TSTP Solution File: COM138+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM138+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 18:06:13 EDT 2022
% Result : Theorem 1.24s 1.05s
% Output : Proof 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM138+1 : TPTP v8.1.0. Released v6.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 15:16:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.24/1.05 % SZS status Theorem
% 1.24/1.05 % SZS output start Proof
% 1.24/1.05 tff(visFreeVar_type, type, (
% 1.24/1.05 visFreeVar: ( $i * $i ) > $o)).
% 1.24/1.05 tff(vvar_type, type, (
% 1.24/1.05 vvar: $i > $i)).
% 1.24/1.05 tff(tptp_fun_Vx_66_type, type, (
% 1.24/1.05 tptp_fun_Vx_66: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Vy_75_type, type, (
% 1.24/1.05 tptp_fun_Vy_75: $i)).
% 1.24/1.05 tff(tptp_fun_VT_74_type, type, (
% 1.24/1.05 tptp_fun_VT_74: $i)).
% 1.24/1.05 tff(vbind_type, type, (
% 1.24/1.05 vbind: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_VC_76_type, type, (
% 1.24/1.05 tptp_fun_VC_76: $i)).
% 1.24/1.05 tff(tptp_fun_VS_77_type, type, (
% 1.24/1.05 tptp_fun_VS_77: $i)).
% 1.24/1.05 tff(tptp_fun_Vx_78_type, type, (
% 1.24/1.05 tptp_fun_Vx_78: $i)).
% 1.24/1.05 tff(vsomeType_type, type, (
% 1.24/1.05 vsomeType: $i > $i)).
% 1.24/1.05 tff(vlookup_type, type, (
% 1.24/1.05 vlookup: ( $i * $i ) > $i)).
% 1.24/1.05 tff(vtcheck_type, type, (
% 1.24/1.05 vtcheck: ( $i * $i * $i ) > $o)).
% 1.24/1.05 tff(tptp_fun_VS_71_type, type, (
% 1.24/1.05 tptp_fun_VS_71: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Ve2_72_type, type, (
% 1.24/1.05 tptp_fun_Ve2_72: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(varrow_type, type, (
% 1.24/1.05 varrow: ( $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Ve1_73_type, type, (
% 1.24/1.05 tptp_fun_Ve1_73: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(vapp_type, type, (
% 1.24/1.05 vapp: ( $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_VT2_67_type, type, (
% 1.24/1.05 tptp_fun_VT2_67: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Ve2_69_type, type, (
% 1.24/1.05 tptp_fun_Ve2_69: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_VT1_68_type, type, (
% 1.24/1.05 tptp_fun_VT1_68: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Vx_70_type, type, (
% 1.24/1.05 tptp_fun_Vx_70: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(vabs_type, type, (
% 1.24/1.05 vabs: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_VC_4_type, type, (
% 1.24/1.05 tptp_fun_VC_4: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_VTy_1_type, type, (
% 1.24/1.05 tptp_fun_VTy_1: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Vy_2_type, type, (
% 1.24/1.05 tptp_fun_Vy_2: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Vx_3_type, type, (
% 1.24/1.05 tptp_fun_Vx_3: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_VC_5_type, type, (
% 1.24/1.05 tptp_fun_VC_5: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Vx_6_type, type, (
% 1.24/1.05 tptp_fun_Vx_6: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Vy_7_type, type, (
% 1.24/1.05 tptp_fun_Vy_7: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_VTy_8_type, type, (
% 1.24/1.05 tptp_fun_VTy_8: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(tptp_fun_Vx_0_type, type, (
% 1.24/1.05 tptp_fun_Vx_0: ( $i * $i * $i ) > $i)).
% 1.24/1.05 tff(vempty_type, type, (
% 1.24/1.05 vempty: $i)).
% 1.24/1.05 tff(vnoType_type, type, (
% 1.24/1.05 vnoType: $i)).
% 1.24/1.05 tff(1,assumption,(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))), introduced(assumption)).
% 1.24/1.05 tff(2,plain,
% 1.24/1.05 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 1.24/1.05 inference(bind,[status(th)],[])).
% 1.24/1.05 tff(3,plain,
% 1.24/1.05 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.24/1.05 inference(quant_intro,[status(thm)],[2])).
% 1.24/1.05 tff(4,plain,
% 1.24/1.05 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.24/1.05 inference(rewrite,[status(thm)],[])).
% 1.24/1.05 tff(5,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 1.24/1.05 tff(6,plain,
% 1.24/1.05 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.24/1.05 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.24/1.05 tff(7,plain,(
% 1.24/1.05 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.24/1.05 inference(skolemize,[status(sab)],[6])).
% 1.24/1.05 tff(8,plain,
% 1.24/1.05 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.24/1.05 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.24/1.05 tff(9,plain,
% 1.24/1.05 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.24/1.05 inference(quant_inst,[status(thm)],[])).
% 1.24/1.05 tff(10,plain,
% 1.24/1.05 ($false),
% 1.24/1.05 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.24/1.05 tff(11,plain,(~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.05 tff(12,plain,
% 1.24/1.05 (((~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), varrow(tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), VT!74))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.24/1.05 inference(tautology,[status(thm)],[])).
% 1.24/1.05 tff(13,plain,
% 1.24/1.05 ((~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), varrow(tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), VT!74))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.24/1.05 inference(unit_resolution,[status(thm)],[12, 11])).
% 1.24/1.05 tff(14,assumption,(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))), introduced(assumption)).
% 1.24/1.05 tff(15,plain,
% 1.24/1.05 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 1.24/1.05 inference(bind,[status(th)],[])).
% 1.24/1.05 tff(16,plain,
% 1.24/1.05 (![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)))),
% 1.24/1.05 inference(quant_intro,[status(thm)],[15])).
% 1.24/1.05 tff(17,plain,
% 1.24/1.05 (![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)))),
% 1.24/1.05 inference(rewrite,[status(thm)],[])).
% 1.24/1.05 tff(18,axiom,(![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-var-abs'')).
% 1.24/1.05 tff(19,plain,
% 1.24/1.05 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 1.24/1.05 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.24/1.05 tff(20,plain,(
% 1.24/1.05 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 1.24/1.05 inference(skolemize,[status(sab)],[19])).
% 1.24/1.05 tff(21,plain,
% 1.24/1.05 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 1.24/1.05 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.24/1.05 tff(22,plain,
% 1.24/1.05 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.24/1.05 inference(quant_inst,[status(thm)],[])).
% 1.24/1.05 tff(23,plain,
% 1.24/1.05 ($false),
% 1.24/1.05 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 1.24/1.05 tff(24,plain,(~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.05 tff(25,plain,
% 1.24/1.05 (((~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.24/1.06 inference(tautology,[status(thm)],[])).
% 1.24/1.06 tff(26,plain,
% 1.24/1.06 ((~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.24/1.06 inference(unit_resolution,[status(thm)],[25, 24])).
% 1.24/1.06 tff(27,plain,
% 1.24/1.06 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT)))),
% 1.24/1.06 inference(rewrite,[status(thm)],[])).
% 1.24/1.06 tff(28,plain,
% 1.24/1.06 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : (((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT)) => vtcheck(VC, vvar(Vy), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT)))),
% 1.24/1.06 inference(rewrite,[status(thm)],[])).
% 1.24/1.06 tff(29,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : (((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT)) => vtcheck(VC, vvar(Vy), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Strong-var'')).
% 1.24/1.06 tff(30,plain,
% 1.24/1.06 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.24/1.06 tff(31,plain,
% 1.24/1.06 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[30, 27])).
% 1.24/1.06 tff(32,plain,
% 1.24/1.06 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[31, 27])).
% 1.24/1.06 tff(33,plain,
% 1.24/1.06 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[32, 27])).
% 1.24/1.06 tff(34,plain,
% 1.24/1.06 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[33, 27])).
% 1.24/1.06 tff(35,plain,
% 1.24/1.06 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[34, 27])).
% 1.24/1.06 tff(36,plain,
% 1.24/1.06 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) | vtcheck(VC, vvar(Vy), VT))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[35, 27])).
% 1.24/1.06 tff(37,plain,(
% 1.24/1.06 ~((~((~visFreeVar(Vx!78, vvar(Vy!75))) & vtcheck(vbind(Vx!78, VS!77, VC!76), vvar(Vy!75), VT!74))) | vtcheck(VC!76, vvar(Vy!75), VT!74))),
% 1.24/1.06 inference(skolemize,[status(sab)],[36])).
% 1.24/1.06 tff(38,plain,
% 1.24/1.06 ((~visFreeVar(Vx!78, vvar(Vy!75))) & vtcheck(vbind(Vx!78, VS!77, VC!76), vvar(Vy!75), VT!74)),
% 1.24/1.06 inference(or_elim,[status(thm)],[37])).
% 1.24/1.06 tff(39,plain,
% 1.24/1.06 (vtcheck(vbind(Vx!78, VS!77, VC!76), vvar(Vy!75), VT!74)),
% 1.24/1.06 inference(and_elim,[status(thm)],[38])).
% 1.24/1.06 tff(40,plain,
% 1.24/1.06 (^[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)))))))),
% 1.24/1.06 inference(bind,[status(th)],[])).
% 1.24/1.06 tff(41,plain,
% 1.24/1.06 (![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))))))),
% 1.24/1.06 inference(quant_intro,[status(thm)],[40])).
% 1.24/1.06 tff(42,plain,
% 1.24/1.06 (^[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))))))))),
% 1.24/1.06 inference(bind,[status(th)],[])).
% 1.24/1.06 tff(43,plain,
% 1.24/1.06 (![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))))))),
% 1.24/1.06 inference(quant_intro,[status(thm)],[42])).
% 1.24/1.06 tff(44,plain,
% 1.24/1.06 (^[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)))))),
% 1.24/1.06 inference(bind,[status(th)],[])).
% 1.24/1.06 tff(45,plain,
% 1.24/1.06 (![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))))),
% 1.24/1.06 inference(quant_intro,[status(thm)],[44])).
% 1.24/1.06 tff(46,plain,
% 1.24/1.06 (![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)))),
% 1.24/1.06 inference(rewrite,[status(thm)],[])).
% 1.24/1.06 tff(47,plain,
% 1.24/1.06 (^[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)))))),
% 1.24/1.06 inference(bind,[status(th)],[])).
% 1.24/1.06 tff(48,plain,
% 1.24/1.06 (![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)))),
% 1.24/1.06 inference(quant_intro,[status(thm)],[47])).
% 1.24/1.06 tff(49,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/sandbox2/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 1.24/1.06 tff(50,plain,
% 1.24/1.06 (![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)))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.24/1.06 tff(51,plain,
% 1.24/1.06 (![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)))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.24/1.06 tff(52,plain,(
% 1.24/1.06 ![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)))),
% 1.24/1.06 inference(skolemize,[status(sab)],[51])).
% 1.24/1.06 tff(53,plain,
% 1.24/1.06 (![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))))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.24/1.06 tff(54,plain,
% 1.24/1.06 (![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))))))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[53, 43])).
% 1.24/1.06 tff(55,plain,
% 1.24/1.06 (![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))))))),
% 1.24/1.06 inference(modus_ponens,[status(thm)],[54, 41])).
% 1.24/1.06 tff(56,plain,
% 1.24/1.06 (((~![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(vbind(Vx!78, VS!77, VC!76), vvar(Vy!75), VT!74)) | (~((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))) | (~((~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), varrow(tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), VT!74))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))))) <=> ((~![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(vbind(Vx!78, VS!77, VC!76), vvar(Vy!75), VT!74)) | (~((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))) | (~((~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), varrow(tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), VT!74))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))))),
% 1.24/1.06 inference(rewrite,[status(thm)],[])).
% 1.24/1.06 tff(57,plain,
% 1.24/1.06 ((~![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(vbind(Vx!78, VS!77, VC!76), vvar(Vy!75), VT!74)) | (~((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))) | (~((~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), varrow(tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), VT!74))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))))),
% 1.24/1.06 inference(quant_inst,[status(thm)],[])).
% 1.24/1.06 tff(58,plain,
% 1.24/1.06 ((~![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(vbind(Vx!78, VS!77, VC!76), vvar(Vy!75), VT!74)) | (~((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))) | (~((~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), varrow(tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), VT!74))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))))),
% 1.24/1.07 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.24/1.07 tff(59,plain,
% 1.24/1.07 ((~((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))) | (~((~(vvar(Vy!75) = vabs(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT1_68(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)), tptp_fun_Ve2_69(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VT2_67(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~(vvar(Vy!75) = vapp(tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve1_73(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), varrow(tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), VT!74))) | (~vtcheck(vbind(Vx!78, VS!77, VC!76), tptp_fun_Ve2_72(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), tptp_fun_VS_71(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))))),
% 1.24/1.07 inference(unit_resolution,[status(thm)],[58, 55, 39])).
% 1.24/1.07 tff(60,plain,
% 1.24/1.07 (~((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))),
% 1.24/1.07 inference(unit_resolution,[status(thm)],[59, 26, 13])).
% 1.24/1.07 tff(61,plain,
% 1.24/1.07 (((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74)))) | (vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.24/1.07 inference(tautology,[status(thm)],[])).
% 1.24/1.07 tff(62,plain,
% 1.24/1.07 (vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))),
% 1.24/1.07 inference(unit_resolution,[status(thm)],[61, 60])).
% 1.24/1.07 tff(63,plain,
% 1.24/1.07 (vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75)),
% 1.24/1.07 inference(symmetry,[status(thm)],[62])).
% 1.24/1.07 tff(64,plain,
% 1.24/1.07 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : refl((~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))))),
% 1.24/1.07 inference(bind,[status(th)],[])).
% 1.24/1.07 tff(65,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 1.24/1.07 inference(quant_intro,[status(thm)],[64])).
% 1.24/1.07 tff(66,plain,
% 1.24/1.07 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : trans(monotonicity(rewrite(((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> ((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))), trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1)) <=> (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> (~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))), rewrite((~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> (((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))), rewrite((((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), ((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) & ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))), rewrite((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) & ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))), ((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))))),
% 1.24/1.07 inference(bind,[status(th)],[])).
% 1.24/1.07 tff(67,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 1.24/1.07 inference(quant_intro,[status(thm)],[66])).
% 1.24/1.07 tff(68,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 1.24/1.07 inference(rewrite,[status(thm)],[])).
% 1.24/1.07 tff(69,plain,
% 1.24/1.07 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : rewrite((((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))))),
% 1.24/1.07 inference(bind,[status(th)],[])).
% 1.24/1.07 tff(70,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 1.24/1.07 inference(quant_intro,[status(thm)],[69])).
% 1.24/1.07 tff(71,axiom,(![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''EQ-bind'')).
% 1.24/1.07 tff(72,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 1.24/1.07 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.24/1.07 tff(73,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 1.24/1.07 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.24/1.07 tff(74,plain,(
% 1.24/1.07 ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 1.24/1.07 inference(skolemize,[status(sab)],[73])).
% 1.24/1.07 tff(75,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 1.24/1.07 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.24/1.07 tff(76,plain,
% 1.24/1.07 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 1.24/1.07 inference(modus_ponens,[status(thm)],[75, 65])).
% 1.24/1.07 tff(77,plain,
% 1.24/1.07 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))))),
% 1.24/1.07 inference(rewrite,[status(thm)],[])).
% 1.24/1.07 tff(78,plain,
% 1.24/1.07 ((~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) <=> (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))))),
% 1.32/1.07 inference(rewrite,[status(thm)],[])).
% 1.32/1.07 tff(79,plain,
% 1.32/1.07 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))))),
% 1.32/1.07 inference(monotonicity,[status(thm)],[78])).
% 1.32/1.07 tff(80,plain,
% 1.32/1.07 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))))),
% 1.32/1.08 inference(transitivity,[status(thm)],[79, 77])).
% 1.32/1.08 tff(81,plain,
% 1.32/1.08 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))))),
% 1.32/1.08 inference(quant_inst,[status(thm)],[])).
% 1.32/1.08 tff(82,plain,
% 1.32/1.08 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))))),
% 1.32/1.08 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.32/1.08 tff(83,plain,
% 1.32/1.08 (~((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))),
% 1.32/1.08 inference(unit_resolution,[status(thm)],[82, 76])).
% 1.32/1.08 tff(84,plain,
% 1.32/1.08 (((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(Vy!75 = Vx!78)) | (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))) | ((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))),
% 1.32/1.08 inference(tautology,[status(thm)],[])).
% 1.32/1.08 tff(85,plain,
% 1.32/1.08 ((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))),
% 1.32/1.08 inference(unit_resolution,[status(thm)],[84, 83])).
% 1.32/1.08 tff(86,assumption,(~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))), introduced(assumption)).
% 1.32/1.08 tff(87,plain,
% 1.32/1.08 (((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))),
% 1.32/1.08 inference(tautology,[status(thm)],[])).
% 1.32/1.08 tff(88,plain,
% 1.32/1.08 (vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.08 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.32/1.08 tff(89,plain,
% 1.32/1.08 (vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vsomeType(VT!74)),
% 1.32/1.08 inference(symmetry,[status(thm)],[88])).
% 1.32/1.08 tff(90,plain,
% 1.32/1.08 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))))),
% 1.32/1.08 inference(quant_inst,[status(thm)],[])).
% 1.32/1.08 tff(91,plain,
% 1.32/1.08 (~((~((~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))),
% 1.32/1.08 inference(unit_resolution,[status(thm)],[90, 76])).
% 1.32/1.08 tff(92,plain,
% 1.32/1.08 (((~((~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)) | (~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))) | ((~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))),
% 1.32/1.08 inference(tautology,[status(thm)],[])).
% 1.32/1.08 tff(93,plain,
% 1.32/1.08 ((~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))),
% 1.32/1.08 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.32/1.08 tff(94,plain,
% 1.32/1.08 (((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))),
% 1.32/1.08 inference(tautology,[status(thm)],[])).
% 1.32/1.08 tff(95,plain,
% 1.32/1.08 (vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.08 inference(unit_resolution,[status(thm)],[94, 86])).
% 1.32/1.08 tff(96,plain,
% 1.32/1.08 (vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)),
% 1.32/1.08 inference(symmetry,[status(thm)],[95])).
% 1.32/1.08 tff(97,plain,
% 1.32/1.08 ((~((~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))),
% 1.32/1.08 inference(tautology,[status(thm)],[])).
% 1.32/1.08 tff(98,plain,
% 1.32/1.08 ((~((~(vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))),
% 1.32/1.08 inference(unit_resolution,[status(thm)],[97, 96])).
% 1.32/1.08 tff(99,plain,
% 1.32/1.08 (~((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[98, 93])).
% 1.32/1.09 tff(100,plain,
% 1.32/1.09 (((~(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = Vx!78)) | (~(tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))) | (tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)),
% 1.32/1.09 inference(tautology,[status(thm)],[])).
% 1.32/1.09 tff(101,plain,
% 1.32/1.09 (tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[100, 99])).
% 1.32/1.09 tff(102,plain,
% 1.32/1.09 (VC!76 = tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)),
% 1.32/1.09 inference(symmetry,[status(thm)],[101])).
% 1.32/1.09 tff(103,plain,
% 1.32/1.09 (((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.09 inference(tautology,[status(thm)],[])).
% 1.32/1.09 tff(104,plain,
% 1.32/1.09 (Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[103, 86])).
% 1.32/1.09 tff(105,plain,
% 1.32/1.09 (vlookup(Vy!75, VC!76) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.09 inference(monotonicity,[status(thm)],[104, 102])).
% 1.32/1.09 tff(106,plain,
% 1.32/1.09 (vlookup(Vy!75, VC!76) = vsomeType(VT!74)),
% 1.32/1.09 inference(transitivity,[status(thm)],[105, 89])).
% 1.32/1.09 tff(107,plain,
% 1.32/1.09 (~vtcheck(VC!76, vvar(Vy!75), VT!74)),
% 1.32/1.09 inference(or_elim,[status(thm)],[37])).
% 1.32/1.09 tff(108,plain,
% 1.32/1.09 (^[VC: $i, Vx: $i, VT: $i] : refl(((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)) <=> ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(109,plain,
% 1.32/1.09 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)) <=> ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[108])).
% 1.32/1.09 tff(110,plain,
% 1.32/1.09 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)) <=> ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 1.32/1.09 inference(rewrite,[status(thm)],[])).
% 1.32/1.09 tff(111,plain,
% 1.32/1.09 (^[VC: $i, Vx: $i, VT: $i] : rewrite(((vlookup(Vx, VC) = vsomeType(VT)) => vtcheck(VC, vvar(Vx), VT)) <=> ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(112,plain,
% 1.32/1.09 (![VC: $i, Vx: $i, VT: $i] : ((vlookup(Vx, VC) = vsomeType(VT)) => vtcheck(VC, vvar(Vx), VT)) <=> ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[111])).
% 1.32/1.09 tff(113,axiom,(![VC: $i, Vx: $i, VT: $i] : ((vlookup(Vx, VC) = vsomeType(VT)) => vtcheck(VC, vvar(Vx), VT))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''T-var'')).
% 1.32/1.09 tff(114,plain,
% 1.32/1.09 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.32/1.09 tff(115,plain,
% 1.32/1.09 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[114, 110])).
% 1.32/1.09 tff(116,plain,(
% 1.32/1.09 ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 1.32/1.09 inference(skolemize,[status(sab)],[115])).
% 1.32/1.09 tff(117,plain,
% 1.32/1.09 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[116, 109])).
% 1.32/1.09 tff(118,plain,
% 1.32/1.09 (((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | ((~(vlookup(Vy!75, VC!76) = vsomeType(VT!74))) | vtcheck(VC!76, vvar(Vy!75), VT!74))) <=> ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | (~(vlookup(Vy!75, VC!76) = vsomeType(VT!74))) | vtcheck(VC!76, vvar(Vy!75), VT!74))),
% 1.32/1.09 inference(rewrite,[status(thm)],[])).
% 1.32/1.09 tff(119,plain,
% 1.32/1.09 ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | ((~(vlookup(Vy!75, VC!76) = vsomeType(VT!74))) | vtcheck(VC!76, vvar(Vy!75), VT!74))),
% 1.32/1.09 inference(quant_inst,[status(thm)],[])).
% 1.32/1.09 tff(120,plain,
% 1.32/1.09 ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | (~(vlookup(Vy!75, VC!76) = vsomeType(VT!74))) | vtcheck(VC!76, vvar(Vy!75), VT!74)),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.32/1.09 tff(121,plain,
% 1.32/1.09 (~(vlookup(Vy!75, VC!76) = vsomeType(VT!74))),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[120, 117, 107])).
% 1.32/1.09 tff(122,plain,
% 1.32/1.09 ($false),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[121, 106])).
% 1.32/1.09 tff(123,plain,((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.09 tff(124,plain,
% 1.32/1.09 (((~(vvar(Vy!75) = vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74)))) | (vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))),
% 1.32/1.09 inference(tautology,[status(thm)],[])).
% 1.32/1.09 tff(125,plain,
% 1.32/1.09 (vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74)),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[124, 60])).
% 1.32/1.09 tff(126,plain,
% 1.32/1.09 (^[VVar0: $i, VVar1: $i] : refl((~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))))) <=> (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))))))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(127,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))))) <=> ![VVar0: $i, VVar1: $i] : (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[126])).
% 1.32/1.09 tff(128,plain,
% 1.32/1.09 (^[VVar0: $i, VVar1: $i] : rewrite((((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))))))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(129,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> ![VVar0: $i, VVar1: $i] : (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[128])).
% 1.32/1.09 tff(130,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 1.32/1.09 inference(rewrite,[status(thm)],[])).
% 1.32/1.09 tff(131,plain,
% 1.32/1.09 (^[VVar0: $i, VVar1: $i] : rewrite((((vvar(VVar0) = vvar(VVar1)) => (VVar0 = VVar1)) & ((VVar0 = VVar1) => (vvar(VVar0) = vvar(VVar1)))) <=> (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(132,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (((vvar(VVar0) = vvar(VVar1)) => (VVar0 = VVar1)) & ((VVar0 = VVar1) => (vvar(VVar0) = vvar(VVar1)))) <=> ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[131])).
% 1.32/1.09 tff(133,axiom,(![VVar0: $i, VVar1: $i] : (((vvar(VVar0) = vvar(VVar1)) => (VVar0 = VVar1)) & ((VVar0 = VVar1) => (vvar(VVar0) = vvar(VVar1))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''EQ-var'')).
% 1.32/1.09 tff(134,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.32/1.09 tff(135,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[134, 130])).
% 1.32/1.09 tff(136,plain,(
% 1.32/1.09 ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 1.32/1.09 inference(skolemize,[status(sab)],[135])).
% 1.32/1.09 tff(137,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[136, 129])).
% 1.32/1.09 tff(138,plain,
% 1.32/1.09 (![VVar0: $i, VVar1: $i] : (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[137, 127])).
% 1.32/1.09 tff(139,plain,
% 1.32/1.09 ((~![VVar0: $i, VVar1: $i] : (~((~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))) | (~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))))) | (~((~((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75))) | (~((~(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75)) | (vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))))))),
% 1.32/1.09 inference(quant_inst,[status(thm)],[])).
% 1.32/1.09 tff(140,plain,
% 1.32/1.09 (~((~((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75))) | (~((~(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75)) | (vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75)))))),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.32/1.09 tff(141,plain,
% 1.32/1.09 (((~((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75))) | (~((~(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75)) | (vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))))) | ((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75))),
% 1.32/1.09 inference(tautology,[status(thm)],[])).
% 1.32/1.09 tff(142,plain,
% 1.32/1.09 ((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75)),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[141, 140])).
% 1.32/1.09 tff(143,plain,
% 1.32/1.09 ((~((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75))) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75)),
% 1.32/1.09 inference(tautology,[status(thm)],[])).
% 1.32/1.09 tff(144,plain,
% 1.32/1.09 ((~((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75))) | (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75)),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[143, 63])).
% 1.32/1.09 tff(145,plain,
% 1.32/1.09 (tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)) = Vy!75),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[144, 142])).
% 1.32/1.09 tff(146,plain,
% 1.32/1.09 (Vy!75 = tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))),
% 1.32/1.09 inference(symmetry,[status(thm)],[145])).
% 1.32/1.09 tff(147,plain,
% 1.32/1.09 (vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vlookup(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)), vbind(Vx!78, VS!77, VC!76))),
% 1.32/1.09 inference(monotonicity,[status(thm)],[146])).
% 1.32/1.09 tff(148,plain,
% 1.32/1.09 (vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74)),
% 1.32/1.09 inference(transitivity,[status(thm)],[147, 125])).
% 1.32/1.09 tff(149,plain,
% 1.32/1.09 ((vsomeType(VT!74) = vnoType) <=> (vnoType = vsomeType(VT!74))),
% 1.32/1.09 inference(commutativity,[status(thm)],[])).
% 1.32/1.09 tff(150,plain,
% 1.32/1.09 ((vnoType = vsomeType(VT!74)) <=> (vsomeType(VT!74) = vnoType)),
% 1.32/1.09 inference(symmetry,[status(thm)],[149])).
% 1.32/1.09 tff(151,plain,
% 1.32/1.09 ((~(vnoType = vsomeType(VT!74))) <=> (~(vsomeType(VT!74) = vnoType))),
% 1.32/1.09 inference(monotonicity,[status(thm)],[150])).
% 1.32/1.09 tff(152,plain,
% 1.32/1.09 (^[VTyp0: $i] : refl((~(vnoType = vsomeType(VTyp0))) <=> (~(vnoType = vsomeType(VTyp0))))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(153,plain,
% 1.32/1.09 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[152])).
% 1.32/1.09 tff(154,plain,
% 1.32/1.09 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 1.32/1.09 inference(rewrite,[status(thm)],[])).
% 1.32/1.09 tff(155,axiom,(![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-noType-someType'')).
% 1.32/1.09 tff(156,plain,
% 1.32/1.09 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.32/1.09 tff(157,plain,(
% 1.32/1.09 ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 1.32/1.09 inference(skolemize,[status(sab)],[156])).
% 1.32/1.09 tff(158,plain,
% 1.32/1.09 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[157, 153])).
% 1.32/1.09 tff(159,plain,
% 1.32/1.09 ((~![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))) | (~(vnoType = vsomeType(VT!74)))),
% 1.32/1.09 inference(quant_inst,[status(thm)],[])).
% 1.32/1.09 tff(160,plain,
% 1.32/1.09 (~(vnoType = vsomeType(VT!74))),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[159, 158])).
% 1.32/1.09 tff(161,plain,
% 1.32/1.09 (~(vsomeType(VT!74) = vnoType)),
% 1.32/1.09 inference(modus_ponens,[status(thm)],[160, 151])).
% 1.32/1.09 tff(162,plain,
% 1.32/1.09 (((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (vsomeType(VT!74) = vnoType)),
% 1.32/1.09 inference(tautology,[status(thm)],[])).
% 1.32/1.09 tff(163,plain,
% 1.32/1.09 ((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))),
% 1.32/1.09 inference(unit_resolution,[status(thm)],[162, 161])).
% 1.32/1.09 tff(164,plain,
% 1.32/1.09 (^[VVar0: $i, VCtx0: $i, RESULT: $i] : rewrite(((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))) <=> ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))))))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(165,plain,
% 1.32/1.09 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[164])).
% 1.32/1.09 tff(166,plain,
% 1.32/1.09 (^[VVar0: $i, VCtx0: $i, RESULT: $i] : rewrite((((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(vlookup(VVar0, VCtx0) = RESULT))) <=> ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))))),
% 1.32/1.09 inference(bind,[status(th)],[])).
% 1.32/1.09 tff(167,plain,
% 1.32/1.09 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(vlookup(VVar0, VCtx0) = RESULT))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))),
% 1.32/1.09 inference(quant_intro,[status(thm)],[166])).
% 1.32/1.09 tff(168,plain,
% 1.32/1.09 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 1.32/1.09 inference(rewrite,[status(thm)],[])).
% 1.32/1.09 tff(169,plain,
% 1.32/1.09 (^[VVar0: $i, VCtx0: $i, RESULT: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))))), quant_intro(proof_bind(^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : trans(monotonicity(rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)))), (((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))), (((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))))), (?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))), (((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))) <=> ((?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))))), rewrite(((?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))), (((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))))), (((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> ((vlookup(VVar0, VCtx0) = RESULT) => (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))))), rewrite(((vlookup(VVar0, VCtx0) = RESULT) => (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))), (((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))))),
% 1.32/1.10 inference(bind,[status(th)],[])).
% 1.32/1.10 tff(170,plain,
% 1.32/1.10 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 1.32/1.10 inference(quant_intro,[status(thm)],[169])).
% 1.32/1.10 tff(171,axiom,(![VVar0: $i, VCtx0: $i, RESULT: $i] : ((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''lookup-INV'')).
% 1.32/1.10 tff(172,plain,
% 1.32/1.10 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 1.32/1.10 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.32/1.10 tff(173,plain,
% 1.32/1.10 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 1.32/1.10 inference(modus_ponens,[status(thm)],[172, 168])).
% 1.32/1.10 tff(174,plain,(
% 1.32/1.10 ![VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 1.32/1.10 inference(skolemize,[status(sab)],[173])).
% 1.32/1.10 tff(175,plain,
% 1.32/1.10 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))),
% 1.32/1.10 inference(modus_ponens,[status(thm)],[174, 167])).
% 1.32/1.10 tff(176,plain,
% 1.32/1.10 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))),
% 1.32/1.10 inference(modus_ponens,[status(thm)],[175, 165])).
% 1.32/1.10 tff(177,plain,
% 1.32/1.10 (((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))) <=> ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))),
% 1.32/1.10 inference(rewrite,[status(thm)],[])).
% 1.32/1.10 tff(178,plain,
% 1.32/1.10 (((~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))))) <=> ((~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))),
% 1.32/1.10 inference(rewrite,[status(thm)],[])).
% 1.32/1.10 tff(179,plain,
% 1.32/1.10 ((~((tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) <=> (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))))),
% 1.32/1.10 inference(rewrite,[status(thm)],[])).
% 1.32/1.10 tff(180,plain,
% 1.32/1.10 ((~((~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) <=> (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))))),
% 1.32/1.10 inference(rewrite,[status(thm)],[])).
% 1.32/1.10 tff(181,plain,
% 1.32/1.10 (((~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))))) <=> ((~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))))),
% 1.32/1.11 inference(monotonicity,[status(thm)],[180, 179])).
% 1.32/1.11 tff(182,plain,
% 1.32/1.11 (((~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))))) <=> ((~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))),
% 1.32/1.11 inference(transitivity,[status(thm)],[181, 178])).
% 1.32/1.11 tff(183,plain,
% 1.32/1.11 (((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))))) <=> ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74)))))),
% 1.32/1.11 inference(monotonicity,[status(thm)],[182])).
% 1.32/1.11 tff(184,plain,
% 1.32/1.11 (((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))))) <=> ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))))),
% 1.32/1.11 inference(transitivity,[status(thm)],[183, 177])).
% 1.32/1.11 tff(185,plain,
% 1.32/1.11 ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))))),
% 1.32/1.11 inference(quant_inst,[status(thm)],[])).
% 1.32/1.11 tff(186,plain,
% 1.32/1.11 ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | (~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74)))),
% 1.32/1.11 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.32/1.11 tff(187,plain,
% 1.32/1.11 ((~((~(vsomeType(VT!74) = vnoType)) | (~(vbind(Vx!78, VS!77, VC!76) = vempty)) | (~(Vy!75 = tptp_fun_Vx_0(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~(vlookup(Vy!75, vbind(Vx!78, VS!77, VC!76)) = vsomeType(VT!74)))),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[186, 176])).
% 1.32/1.12 tff(188,plain,
% 1.32/1.12 ((~((~(Vy!75 = tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_8(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_7(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) | (~(vsomeType(VT!74) = vlookup(tptp_fun_Vx_6(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_5(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))) | (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))))),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[187, 163, 148])).
% 1.32/1.12 tff(189,plain,
% 1.32/1.12 (~((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))))),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[188, 123])).
% 1.32/1.12 tff(190,plain,
% 1.32/1.12 (((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))),
% 1.32/1.12 inference(tautology,[status(thm)],[])).
% 1.32/1.12 tff(191,plain,
% 1.32/1.12 (vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[190, 189])).
% 1.32/1.12 tff(192,plain,
% 1.32/1.12 (vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)),
% 1.32/1.12 inference(symmetry,[status(thm)],[191])).
% 1.32/1.12 tff(193,plain,
% 1.32/1.12 (((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.12 inference(tautology,[status(thm)],[])).
% 1.32/1.12 tff(194,plain,
% 1.32/1.12 (tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[193, 189])).
% 1.32/1.12 tff(195,plain,
% 1.32/1.12 (((~(tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vbind(Vx!78, VS!77, VC!76) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)))) | (~(Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))) | (~(vsomeType(VT!74) = vsomeType(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))))) | (Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.12 inference(tautology,[status(thm)],[])).
% 1.32/1.12 tff(196,plain,
% 1.32/1.12 (Vy!75 = tptp_fun_Vx_3(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[195, 189])).
% 1.32/1.12 tff(197,plain,
% 1.32/1.12 (Vy!75 = tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)),
% 1.32/1.12 inference(transitivity,[status(thm)],[196, 194])).
% 1.32/1.12 tff(198,plain,
% 1.32/1.12 (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(tptp_fun_Vy_2(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75))),
% 1.32/1.12 inference(monotonicity,[status(thm)],[197])).
% 1.32/1.12 tff(199,plain,
% 1.32/1.12 (vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76)),
% 1.32/1.12 inference(transitivity,[status(thm)],[198, 192])).
% 1.32/1.12 tff(200,plain,
% 1.32/1.12 ((~((~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))))) | (~(vbind(Vy!75, tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75), tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75)) = vbind(Vx!78, VS!77, VC!76))) | (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))))),
% 1.32/1.12 inference(tautology,[status(thm)],[])).
% 1.32/1.12 tff(201,plain,
% 1.32/1.12 (~((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76)))),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[200, 199, 85])).
% 1.32/1.12 tff(202,plain,
% 1.32/1.12 (((~(Vy!75 = Vx!78)) | (~(tptp_fun_VTy_1(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VS!77)) | (~(tptp_fun_VC_4(vsomeType(VT!74), vbind(Vx!78, VS!77, VC!76), Vy!75) = VC!76))) | (Vy!75 = Vx!78)),
% 1.32/1.12 inference(tautology,[status(thm)],[])).
% 1.32/1.12 tff(203,plain,
% 1.32/1.12 (Vy!75 = Vx!78),
% 1.32/1.12 inference(unit_resolution,[status(thm)],[202, 201])).
% 1.32/1.12 tff(204,plain,
% 1.32/1.12 (visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))) <=> visFreeVar(Vx!78, vvar(Vy!75))),
% 1.32/1.12 inference(monotonicity,[status(thm)],[203, 63])).
% 1.32/1.12 tff(205,plain,
% 1.32/1.12 (visFreeVar(Vx!78, vvar(Vy!75)) <=> visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.32/1.12 inference(symmetry,[status(thm)],[204])).
% 1.32/1.12 tff(206,plain,
% 1.32/1.12 ((~visFreeVar(Vx!78, vvar(Vy!75))) <=> (~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.12 inference(monotonicity,[status(thm)],[205])).
% 1.32/1.12 tff(207,plain,
% 1.32/1.12 (~visFreeVar(Vx!78, vvar(Vy!75))),
% 1.32/1.12 inference(and_elim,[status(thm)],[38])).
% 1.32/1.12 tff(208,plain,
% 1.32/1.12 (~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.32/1.12 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.32/1.12 tff(209,plain,
% 1.32/1.12 (^[VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = Vv) & (VExp0 = vvar(Vx))) <=> (~((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))), ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) <=> (~(~((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))))), rewrite((~(~((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))))), ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))), rewrite((((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))) <=> (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))), (((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> (((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))))), rewrite((((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))), (((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))))),
% 1.32/1.12 inference(bind,[status(th)],[])).
% 1.32/1.12 tff(210,plain,
% 1.32/1.12 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 1.32/1.12 inference(quant_intro,[status(thm)],[209])).
% 1.32/1.12 tff(211,plain,
% 1.32/1.12 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 1.32/1.12 inference(rewrite,[status(thm)],[])).
% 1.32/1.12 tff(212,plain,
% 1.32/1.12 (^[VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : trans(monotonicity(rewrite((((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))) <=> (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))), rewrite((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 1.32/1.12 inference(bind,[status(th)],[])).
% 1.32/1.12 tff(213,plain,
% 1.32/1.12 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 1.32/1.12 inference(quant_intro,[status(thm)],[212])).
% 1.32/1.12 tff(214,axiom,(![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','isFreeVar0')).
% 1.32/1.12 tff(215,plain,
% 1.32/1.12 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 1.32/1.12 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.32/1.12 tff(216,plain,
% 1.32/1.12 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 1.32/1.12 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.32/1.12 tff(217,plain,(
% 1.32/1.12 ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 1.32/1.12 inference(skolemize,[status(sab)],[216])).
% 1.32/1.12 tff(218,plain,
% 1.32/1.12 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 1.32/1.12 inference(modus_ponens,[status(thm)],[217, 210])).
% 1.32/1.12 tff(219,plain,
% 1.32/1.12 (((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) <=> ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.12 inference(rewrite,[status(thm)],[])).
% 1.32/1.12 tff(220,plain,
% 1.32/1.12 (($false | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) <=> ((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.12 inference(rewrite,[status(thm)],[])).
% 1.32/1.12 tff(221,plain,
% 1.32/1.12 ((~(~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) <=> visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(222,plain,
% 1.32/1.13 (((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | $false) <=> (~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(223,plain,
% 1.32/1.13 ((~$true) <=> $false),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(224,plain,
% 1.32/1.13 (((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | $true) <=> $true),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(225,plain,
% 1.32/1.13 ((Vy!75 = Vy!75) <=> $true),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(226,plain,
% 1.32/1.13 (((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75)) <=> ((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | $true)),
% 1.32/1.13 inference(monotonicity,[status(thm)],[225])).
% 1.32/1.13 tff(227,plain,
% 1.32/1.13 (((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75)) <=> $true),
% 1.32/1.13 inference(transitivity,[status(thm)],[226, 224])).
% 1.32/1.13 tff(228,plain,
% 1.32/1.13 ((~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75))) <=> (~$true)),
% 1.32/1.13 inference(monotonicity,[status(thm)],[227])).
% 1.32/1.13 tff(229,plain,
% 1.32/1.13 ((~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75))) <=> $false),
% 1.32/1.13 inference(transitivity,[status(thm)],[228, 223])).
% 1.32/1.13 tff(230,plain,
% 1.32/1.13 ((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) <=> (~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(231,plain,
% 1.32/1.13 (((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75)))) <=> ((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | $false)),
% 1.32/1.13 inference(monotonicity,[status(thm)],[230, 229])).
% 1.32/1.13 tff(232,plain,
% 1.32/1.13 (((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75)))) <=> (~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.13 inference(transitivity,[status(thm)],[231, 222])).
% 1.32/1.13 tff(233,plain,
% 1.32/1.13 ((~((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75))))) <=> (~(~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))))),
% 1.32/1.13 inference(monotonicity,[status(thm)],[232])).
% 1.32/1.13 tff(234,plain,
% 1.32/1.13 ((~((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75))))) <=> visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.32/1.13 inference(transitivity,[status(thm)],[233, 221])).
% 1.32/1.13 tff(235,plain,
% 1.32/1.13 ((~(Vy!75 = Vy!75)) <=> (~$true)),
% 1.32/1.13 inference(monotonicity,[status(thm)],[225])).
% 1.32/1.13 tff(236,plain,
% 1.32/1.13 ((~(Vy!75 = Vy!75)) <=> $false),
% 1.32/1.13 inference(transitivity,[status(thm)],[235, 223])).
% 1.32/1.13 tff(237,plain,
% 1.32/1.13 (((~(Vy!75 = Vy!75)) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (~((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75)))))) <=> ($false | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.13 inference(monotonicity,[status(thm)],[236, 234])).
% 1.32/1.13 tff(238,plain,
% 1.32/1.13 (((~(Vy!75 = Vy!75)) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (~((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75)))))) <=> ((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.13 inference(transitivity,[status(thm)],[237, 220])).
% 1.32/1.13 tff(239,plain,
% 1.32/1.13 (((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(Vy!75 = Vy!75)) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (~((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75))))))) <=> ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))))),
% 1.32/1.13 inference(monotonicity,[status(thm)],[238])).
% 1.32/1.13 tff(240,plain,
% 1.32/1.13 (((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(Vy!75 = Vy!75)) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (~((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75))))))) <=> ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))),
% 1.32/1.13 inference(transitivity,[status(thm)],[239, 219])).
% 1.32/1.13 tff(241,plain,
% 1.32/1.13 ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(Vy!75 = Vy!75)) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | (~((~((~(Vy!75 = Vy!75)) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75)))))) | (~((~visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))) | (Vy!75 = Vy!75))))))),
% 1.32/1.13 inference(quant_inst,[status(thm)],[])).
% 1.32/1.13 tff(242,plain,
% 1.32/1.13 ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))) = vvar(Vy!75))) | visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.32/1.13 tff(243,plain,
% 1.32/1.13 (visFreeVar(Vy!75, vvar(tptp_fun_Vx_66(vbind(Vx!78, VS!77, VC!76), VT!74, vvar(Vy!75))))),
% 1.32/1.13 inference(unit_resolution,[status(thm)],[242, 218, 63])).
% 1.32/1.13 tff(244,plain,
% 1.32/1.13 ($false),
% 1.32/1.13 inference(unit_resolution,[status(thm)],[243, 208])).
% 1.32/1.13 % SZS output end Proof
%------------------------------------------------------------------------------