U_2447) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_2449,U_2448,U_2447,U_2446] :
( ! [U_2445,U_2444] : ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2444,tc_fun(U_2445,tc_HOL_Obool)),U_2446,U_2447)
| hBOOL(hAPP(hAPP(U_2447,U_2448),U_2449))
| ~ hBOOL(hAPP(hAPP(U_2446,U_2448),U_2449)) ),
inference(miniscope,[status(thm)],[f_473_2]) ).
cnf(f_473_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2444,tc_fun(U_2445,tc_HOL_Obool)),U_2446,U_2447)
| hBOOL(hAPP(hAPP(U_2447,U_2448),U_2449))
| ~ hBOOL(hAPP(hAPP(U_2446,U_2448),U_2449)) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_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_474_2,plain,
! [U_2455,U_2454,U_2453,U_2452,U_2451,U_2450] :
( hBOOL(hAPP(hAPP(U_2455,U_2451),U_2452))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2453,tc_fun(U_2454,tc_HOL_Obool)),U_2450,U_2455)
| ~ hBOOL(hAPP(hAPP(U_2450,U_2451),U_2452)) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
( hBOOL(hAPP(hAPP(U_2455,U_2451),U_2452))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2453,tc_fun(U_2454,tc_HOL_Obool)),U_2450,U_2455)
| ~ hBOOL(hAPP(hAPP(U_2450,U_2451),U_2452)) ),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_1,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(fof_nnf,[status(thm)],[fact_wf__pair__less]) ).
cnf(f_475_2,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_475_1]) ).
fof(f_476_1,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_pair__less__def]) ).
cnf(f_476_2,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_476_1]) ).
fof(f_477_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_477_2,plain,
! [U_2459,U_2458,U_2457,U_2456] :
( 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_2456),U_2458)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2457),U_2459))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2456,U_2457) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
cnf(f_477_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2456),U_2458)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_2457),U_2459))),c_FunDef_Opair__less))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2456,U_2457) ),
inference(clausify,[status(thm)],[f_477_2]) ).
fof(f_478_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_478_2,plain,
! [U_2463,U_2462,U_2461,U_2460] :
( 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_2462,U_2463)),U_2461)),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_2463),U_2461)),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_2462),U_2460)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2460),U_2461)) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
cnf(f_478_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2462,U_2463)),U_2461)),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_2463),U_2461)),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_2462),U_2460)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2460),U_2461)) ),
inference(clausify,[status(thm)],[f_478_2]) ).
fof(f_479_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_479_2,plain,
! [U_2467,U_2466,U_2465,U_2464] :
( 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_2465),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2466,U_2467))),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_2465),U_2467)),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_2464),U_2466)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2464),U_2465)) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
cnf(f_479_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_2465),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2466,U_2467))),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_2465),U_2467)),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_2464),U_2466)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2464),U_2465)) ),
inference(clausify,[status(thm)],[f_479_2]) ).
fof(f_480_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_480_2,plain,
! [U_2471,U_2470,U_2469,U_2468] :
( 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_2469),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2470,U_2471))),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_2469),U_2471)),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_2468),U_2470)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2468),U_2469)) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_2469),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2470,U_2471))),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_2469),U_2471)),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_2468),U_2470)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2468),U_2469)) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_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_481_2,plain,
! [U_2475,U_2474,U_2473,U_2472] :
( 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_2474,U_2475)),U_2473)),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_2475),U_2473)),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_2474),U_2472)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2472),U_2473)) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),U_2474,U_2475)),U_2473)),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_2475),U_2473)),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_2474),U_2472)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_2472),U_2473)) ),
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_1,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
inference(fof_nnf,[status(thm)],[fact_min__rpair__set]) ).
cnf(f_482_2,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
inference(clausify,[status(thm)],[f_482_1]) ).
fof(f_483_1,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
inference(fof_nnf,[status(thm)],[fact_max__rpair__set]) ).
cnf(f_483_2,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
inference(clausify,[status(thm)],[f_483_1]) ).
fof(f_484_1,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(fof_nnf,[status(thm)],[fact_min__strict__def]) ).
cnf(f_484_2,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_484_1]) ).
fof(f_485_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_485_2,plain,
! [U_2479,U_2478,U_2477,U_2476] :
( c_FunDef_Oreduction__pair(U_2478,hAPP(hAPP(c_FunDef_Orp__inv__image(U_2476,U_2478),U_2477),U_2479))
| ~ c_FunDef_Oreduction__pair(U_2476,U_2477) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
( c_FunDef_Oreduction__pair(U_2478,hAPP(hAPP(c_FunDef_Orp__inv__image(U_2476,U_2478),U_2477),U_2479))
| ~ c_FunDef_Oreduction__pair(U_2476,U_2477) ),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_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_486_2,plain,
! [U_2481,U_2480] :
( c_Wellfounded_Owf(tc_fun(U_2480,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_2480,U_2481))
| ~ c_Wellfounded_Owf(U_2480,U_2481) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
( c_Wellfounded_Owf(tc_fun(U_2480,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_2480,U_2481))
| ~ c_Wellfounded_Owf(U_2480,U_2481) ),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_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_487_2,plain,
! [U_2484,U_2483,U_2482] :
( c_FunDef_Oreduction__pair(U_2482,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_2482,U_2482),tc_HOL_Obool),tc_fun(tc_prod(U_2482,U_2482),tc_HOL_Obool)),U_2483),U_2484))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2482,U_2482),tc_HOL_Obool),c_Relation_Orel__comp(U_2482,U_2482,U_2482,U_2483,U_2484),U_2483)
| ~ c_Wellfounded_Owf(U_2482,U_2483) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
( c_FunDef_Oreduction__pair(U_2482,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_2482,U_2482),tc_HOL_Obool),tc_fun(tc_prod(U_2482,U_2482),tc_HOL_Obool)),U_2483),U_2484))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2482,U_2482),tc_HOL_Obool),c_Relation_Orel__comp(U_2482,U_2482,U_2482,U_2483,U_2484),U_2483)
| ~ c_Wellfounded_Owf(U_2482,U_2483) ),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_1,plain,
! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(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_488_2,plain,
! [U_2486,U_2485] : c_FunDef_Orp__inv__image(U_2485,U_2486) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool)),c_COMBS(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(U_2486,U_2485)),c_Product__Type_OPair(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),c_Relation_Oinv__image(U_2485,U_2486))))),c_Relation_Oinv__image(U_2485,U_2486))),
inference(variable_rename,[status(thm)],[f_488_1]) ).
cnf(f_488_3,plain,
c_FunDef_Orp__inv__image(U_2485,U_2486) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool)),c_COMBS(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)),tc_fun(tc_fun(U_2486,U_2485),tc_fun(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),tc_fun(tc_prod(U_2485,U_2485),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool))),tc_fun(U_2486,U_2485)),c_Product__Type_OPair(tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool),tc_fun(tc_prod(U_2486,U_2486),tc_HOL_Obool)))),c_Relation_Oinv__image(U_2485,U_2486))))),c_Relation_Oinv__image(U_2485,U_2486))),
inference(clausify,[status(thm)],[f_488_2]) ).
fof(f_489_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_489_2,plain,
! [U_2494,U_2493,U_2492,U_2491,U_2490,U_2489,U_2488,U_2487] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2487,U_2492)),hAPP(hAPP(c_Product__Type_OPair(U_2487,U_2492),U_2489),U_2493)),c_Relation_Orel__comp(U_2487,U_2488,U_2492,U_2491,U_2494)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2488,U_2492)),hAPP(hAPP(c_Product__Type_OPair(U_2488,U_2492),U_2490),U_2493)),U_2494))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2487,U_2488)),hAPP(hAPP(c_Product__Type_OPair(U_2487,U_2488),U_2489),U_2490)),U_2491)) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_2487,U_2492)),hAPP(hAPP(c_Product__Type_OPair(U_2487,U_2492),U_2489),U_2493)),c_Relation_Orel__comp(U_2487,U_2488,U_2492,U_2491,U_2494)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2488,U_2492)),hAPP(hAPP(c_Product__Type_OPair(U_2488,U_2492),U_2490),U_2493)),U_2494))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_2487,U_2488)),hAPP(hAPP(c_Product__Type_OPair(U_2487,U_2488),U_2489),U_2490)),U_2491)) ),
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_1,plain,
! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_H_2,V_s_H_2),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_s_H_2,V_s_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_H_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_rel__comp__mono]) ).
fof(f_490_2,plain,
! [U_2501,U_2500,U_2499,U_2498,U_2497,U_2496,U_2495] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2495,U_2499),tc_HOL_Obool),c_Relation_Orel__comp(U_2495,U_2496,U_2499,U_2497,U_2500),c_Relation_Orel__comp(U_2495,U_2496,U_2499,U_2498,U_2501))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2496,U_2499),tc_HOL_Obool),U_2500,U_2501)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2495,U_2496),tc_HOL_Obool),U_2497,U_2498) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2495,U_2499),tc_HOL_Obool),c_Relation_Orel__comp(U_2495,U_2496,U_2499,U_2497,U_2500),c_Relation_Orel__comp(U_2495,U_2496,U_2499,U_2498,U_2501))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2496,U_2499),tc_HOL_Obool),U_2500,U_2501)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_2495,U_2496),tc_HOL_Obool),U_2497,U_2498) ),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_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_491_2,plain,
! [U_2503,U_2502] : c_Transitive__Closure_Otrancl(U_2502,U_2503) = c_Relation_Orel__comp(U_2502,U_2502,U_2502,U_2503,c_Transitive__Closure_Ortrancl(U_2502,U_2503)),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
c_Transitive__Closure_Otrancl(U_2502,U_2503) = c_Relation_Orel__comp(U_2502,U_2502,U_2502,U_2503,c_Transitive__Closure_Ortrancl(U_2502,U_2503)),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_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_492_2,plain,
! [U_2505,U_2504] : c_Transitive__Closure_Otrancl(U_2504,U_2505) = c_Relation_Orel__comp(U_2504,U_2504,U_2504,c_Transitive__Closure_Ortrancl(U_2504,U_2505),U_2505),
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
c_Transitive__Closure_Otrancl(U_2504,U_2505) = c_Relation_Orel__comp(U_2504,U_2504,U_2504,c_Transitive__Closure_Ortrancl(U_2504,U_2505),U_2505),
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_1,plain,
! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),
inference(fof_nnf,[status(thm)],[fact_internal__split__def]) ).
fof(f_493_2,plain,
! [U_2508,U_2507,U_2506] : c_Product__Type_Ointernal__split(U_2506,U_2507,U_2508) = c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508),
inference(variable_rename,[status(thm)],[f_493_1]) ).
cnf(f_493_3,plain,
c_Product__Type_Ointernal__split(U_2506,U_2507,U_2508) = c_Product__Type_Oprod_Oprod__case(U_2506,U_2507,U_2508),
inference(clausify,[status(thm)],[f_493_2]) ).
fof(f_494_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_494_2,plain,
! [U_2513,U_2512,U_2511,U_2510,U_2509] :
( c_Relation_Osingle__valued(U_2509,U_2512,c_Relation_Orel__comp(U_2509,U_2510,U_2512,U_2511,U_2513))
| ~ c_Relation_Osingle__valued(U_2510,U_2512,U_2513)
| ~ c_Relation_Osingle__valued(U_2509,U_2510,U_2511) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
cnf(f_494_3,plain,
( c_Relation_Osingle__valued(U_2509,U_2512,c_Relation_Orel__comp(U_2509,U_2510,U_2512,U_2511,U_2513))
| ~ c_Relation_Osingle__valued(U_2510,U_2512,U_2513)
| ~ c_Relation_Osingle__valued(U_2509,U_2510,U_2511) ),
inference(clausify,[status(thm)],[f_494_2]) ).
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_2515,U_2514] :
( class_Lattices_Osemilattice__inf(tc_fun(U_2515,U_2514))
| ~ class_Lattices_Olattice(U_2514) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
( class_Lattices_Osemilattice__inf(tc_fun(U_2515,U_2514))
| ~ class_Lattices_Olattice(U_2514) ),
inference(clausify,[status(thm)],[f_495_2]) ).
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_2517,U_2516] :
( class_Orderings_Opreorder(tc_fun(U_2517,U_2516))
| ~ class_Orderings_Opreorder(U_2516) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
cnf(f_496_3,plain,
( class_Orderings_Opreorder(tc_fun(U_2517,U_2516))
| ~ class_Orderings_Opreorder(U_2516) ),
inference(clausify,[status(thm)],[f_496_2]) ).
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_2519,U_2518] :
( class_Lattices_Olattice(tc_fun(U_2519,U_2518))
| ~ class_Lattices_Olattice(U_2518) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
( class_Lattices_Olattice(tc_fun(U_2519,U_2518))
| ~ class_Lattices_Olattice(U_2518) ),
inference(clausify,[status(thm)],[f_497_2]) ).
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_2521,U_2520] :
( class_Orderings_Oorder(tc_fun(U_2521,U_2520))
| ~ class_Orderings_Oorder(U_2520) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
( class_Orderings_Oorder(tc_fun(U_2521,U_2520))
| ~ class_Orderings_Oorder(U_2520) ),
inference(clausify,[status(thm)],[f_498_2]) ).
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_2523,U_2522] :
( class_Orderings_Oord(tc_fun(U_2523,U_2522))
| ~ class_Orderings_Oord(U_2522) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
cnf(f_499_3,plain,
( class_Orderings_Oord(tc_fun(U_2523,U_2522))
| ~ class_Orderings_Oord(U_2522) ),
inference(clausify,[status(thm)],[f_499_2]) ).
fof(f_500_1,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]) ).
cnf(f_500_2,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_500_1]) ).
fof(f_501_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(f_501_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_501_1]) ).
fof(f_502_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
cnf(f_502_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_502_1]) ).
fof(f_503_1,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]) ).
cnf(f_503_2,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_503_1]) ).
fof(f_504_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
cnf(f_504_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_504_1]) ).
fof(f_505_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
cnf(f_505_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_505_1]) ).
fof(f_506_1,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]) ).
cnf(f_506_2,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_506_1]) ).
fof(f_507_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
cnf(f_507_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_507_1]) ).
fof(f_508_1,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]) ).
cnf(f_508_2,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_508_1]) ).
fof(f_509_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
cnf(f_509_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_509_1]) ).
fof(f_510_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
cnf(f_510_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_510_1]) ).
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_2525,U_2524] : hAPP(c_COMBI(U_2524),U_2525) = U_2525,
inference(variable_rename,[status(thm)],[f_511_1]) ).
cnf(f_511_3,plain,
hAPP(c_COMBI(U_2524),U_2525) = U_2525,
inference(clausify,[status(thm)],[f_511_2]) ).
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_2529,U_2528,U_2527,U_2526] : hAPP(c_COMBK(U_2526,U_2527,U_2528),U_2529) = U_2528,
inference(variable_rename,[status(thm)],[f_512_1]) ).
cnf(f_512_3,plain,
hAPP(c_COMBK(U_2526,U_2527,U_2528),U_2529) = U_2528,
inference(clausify,[status(thm)],[f_512_2]) ).
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_2535,U_2534,U_2533,U_2532,U_2531,U_2530] : hAPP(hAPP(hAPP(c_COMBB(U_2530,U_2531,U_2532),U_2533),U_2534),U_2535) = hAPP(U_2533,hAPP(U_2534,U_2535)),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
hAPP(hAPP(hAPP(c_COMBB(U_2530,U_2531,U_2532),U_2533),U_2534),U_2535) = hAPP(U_2533,hAPP(U_2534,U_2535)),
inference(clausify,[status(thm)],[f_513_2]) ).
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_2541,U_2540,U_2539,U_2538,U_2537,U_2536] : hAPP(hAPP(hAPP(c_COMBC(U_2536,U_2537,U_2538),U_2539),U_2540),U_2541) = hAPP(hAPP(U_2539,U_2541),U_2540),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
hAPP(hAPP(hAPP(c_COMBC(U_2536,U_2537,U_2538),U_2539),U_2540),U_2541) = hAPP(hAPP(U_2539,U_2541),U_2540),
inference(clausify,[status(thm)],[f_514_2]) ).
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_2547,U_2546,U_2545,U_2544,U_2543,U_2542] : hAPP(hAPP(hAPP(c_COMBS(U_2542,U_2543,U_2544),U_2545),U_2546),U_2547) = hAPP(hAPP(U_2545,U_2547),hAPP(U_2546,U_2547)),
inference(variable_rename,[status(thm)],[f_515_1]) ).
cnf(f_515_3,plain,
hAPP(hAPP(hAPP(c_COMBS(U_2542,U_2543,U_2544),U_2545),U_2546),U_2547) = hAPP(hAPP(U_2545,U_2547),hAPP(U_2546,U_2547)),
inference(clausify,[status(thm)],[f_515_2]) ).
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_2549,U_2548] :
( U_2548 = U_2549
| ~ hBOOL(hAPP(hAPP(c_fequal,U_2548),U_2549)) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
cnf(f_516_3,plain,
( U_2548 = U_2549
| ~ hBOOL(hAPP(hAPP(c_fequal,U_2548),U_2549)) ),
inference(clausify,[status(thm)],[f_516_2]) ).
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_2551,U_2550] :
( hBOOL(hAPP(hAPP(c_fequal,U_2550),U_2551))
| U_2550 != U_2551 ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
( hBOOL(hAPP(hAPP(c_fequal,U_2550),U_2551))
| U_2550 != U_2551 ),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_1,plain,
~ hBOOL(c_fFalse),
inference(fof_nnf,[status(thm)],[help_c__fFalse__1]) ).
cnf(f_518_2,plain,
~ hBOOL(c_fFalse),
inference(clausify,[status(thm)],[f_518_1]) ).
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_2552] :
( ~ hBOOL(U_2552)
| ~ hBOOL(hAPP(c_fNot,U_2552)) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
cnf(f_519_3,plain,
( ~ hBOOL(U_2552)
| ~ hBOOL(hAPP(c_fNot,U_2552)) ),
inference(clausify,[status(thm)],[f_519_2]) ).
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_2553] :
( hBOOL(hAPP(c_fNot,U_2553))
| hBOOL(U_2553) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
cnf(f_520_3,plain,
( hBOOL(hAPP(c_fNot,U_2553))
| hBOOL(U_2553) ),
inference(clausify,[status(thm)],[f_520_2]) ).
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_2555,U_2554] :
( hBOOL(hAPP(hAPP(c_fconj,U_2554),U_2555))
| ~ hBOOL(U_2555)
| ~ hBOOL(U_2554) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
! [U_2555] :
( ! [U_2554] :
( hBOOL(hAPP(hAPP(c_fconj,U_2554),U_2555))
| ~ hBOOL(U_2554) )
| ~ hBOOL(U_2555) ),
inference(miniscope,[status(thm)],[f_521_2]) ).
cnf(f_521_4,plain,
( hBOOL(hAPP(hAPP(c_fconj,U_2554),U_2555))
| ~ hBOOL(U_2554)
| ~ hBOOL(U_2555) ),
inference(clausify,[status(thm)],[f_521_3]) ).
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_2557,U_2556] :
( hBOOL(U_2556)
| ~ hBOOL(hAPP(hAPP(c_fconj,U_2556),U_2557)) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( hBOOL(U_2556)
| ~ hBOOL(hAPP(hAPP(c_fconj,U_2556),U_2557)) ),
inference(clausify,[status(thm)],[f_522_2]) ).
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_2559,U_2558] :
( hBOOL(U_2559)
| ~ hBOOL(hAPP(hAPP(c_fconj,U_2558),U_2559)) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
! [U_2559] :
( ! [U_2558] : ~ hBOOL(hAPP(hAPP(c_fconj,U_2558),U_2559))
| hBOOL(U_2559) ),
inference(miniscope,[status(thm)],[f_523_2]) ).
cnf(f_523_4,plain,
( ~ hBOOL(hAPP(hAPP(c_fconj,U_2558),U_2559))
| hBOOL(U_2559) ),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_1,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_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_b____),v_a____)),hAPP(v_F,v_P_H____))) ),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_524_2,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_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_b____),v_a____)),hAPP(v_F,v_P_H____))) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,v_P_H____)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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)],[f_524_1]) ).
fof(f_524_3,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_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ sP1 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,v_P_H____)))
| ~ sP1 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,v_P_H____)))
| ~ sP0 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____)))
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_524_2]) ).
cnf(f_524_4,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_524_3]) ).
cnf(f_524_5,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_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_524_3]) ).
cnf(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(v_F,v_P_H____)))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_524_3]) ).
cnf(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(v_F,v_P_H____)))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_524_3]) ).
cnf(f_524_8,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_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_524_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_6]) ).
cnf(f_7_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_7]) ).
cnf(f_8_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_7]) ).
cnf(f_33_23_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_23]) ).
cnf(f_33_24_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_24]) ).
cnf(f_37_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_7]) ).
cnf(f_37_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_8]) ).
cnf(f_37_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_15]) ).
cnf(f_47_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_7]) ).
cnf(f_47_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_8]) ).
cnf(f_47_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_15]) ).
cnf(f_218_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_218_3]) ).
cnf(f_220_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_220_4]) ).
cnf(f_265_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_265_3]) ).
cnf(f_429_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_429_4]) ).
cnf(f_429_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_429_5]) ).
cnf(f_429_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_429_6]) ).
cnf(f_429_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_429_7]) ).
cnf(f_429_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_429_8]) ).
cnf(f_429_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_429_9]) ).
cnf(f_429_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_429_10]) ).
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,
( 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_11,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_12,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_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_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_16,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_17,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_18,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_19,axiom,
( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,axiom,
( c_Product__Type_Ointernal__split(Eq_x_0,Eq_x_1,Eq_x_2) = c_Product__Type_Ointernal__split(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_Product__Type_Ocurry(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Product__Type_Ocurry(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_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_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_42,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_43,axiom,
( c_Relation_OId(Eq_x_0) = c_Relation_OId(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_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_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_54,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_55,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_56,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_57,axiom,
( c_Product__Type_Oprod_Oprod__case(Eq_x_0,Eq_x_1,Eq_x_2) = c_Product__Type_Oprod_Oprod__case(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,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_59,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK2(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_60,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK3(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_61,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK4(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_62,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK5(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,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK6(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_64,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK7(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_65,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,
( 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_83,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_84,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_85,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_86,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_87,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_88,axiom,
( sK31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK31(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,
( sK32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK32(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,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK33(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) = sK37(Eq_y_0,Eq_y_1,Eq_y_2)
| 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) = sK39(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_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) = sK41(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK43(Eq_x_0,Eq_x_1,Eq_x_2) = sK43(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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) = sK45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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) = sK47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK50(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_107,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK51(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_108,axiom,
( sK52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK52(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_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) = sK56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_6,Eq_x_7) = sK59(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_116,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK60(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_117,axiom,
( sK61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK61(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_118,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK62(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_119,axiom,
( sK63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK63(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_120,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK64(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_121,axiom,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK65(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_122,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK66(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_123,axiom,
( sK67(Eq_x_0,Eq_x_1) = sK67(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( 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) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_3) = sK76(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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) = sK78(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,Eq_x_4) = sK79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_2,Eq_x_3) = sK81(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( 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) = sK83(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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) = sK86(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_2,Eq_x_3) = sK88(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| 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,Eq_x_2,Eq_x_3) = sK89(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK92(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK92(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,Eq_x_3,Eq_x_4) = sK93(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_150,axiom,
( sK94(Eq_x_0,Eq_x_1,Eq_x_2) = sK94(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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) = sK96(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_153,axiom,
( sK97(Eq_x_0,Eq_x_1,Eq_x_2) = sK97(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| 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) = sK101(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( sK102(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK102(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( c_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_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,
( hBOOL(Eq_y_0)
| ~ hBOOL(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_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_164,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_165,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_166,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_167,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_168,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_169,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_170,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_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,
( 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_173,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_174,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_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,
( 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_179,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_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,
( 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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT149+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n019.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 19 21:19:26 UTC 2026
% 0.09/5.37 % CPUTime :
% 1.96/7.21 % SZS status Theorem for theBenchmark
% 1.96/7.21 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------