%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM127+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:01:06 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM127+1 : TPTP v9.0.0. Released v6.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:24:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(vabs_type, type, (
% 0.19/0.43 vabs: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Ve2_45_type, type, (
% 0.19/0.43 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(vvar_type, type, (
% 0.19/0.43 vvar: $i > $i)).
% 0.19/0.43 tff(tptp_fun_Vy_51_type, type, (
% 0.19/0.43 tptp_fun_Vy_51: $i)).
% 0.19/0.43 tff(tptp_fun_VT_50_type, type, (
% 0.19/0.43 tptp_fun_VT_50: $i)).
% 0.19/0.43 tff(tptp_fun_VC_52_type, type, (
% 0.19/0.43 tptp_fun_VC_52: $i)).
% 0.19/0.43 tff(tptp_fun_VT1_44_type, type, (
% 0.19/0.43 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Vx_46_type, type, (
% 0.19/0.43 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(vtcheck_type, type, (
% 0.19/0.43 vtcheck: ( $i * $i * $i ) > $o)).
% 0.19/0.43 tff(tptp_fun_VT2_43_type, type, (
% 0.19/0.43 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(vbind_type, type, (
% 0.19/0.43 vbind: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(varrow_type, type, (
% 0.19/0.43 varrow: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VS_47_type, type, (
% 0.19/0.43 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Ve2_48_type, type, (
% 0.19/0.43 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Ve1_49_type, type, (
% 0.19/0.43 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(vapp_type, type, (
% 0.19/0.43 vapp: ( $i * $i ) > $i)).
% 0.19/0.43 tff(vsomeType_type, type, (
% 0.19/0.43 vsomeType: $i > $i)).
% 0.19/0.43 tff(vlookup_type, type, (
% 0.19/0.43 vlookup: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Vx_42_type, type, (
% 0.19/0.43 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VS_53_type, type, (
% 0.19/0.43 tptp_fun_VS_53: $i)).
% 0.19/0.43 tff(tptp_fun_Vx_54_type, type, (
% 0.19/0.43 tptp_fun_Vx_54: $i)).
% 0.19/0.43 tff(visFreeVar_type, type, (
% 0.19/0.43 visFreeVar: ( $i * $i ) > $o)).
% 0.19/0.43 tff(1,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)).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(5,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.43 tff(7,plain,(
% 0.19/0.43 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[6])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_48(VC!52, VT!50, vvar(Vy!51)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.43 tff(11,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,[]))).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (((~(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))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((~(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))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.43 tff(14,assumption,(~((~(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))))), introduced(assumption)).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (((~(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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vsomeType(VT!50)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.43 tff(24,axiom,(![VVar0: $i, VVar1: $i] : (((vvar(VVar0) = vvar(VVar1)) => (VVar0 = VVar1)) & ((VVar0 = VVar1) => (vvar(VVar0) = vvar(VVar1))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-var'')).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.43 tff(27,plain,(
% 0.19/0.43 ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[26])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 ((~![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)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (~((~((~(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))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (((~((~(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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 ((~(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)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (((~(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))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (vvar(Vy!51) = vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[34, 14])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (vvar(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51))) = vvar(Vy!51)),
% 0.19/0.43 inference(symmetry,[status(thm)],[35])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 ((~((~(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)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 ((~((~(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)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)) = Vy!51),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52) = vlookup(Vy!51, VC!52)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (vlookup(Vy!51, VC!52) = vlookup(tptp_fun_Vx_42(VC!52, VT!50, vvar(Vy!51)), VC!52)),
% 0.19/0.43 inference(symmetry,[status(thm)],[40])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (^[Vx: $i, Vv: $i] : refl((~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))) <=> (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))) <=> ![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (^[Vx: $i, Vv: $i] : rewrite((((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (![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] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.43 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[48, 47])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.43 tff(53,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/sandbox/benchmark/Axioms/COM001+0.ax','isFreeVar0')).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[54, 46])).
% 0.19/0.44 tff(56,plain,(
% 0.19/0.44 ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[55])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[56, 45])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[57, 43])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 ((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | (~((~((~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51)))) | (~((~visFreeVar(Vx!54, vvar(Vy!51))) | (Vy!51 = Vx!54)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 (~((~((~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51)))) | (~((~visFreeVar(Vx!54, vvar(Vy!51))) | (Vy!51 = Vx!54))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (((~((~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51)))) | (~((~visFreeVar(Vx!54, vvar(Vy!51))) | (Vy!51 = Vx!54)))) | ((~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 ((~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : (((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT)) => vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(65,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : (((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT)) => vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-FreeVar-var'')).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VT: $i] : ((~((~visFreeVar(Vx, vvar(Vy))) & vtcheck(VC, vvar(Vy), VT))) | vtcheck(vbind(Vx, VS, VC), vvar(Vy), VT))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[68, 63])).
% 0.19/0.44 tff(70,plain,(
% 0.19/0.44 ~((~((~visFreeVar(Vx!54, vvar(Vy!51))) & vtcheck(VC!52, vvar(Vy!51), VT!50))) | vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50))),
% 0.19/0.44 inference(skolemize,[status(sab)],[69])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 ((~visFreeVar(Vx!54, vvar(Vy!51))) & vtcheck(VC!52, vvar(Vy!51), VT!50)),
% 0.19/0.44 inference(or_elim,[status(thm)],[70])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (~visFreeVar(Vx!54, vvar(Vy!51))),
% 0.19/0.44 inference(and_elim,[status(thm)],[71])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 ((~((~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51)))) | (~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 ((~((~(Vy!51 = Vx!54)) | visFreeVar(Vx!54, vvar(Vy!51)))) | (~(Vy!51 = Vx!54))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (~(Vy!51 = Vx!54)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[74, 62])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(transitivity,[status(thm)],[82, 81])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[83, 80])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (^[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)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (![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)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[86, 84])).
% 0.19/0.44 tff(88,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/sandbox/benchmark/Axioms/COM001+0.ax','lookup2')).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[89, 78])).
% 0.19/0.44 tff(91,plain,(
% 0.19/0.44 ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[90])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[91, 77])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vlookup(Vy!51, VC!52)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[95, 92, 75])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50)),
% 0.19/0.44 inference(transitivity,[status(thm)],[96, 41, 16])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (~vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50)),
% 0.19/0.44 inference(or_elim,[status(thm)],[70])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (^[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)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (^[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)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.44 tff(104,axiom,(![VC: $i, Vx: $i, VT: $i] : ((vlookup(Vx, VC) = vsomeType(VT)) => vtcheck(VC, vvar(Vx), VT))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-var'')).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.44 tff(107,plain,(
% 0.19/0.44 ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.19/0.44 inference(skolemize,[status(sab)],[106])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | (~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))) | vtcheck(vbind(Vx!54, VS!53, VC!52), vvar(Vy!51), VT!50)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (~(vlookup(Vy!51, vbind(Vx!54, VS!53, VC!52)) = vsomeType(VT!50))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[111, 108, 98])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[112, 97])).
% 0.19/0.44 tff(114,plain,((~(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)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 (vtcheck(VC!52, vvar(Vy!51), VT!50)),
% 0.19/0.44 inference(and_elim,[status(thm)],[71])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 (^[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)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 (^[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))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.45 tff(125,axiom,(![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.19/0.45 tff(128,plain,(
% 0.19/0.45 ![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)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[127])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (![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))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 (![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))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[130, 117])).
% 0.19/0.45 tff(132,plain,
% 0.19/0.45 (((~![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)))))))) <=> ((~![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)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 ((~![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)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 ((~![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))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 ((~((~(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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[134, 131, 115])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 ((~((~(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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[135, 114])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (~((~(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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[136, 13])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 (((~(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))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (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)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(143,axiom,(![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-abs'')).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.46 tff(145,plain,(
% 0.19/0.46 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[144])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(VC!52, VT!50, vvar(Vy!51)), tptp_fun_VT1_44(VC!52, VT!50, vvar(Vy!51)), tptp_fun_Ve2_45(VC!52, VT!50, vvar(Vy!51)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[147, 146, 139])).
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------