TSTP Solution File: COM123+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM123+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 18:06:10 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM123+1 : TPTP v8.1.0. Released v6.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 15:10:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(vabs_type, type, (
% 0.20/0.43 vabs: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(veabs_type, type, (
% 0.20/0.43 veabs: $i)).
% 0.20/0.43 tff(tptp_fun_VS1_75_type, type, (
% 0.20/0.43 tptp_fun_VS1_75: $i)).
% 0.20/0.43 tff(tptp_fun_Vy_76_type, type, (
% 0.20/0.43 tptp_fun_Vy_76: $i)).
% 0.20/0.43 tff(vvar_type, type, (
% 0.20/0.43 vvar: $i > $i)).
% 0.20/0.43 tff(tptp_fun_Vx_66_type, type, (
% 0.20/0.43 tptp_fun_Vx_66: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_VT_74_type, type, (
% 0.20/0.43 tptp_fun_VT_74: $i)).
% 0.20/0.43 tff(tptp_fun_VC_77_type, type, (
% 0.20/0.43 tptp_fun_VC_77: $i)).
% 0.20/0.43 tff(vsomeType_type, type, (
% 0.20/0.43 vsomeType: $i > $i)).
% 0.20/0.43 tff(vlookup_type, type, (
% 0.20/0.43 vlookup: ( $i * $i ) > $i)).
% 0.20/0.43 tff(vtcheck_type, type, (
% 0.20/0.43 vtcheck: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_VS_71_type, type, (
% 0.20/0.43 tptp_fun_VS_71: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_Ve2_72_type, type, (
% 0.20/0.43 tptp_fun_Ve2_72: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(varrow_type, type, (
% 0.20/0.43 varrow: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_Ve1_73_type, type, (
% 0.20/0.43 tptp_fun_Ve1_73: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(vapp_type, type, (
% 0.20/0.43 vapp: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_VT2_67_type, type, (
% 0.20/0.44 tptp_fun_VT2_67: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_Ve2_69_type, type, (
% 0.20/0.44 tptp_fun_Ve2_69: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(vbind_type, type, (
% 0.20/0.44 vbind: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_VT1_68_type, type, (
% 0.20/0.44 tptp_fun_VT1_68: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_Vx_70_type, type, (
% 0.20/0.44 tptp_fun_Vx_70: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(visFreeVar_type, type, (
% 0.20/0.44 visFreeVar: ( $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_Vx_79_type, type, (
% 0.20/0.44 tptp_fun_Vx_79: $i)).
% 0.20/0.44 tff(tptp_fun_VS_78_type, type, (
% 0.20/0.44 tptp_fun_VS_78: $i)).
% 0.20/0.44 tff(1,assumption,(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))), introduced(assumption)).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : refl((~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(5,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-abs-app'')).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.44 tff(7,plain,(
% 0.20/0.44 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[6])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.44 tff(11,plain,(~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 ((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.44 tff(14,assumption,(~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))), introduced(assumption)).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)),
% 0.20/0.44 inference(symmetry,[status(thm)],[16])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) <=> visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) <=> visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.44 inference(symmetry,[status(thm)],[18])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 ((~visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))) <=> (~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(23,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-FreeVar-abs-1'')).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.44 tff(31,plain,(
% 0.20/0.44 ~((~((~(Vx!79 = Vy!76)) & (~visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))) & vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74))),
% 0.20/0.44 inference(skolemize,[status(sab)],[30])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 ((~(Vx!79 = Vy!76)) & (~visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))) & vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)),
% 0.20/0.44 inference(or_elim,[status(thm)],[31])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (~visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[33, 20])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (^[VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : refl(((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (^[VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) <=> (~((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve)))))), ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) <=> (~(~((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve)))))))), rewrite((~(~((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve)))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))))), ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve)))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vv)) & visFreeVar(Vv, Ve)) <=> (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))), ((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> (~(~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))), rewrite((~(~((Vx = Vv) | (~visFreeVar(Vv, Ve))))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve)))), ((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve))))), (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) <=> (((Vx = Vv) | (~visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)))), rewrite((((Vx = Vv) | (~visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) <=> ((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))), (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) <=> ((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve))))), rewrite(((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> ((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))), ((((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve))) & ((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))), rewrite((((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve))) & ((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))) <=> (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))), ((((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))), (((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> (((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve)))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))))), rewrite((((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve)))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))), (((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (^[VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : trans(monotonicity(rewrite(((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))), ((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))))), rewrite((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))), ((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.45 tff(42,axiom,(![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isFreeVar1')).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.45 tff(45,plain,(
% 0.20/0.45 ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[44])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))) <=> ((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (($false | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs))))))))) <=> ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 ((~((~((Vy!76 = Vx!79) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | (~visFreeVar(Vx!79, veabs)))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))) <=> (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 ((~$true) <=> $false),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((Vx!79 = Vx!79) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~(Vx!79 = Vx!79)) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 ((~(Vx!79 = Vx!79)) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[53, 51])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (((~(Vx!79 = Vx!79)) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | (~visFreeVar(Vx!79, veabs)))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs))))))))) <=> ($false | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[54, 50])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (((~(Vx!79 = Vx!79)) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | (~visFreeVar(Vx!79, veabs)))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs))))))))) <=> ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[55, 49])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | ((~(Vx!79 = Vx!79)) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | (~visFreeVar(Vx!79, veabs)))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))) <=> ((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | ((~(Vx!79 = Vx!79)) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | (~visFreeVar(Vx!79, veabs)))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))) <=> ((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[57, 48])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 ((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | ((~(Vx!79 = Vx!79)) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | (~visFreeVar(Vx!79, veabs)))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 ((~![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vabs(Vx, VT, Ve))) | (~((~((Vx = Vv) | visFreeVar(VVar0, VExp0) | (~visFreeVar(Vv, Ve)))) | (~((~visFreeVar(VVar0, VExp0)) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (~((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 47, 17])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs))))))) | ((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 ((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : refl((~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : trans(monotonicity(rewrite(((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1)) <=> (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> (~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), rewrite((~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> (((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))), rewrite((((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), rewrite((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : rewrite((((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.46 tff(71,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-abs'')).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.46 tff(74,plain,(
% 0.20/0.46 ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[73])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))) | (~((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)) | (~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (~((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)) | (~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)) | (~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))) | ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 ((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 ((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[81, 17])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[82, 80])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))) | (tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (veabs = tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))),
% 0.20/0.47 inference(symmetry,[status(thm)],[85])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[87])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[89, 14])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[90, 88])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))) | (tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[92, 83])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (VS1!75 = tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))),
% 0.20/0.47 inference(symmetry,[status(thm)],[93])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))) | (tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[95, 83])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (Vy!76 = tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))),
% 0.20/0.47 inference(symmetry,[status(thm)],[96])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[97, 94])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vbind(Vy!76, VS1!75, VC!77)),
% 0.20/0.47 inference(symmetry,[status(thm)],[98])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)) = vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[101])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) <=> (~vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)) = vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[97, 94])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[104, 86])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[105])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) <=> (~vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[108, 14])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = VT!74),
% 0.20/0.47 inference(symmetry,[status(thm)],[109])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) <=> vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[17, 110])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) <=> vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.47 inference(symmetry,[status(thm)],[111])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 ((~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74)) <=> (~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74)),
% 0.20/0.48 inference(or_elim,[status(thm)],[31])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (^[VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : refl(((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (^[VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : rewrite((vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.48 tff(121,axiom,(![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-abs'')).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.20/0.48 tff(124,plain,(
% 0.20/0.48 ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[123])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[129, 115])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (~vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[130, 107])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (~(Vx!79 = Vy!76)),
% 0.20/0.48 inference(and_elim,[status(thm)],[32])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : refl((vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) <=> (~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))), ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> (~(~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))))), rewrite((~(~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))) <=> ((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))), ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))), (((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)))), rewrite((((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))), (((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : rewrite((((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.48 tff(140,axiom,(![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-Context-Swap'')).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.20/0.48 tff(143,plain,(
% 0.20/0.48 ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.20/0.48 inference(skolemize,[status(sab)],[142])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | ((Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 ((vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) <=> ((Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | ((Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[148, 146])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[151, 145, 132, 131])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (~vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[152, 103])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) <=> (~(visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))), ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) <=> (~(~(visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))))), rewrite((~(~(visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))) <=> (visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))), ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) <=> (visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))), (((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ((visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))), rewrite(((visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))), (((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.49 tff(161,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-FreeVar-abs-IH'')).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.20/0.49 tff(164,plain,(
% 0.20/0.49 ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.20/0.49 inference(skolemize,[status(sab)],[163])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[165, 155])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | (vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | visFreeVar(Vx!79, veabs) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | visFreeVar(Vx!79, veabs) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | (vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | visFreeVar(Vx!79, veabs) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | visFreeVar(Vx!79, veabs) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (vtcheck(vbind(Vx!79, VS!78, vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | visFreeVar(Vx!79, veabs) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[169, 166])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (visFreeVar(Vx!79, veabs)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[170, 153, 91])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 ((Vy!76 = Vx!79) <=> (Vx!79 = Vy!76)),
% 0.20/0.49 inference(commutativity,[status(thm)],[])).
% 0.20/0.49 tff(173,plain,
% 0.20/0.49 ((Vx!79 = Vy!76) <=> (Vy!76 = Vx!79)),
% 0.20/0.49 inference(symmetry,[status(thm)],[172])).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 ((~(Vx!79 = Vy!76)) <=> (~(Vy!76 = Vx!79))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 (~(Vy!76 = Vx!79)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[132, 174])).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 ((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 ((~((Vy!76 = Vx!79) | (~visFreeVar(Vx!79, veabs)) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[176, 175, 171])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 (visFreeVar(Vx!79, vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[177, 63])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[178, 34])).
% 0.20/0.49 tff(180,plain,((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 (vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)),
% 0.20/0.49 inference(and_elim,[status(thm)],[32])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 (^[Ve: $i, VT: $i, VC: $i] : refl(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[182])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(rewrite(((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) <=> (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT)))))), rewrite(((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) <=> (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))))), rewrite(((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) <=> (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))))), rewrite(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[184])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.49 tff(191,axiom,(![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.49 tff(194,plain,(
% 0.20/0.49 ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[193])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[195, 185])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[196, 183])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 ((~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[200, 197, 181])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[201, 180, 13])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 (((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74)))) | (vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 (vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)),
% 0.20/0.50 inference(symmetry,[status(thm)],[204])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[206])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(209,axiom,(![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-abs'')).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.20/0.50 tff(211,plain,(
% 0.20/0.50 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[210])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[213, 212, 205])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------