%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM143+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:01:08 AM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM143+1 : TPTP v9.0.0. Released v6.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 12:25:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(vsomeType_type, type, (
% 0.21/0.43 vsomeType: $i > $i)).
% 0.21/0.43 tff(tptp_fun_VT_50_type, type, (
% 0.21/0.43 tptp_fun_VT_50: $i)).
% 0.21/0.43 tff(vnoType_type, type, (
% 0.21/0.43 vnoType: $i)).
% 0.21/0.43 tff(vlookup_type, type, (
% 0.21/0.43 vlookup: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_VC_52_type, type, (
% 0.21/0.43 tptp_fun_VC_52: $i)).
% 0.21/0.43 tff(tptp_fun_Vx_42_type, type, (
% 0.21/0.43 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(vvar_type, type, (
% 0.21/0.43 vvar: $i > $i)).
% 0.21/0.43 tff(tptp_fun_Vy_51_type, type, (
% 0.21/0.43 tptp_fun_Vy_51: $i)).
% 0.21/0.43 tff(vtcheck_type, type, (
% 0.21/0.43 vtcheck: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_VT2_43_type, type, (
% 0.21/0.43 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Ve2_45_type, type, (
% 0.21/0.43 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(vbind_type, type, (
% 0.21/0.43 vbind: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_VT1_44_type, type, (
% 0.21/0.43 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Vx_46_type, type, (
% 0.21/0.43 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(varrow_type, type, (
% 0.21/0.43 varrow: ( $i * $i ) > $i)).
% 0.21/0.43 tff(vabs_type, type, (
% 0.21/0.43 vabs: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_VS_47_type, type, (
% 0.21/0.43 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Ve2_48_type, type, (
% 0.21/0.43 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Ve1_49_type, type, (
% 0.21/0.43 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(vapp_type, type, (
% 0.21/0.43 vapp: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Vx_54_type, type, (
% 0.21/0.43 tptp_fun_Vx_54: $i)).
% 0.21/0.43 tff(tptp_fun_VS_53_type, type, (
% 0.21/0.43 tptp_fun_VS_53: $i)).
% 0.21/0.43 tff(1,assumption,(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)))), introduced(assumption)).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(5,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'')).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.43 tff(7,plain,(
% 0.21/0.43 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[6])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.43 tff(11,plain,(~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 ((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.43 tff(14,assumption,(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)))), introduced(assumption)).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.43 tff(20,plain,(
% 0.21/0.43 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[19])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.21/0.43 tff(24,plain,(~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(VC!52, tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)), VT!50))) | (~vtcheck(VC!52, tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51))))) | (vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 ((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(VC!52, tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)), VT!50))) | (~vtcheck(VC!52, tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT)) => vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(29,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT)) => vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak-var'')).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.21/0.43 tff(34,plain,(
% 0.21/0.43 ~((~((vlookup(Vx!54, VC!52) = vnoType) & vtcheck(VC!52, vvar(Vy!51), VT!50))) | vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50))),
% 0.21/0.43 inference(skolemize,[status(sab)],[33])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 ((vlookup(Vx!54, VC!52) = vnoType) & vtcheck(VC!52, vvar(Vy!51), VT!50)),
% 0.21/0.43 inference(or_elim,[status(thm)],[34])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (vtcheck(VC!52, vvar(Vy!51), VT!50)),
% 0.21/0.43 inference(and_elim,[status(thm)],[35])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (^[Ve: $i, VT: $i, VC: $i] : refl(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(rewrite(((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) <=> (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT)))))), rewrite(((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) <=> (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))))), rewrite(((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) <=> (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))), rewrite(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.44 tff(46,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'')).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.44 tff(49,plain,(
% 0.21/0.44 ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[51, 38])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(VC!52, vvar(Vy!51), VT!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(VC!52, tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)), VT!50))) | (~vtcheck(VC!52, tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(VC!52, vvar(Vy!51), VT!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(VC!52, tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)), VT!50))) | (~vtcheck(VC!52, tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(VC!52, vvar(Vy!51), VT!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(VC!52, tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)), VT!50))) | (~vtcheck(VC!52, tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(VC!52, vvar(Vy!51), VT!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(VC!52, tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)), VT!50))) | (~vtcheck(VC!52, tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 ((~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(VC!52, tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51)), VT!50))) | (~vtcheck(VC!52, tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VS_47(VC!52, VT!50, vvar(Vy!51))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[55, 52, 36])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 ((~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), VC!52), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT2_43(VC!52, VT!50, vvar(Vy!51))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[56, 26])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[57, 13])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50)))) | (vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (^[VVar0: $i, VVar1: $i] : refl((~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))) <=> (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))) <=> ![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (^[VVar0: $i, VVar1: $i] : rewrite((((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> ![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.45 tff(68,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'')).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.45 tff(71,plain,(
% 0.21/0.45 ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[70])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))) | (~((~((~(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)) | (vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51)))) | (~((~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (~((~((~(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)) | (vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51)))) | (~((~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (((~((~(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)) | (vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51)))) | (~((~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)))) | ((~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 ((~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50)))) | (vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[78, 58])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51)),
% 0.21/0.46 inference(symmetry,[status(thm)],[79])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 ((~((~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51))) | (~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 ((~((~(vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51))) | (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[82, 77])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (Vy!51 = tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))),
% 0.21/0.46 inference(symmetry,[status(thm)],[83])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (vlookup(Vy!51, VC!52) = vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (vlookup(Vy!51, VC!52) = vsomeType(VT!50)),
% 0.21/0.46 inference(transitivity,[status(thm)],[85, 60])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 ((vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52)) <=> (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 ((vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50)) <=> (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52))),
% 0.21/0.46 inference(symmetry,[status(thm)],[87])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 ((~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))) <=> (~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (~vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50)),
% 0.21/0.46 inference(or_elim,[status(thm)],[34])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (^[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)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (![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))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![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))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (^[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)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (![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))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.46 tff(96,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'')).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.21/0.46 tff(99,plain,(
% 0.21/0.46 ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.46 inference(skolemize,[status(sab)],[98])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | ((~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))) | vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50))) <=> ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | (~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))) | vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | ((~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))) | vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | (~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))) | vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 100, 90])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[104, 89])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : refl(((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : rewrite(((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.46 inference(transitivity,[status(thm)],[112, 111])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[113, 110])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 (^[VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite(((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))) <=> ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))), (((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))) <=> ((~(Vx = Vy)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))))), rewrite(((~(Vx = Vy)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))), (((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[116, 114])).
% 0.21/0.46 tff(118,axiom,(![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','lookup2')).
% 0.21/0.46 tff(119,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[119, 108])).
% 0.21/0.46 tff(121,plain,(
% 0.21/0.46 ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[120])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[121, 107])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 (((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | ((Vy!51 = Vx!54) | (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52)))) <=> ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | (Vy!51 = Vx!54) | (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | ((Vy!51 = Vx!54) | (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | (Vy!51 = Vx!54) | (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 ((Vy!51 = Vx!54) | (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (Vy!51 = Vx!54),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[126, 105])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (Vx!54 = Vy!51),
% 0.21/0.47 inference(symmetry,[status(thm)],[127])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (vlookup(Vx!54, VC!52) = vlookup(Vy!51, VC!52)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (vlookup(Vx!54, VC!52) = vnoType),
% 0.21/0.47 inference(and_elim,[status(thm)],[35])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (vnoType = vlookup(Vx!54, VC!52)),
% 0.21/0.47 inference(symmetry,[status(thm)],[130])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (vnoType = vsomeType(VT!50)),
% 0.21/0.47 inference(transitivity,[status(thm)],[131, 129, 85, 60])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (^[VTyp0: $i] : refl((~(vnoType = vsomeType(VTyp0))) <=> (~(vnoType = vsomeType(VTyp0))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(136,axiom,(![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-noType-someType'')).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.47 tff(138,plain,(
% 0.21/0.47 ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[137])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 ((~![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))) | (~(vnoType = vsomeType(VT!50)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (~(vnoType = vsomeType(VT!50))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[141, 132])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------