%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM137+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:01:07 AM UTC 2025
% Result : Theorem 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : COM137+1 : TPTP v9.0.0. Released v6.4.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 12:26:16 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 % SZS output start Proof
% 0.22/0.46 tff(vapp_type, type, (
% 0.22/0.46 vapp: ( $i * $i ) > $i)).
% 0.22/0.46 tff(ve2app_type, type, (
% 0.22/0.46 ve2app: $i)).
% 0.22/0.46 tff(ve1app_type, type, (
% 0.22/0.46 ve1app: $i)).
% 0.22/0.46 tff(vabs_type, type, (
% 0.22/0.46 vabs: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_Ve2_45_type, type, (
% 0.22/0.46 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_VT_50_type, type, (
% 0.22/0.46 tptp_fun_VT_50: $i)).
% 0.22/0.46 tff(vbind_type, type, (
% 0.22/0.46 vbind: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_VC_51_type, type, (
% 0.22/0.46 tptp_fun_VC_51: $i)).
% 0.22/0.46 tff(tptp_fun_VS_52_type, type, (
% 0.22/0.46 tptp_fun_VS_52: $i)).
% 0.22/0.46 tff(tptp_fun_Vx_53_type, type, (
% 0.22/0.46 tptp_fun_Vx_53: $i)).
% 0.22/0.46 tff(tptp_fun_VT1_44_type, type, (
% 0.22/0.46 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_Vx_46_type, type, (
% 0.22/0.46 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(vtcheck_type, type, (
% 0.22/0.46 vtcheck: ( $i * $i * $i ) > $o)).
% 0.22/0.46 tff(tptp_fun_VT2_43_type, type, (
% 0.22/0.46 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(varrow_type, type, (
% 0.22/0.46 varrow: ( $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_VS_47_type, type, (
% 0.22/0.46 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_Ve2_48_type, type, (
% 0.22/0.46 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_Ve1_49_type, type, (
% 0.22/0.46 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(visFreeVar_type, type, (
% 0.22/0.46 visFreeVar: ( $i * $i ) > $o)).
% 0.22/0.46 tff(vsomeType_type, type, (
% 0.22/0.46 vsomeType: $i > $i)).
% 0.22/0.46 tff(vlookup_type, type, (
% 0.22/0.46 vlookup: ( $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_Vx_42_type, type, (
% 0.22/0.46 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(vvar_type, type, (
% 0.22/0.46 vvar: $i > $i)).
% 0.22/0.46 tff(1,assumption,(~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))), introduced(assumption)).
% 0.22/0.46 tff(2,plain,
% 0.22/0.46 (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(3,plain,
% 0.22/0.46 (vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.22/0.46 tff(4,plain,
% 0.22/0.46 (vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)),
% 0.22/0.46 inference(symmetry,[status(thm)],[3])).
% 0.22/0.46 tff(5,plain,
% 0.22/0.46 (vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50) <=> vtcheck(VC!51, vapp(ve1app, ve2app), VT!50)),
% 0.22/0.46 inference(monotonicity,[status(thm)],[4])).
% 0.22/0.46 tff(6,plain,
% 0.22/0.46 (vtcheck(VC!51, vapp(ve1app, ve2app), VT!50) <=> vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50)),
% 0.22/0.46 inference(symmetry,[status(thm)],[5])).
% 0.22/0.46 tff(7,plain,
% 0.22/0.46 ((~vtcheck(VC!51, vapp(ve1app, ve2app), VT!50)) <=> (~vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[6])).
% 0.22/0.46 tff(8,plain,
% 0.22/0.46 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(9,plain,
% 0.22/0.46 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT)) => vtcheck(VC, vapp(ve1app, ve2app), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(10,axiom,(~![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT)) => vtcheck(VC, vapp(ve1app, ve2app), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Strong-app'')).
% 0.22/0.46 tff(11,plain,
% 0.22/0.46 (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.22/0.46 tff(12,plain,
% 0.22/0.46 (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.22/0.46 tff(13,plain,
% 0.22/0.46 (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.46 tff(14,plain,
% 0.22/0.46 (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.22/0.46 tff(15,plain,(
% 0.22/0.46 ~((~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx!53, VS!52, VC!51), vapp(ve1app, ve2app), VT!50))) | vtcheck(VC!51, vapp(ve1app, ve2app), VT!50))),
% 0.22/0.46 inference(skolemize,[status(sab)],[14])).
% 0.22/0.46 tff(16,plain,
% 0.22/0.46 (~vtcheck(VC!51, vapp(ve1app, ve2app), VT!50)),
% 0.22/0.46 inference(or_elim,[status(thm)],[15])).
% 0.22/0.46 tff(17,plain,
% 0.22/0.46 (~vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.22/0.46 tff(18,plain,
% 0.22/0.46 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : refl((~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(19,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.46 tff(20,plain,
% 0.22/0.46 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : trans(monotonicity(rewrite(((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), trans(monotonicity(trans(monotonicity(rewrite(((VExp0 = VExp2) & (VExp1 = VExp3)) <=> (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> (~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), rewrite((~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> (((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), rewrite((((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), rewrite((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(21,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.46 tff(22,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(23,plain,
% 0.22/0.46 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : rewrite((((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(24,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.46 tff(25,axiom,(![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-app'')).
% 0.22/0.46 tff(26,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.22/0.46 tff(27,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.22/0.46 tff(28,plain,(
% 0.22/0.46 ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[27])).
% 0.22/0.46 tff(29,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.22/0.46 tff(30,plain,
% 0.22/0.46 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.22/0.46 tff(31,plain,
% 0.22/0.46 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(32,plain,
% 0.22/0.46 (~((~((~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.22/0.46 tff(33,plain,
% 0.22/0.46 (((~((~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app))))) | ((~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(34,plain,
% 0.22/0.47 ((~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.22/0.47 tff(35,plain,
% 0.22/0.47 ((~((~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))))) | (~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(36,plain,
% 0.22/0.47 ((~((~(vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))))) | (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[35, 4])).
% 0.22/0.47 tff(37,plain,
% 0.22/0.47 (~((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[36, 34])).
% 0.22/0.47 tff(38,plain,
% 0.22/0.47 (((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app))) | (tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app)),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(39,plain,
% 0.22/0.47 (tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.22/0.47 tff(40,plain,
% 0.22/0.47 (vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) <=> vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[39])).
% 0.22/0.47 tff(41,plain,
% 0.22/0.47 (vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) <=> vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.47 inference(symmetry,[status(thm)],[40])).
% 0.22/0.47 tff(42,plain,
% 0.22/0.47 (ve2app = tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))),
% 0.22/0.47 inference(symmetry,[status(thm)],[39])).
% 0.22/0.47 tff(43,plain,
% 0.22/0.47 (vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) <=> vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[42])).
% 0.22/0.47 tff(44,plain,
% 0.22/0.47 (vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) <=> vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.47 inference(symmetry,[status(thm)],[43])).
% 0.22/0.47 tff(45,plain,
% 0.22/0.47 (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(46,plain,
% 0.22/0.47 (vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[45, 1])).
% 0.22/0.47 tff(47,plain,
% 0.22/0.47 (vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[46, 44])).
% 0.22/0.47 tff(48,plain,
% 0.22/0.47 (^[Ve1: $i, Vv: $i, Ve2: $i] : refl((~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(49,plain,
% 0.22/0.47 (![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.22/0.47 tff(50,plain,
% 0.22/0.47 (^[Ve1: $i, Vv: $i, Ve2: $i] : trans(monotonicity(monotonicity(rewrite((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) <=> (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))), (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) <=> ((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))))), rewrite((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))) <=> (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))), ((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))), rewrite((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))), ((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(51,plain,
% 0.22/0.47 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.47 tff(52,plain,
% 0.22/0.47 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(53,plain,
% 0.22/0.47 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.47 tff(54,plain,
% 0.22/0.47 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.47 tff(55,plain,
% 0.22/0.47 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[54, 53])).
% 0.22/0.47 tff(56,plain,
% 0.22/0.47 (^[VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : trans(monotonicity(rewrite((((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))) <=> (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))), ((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))), rewrite((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))), ((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(57,plain,
% 0.22/0.47 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.22/0.47 tff(58,plain,
% 0.22/0.47 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[57, 55])).
% 0.22/0.47 tff(59,axiom,(![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isFreeVar2')).
% 0.22/0.47 tff(60,plain,
% 0.22/0.47 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.22/0.47 tff(61,plain,
% 0.22/0.47 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[60, 52])).
% 0.22/0.47 tff(62,plain,(
% 0.22/0.47 ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[61])).
% 0.22/0.47 tff(63,plain,
% 0.22/0.47 (![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[62, 51])).
% 0.22/0.47 tff(64,plain,
% 0.22/0.47 (![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[63, 49])).
% 0.22/0.47 tff(65,plain,
% 0.22/0.47 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app)))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(66,plain,
% 0.22/0.48 ((~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app) | (~visFreeVar(Vx!53, vapp(ve1app, ve2app))))))) <=> (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(67,plain,
% 0.22/0.48 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app) | (~visFreeVar(Vx!53, vapp(ve1app, ve2app)))))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[66])).
% 0.22/0.48 tff(68,plain,
% 0.22/0.48 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app) | (~visFreeVar(Vx!53, vapp(ve1app, ve2app)))))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[67, 65])).
% 0.22/0.48 tff(69,plain,
% 0.22/0.48 ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app) | (~visFreeVar(Vx!53, vapp(ve1app, ve2app)))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(70,plain,
% 0.22/0.48 ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.48 tff(71,plain,
% 0.22/0.48 (~((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.22/0.48 tff(72,plain,
% 0.22/0.48 (((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app)))) | ((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(73,plain,
% 0.22/0.48 ((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.22/0.48 tff(74,plain,
% 0.22/0.48 ((~visFreeVar(Vx!53, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx!53, VS!52, VC!51), vapp(ve1app, ve2app), VT!50)),
% 0.22/0.48 inference(or_elim,[status(thm)],[15])).
% 0.22/0.48 tff(75,plain,
% 0.22/0.48 (~visFreeVar(Vx!53, vapp(ve1app, ve2app))),
% 0.22/0.48 inference(and_elim,[status(thm)],[74])).
% 0.22/0.48 tff(76,plain,
% 0.22/0.48 ((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(77,plain,
% 0.22/0.48 ((~((~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))) | visFreeVar(Vx!53, vapp(ve1app, ve2app)))) | (~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.22/0.48 tff(78,plain,
% 0.22/0.48 (~(visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.22/0.48 tff(79,plain,
% 0.22/0.48 ((visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app)) | (~visFreeVar(Vx!53, ve2app))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(80,plain,
% 0.22/0.48 (~visFreeVar(Vx!53, ve2app)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.22/0.48 tff(81,plain,
% 0.22/0.48 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(82,plain,
% 0.22/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[81])).
% 0.22/0.48 tff(83,plain,
% 0.22/0.48 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> (~(visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))), ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> (~(~(visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))))), rewrite((~(~(visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))) <=> (visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))), ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> (visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))), (((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> ((visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)))), rewrite(((visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))), (((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(84,plain,
% 0.22/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[83])).
% 0.22/0.49 tff(85,plain,
% 0.22/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(86,plain,
% 0.22/0.49 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) => vtcheck(VC, ve2app, VT)) <=> ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(87,plain,
% 0.22/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) => vtcheck(VC, ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[86])).
% 0.22/0.49 tff(88,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) => vtcheck(VC, ve2app, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Strong-app-IH2'')).
% 0.22/0.49 tff(89,plain,
% 0.22/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.22/0.49 tff(90,plain,
% 0.22/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.22/0.49 tff(91,plain,(
% 0.22/0.49 ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 0.22/0.49 inference(skolemize,[status(sab)],[90])).
% 0.22/0.49 tff(92,plain,
% 0.22/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.22/0.49 tff(93,plain,
% 0.22/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.22/0.49 tff(94,plain,
% 0.22/0.49 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | (visFreeVar(Vx!53, ve2app) | vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | visFreeVar(Vx!53, ve2app) | vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(95,plain,
% 0.22/0.49 ((vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve2app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) <=> (visFreeVar(Vx!53, ve2app) | vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(96,plain,
% 0.22/0.49 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | (vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve2app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | (visFreeVar(Vx!53, ve2app) | vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[95])).
% 0.22/0.49 tff(97,plain,
% 0.22/0.49 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | (vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve2app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | visFreeVar(Vx!53, ve2app) | vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[96, 94])).
% 0.22/0.49 tff(98,plain,
% 0.22/0.49 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | (vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | visFreeVar(Vx!53, ve2app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(99,plain,
% 0.22/0.49 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | visFreeVar(Vx!53, ve2app) | vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.22/0.49 tff(100,plain,
% 0.22/0.49 (vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[99, 93, 80])).
% 0.22/0.49 tff(101,plain,
% 0.22/0.49 (vtcheck(VC!51, ve2app, tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[100, 47])).
% 0.22/0.49 tff(102,plain,
% 0.22/0.49 (vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[101, 41])).
% 0.22/0.49 tff(103,plain,
% 0.22/0.49 (((~(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve2app))) | (tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app)),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(104,plain,
% 0.22/0.49 (tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)) = ve1app),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[103, 37])).
% 0.22/0.49 tff(105,plain,
% 0.22/0.49 (vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) <=> vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[104])).
% 0.22/0.49 tff(106,plain,
% 0.22/0.49 (vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) <=> vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.49 inference(symmetry,[status(thm)],[105])).
% 0.22/0.49 tff(107,plain,
% 0.22/0.49 (ve1app = tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))),
% 0.22/0.49 inference(symmetry,[status(thm)],[104])).
% 0.22/0.49 tff(108,plain,
% 0.22/0.49 (vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) <=> vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[107])).
% 0.22/0.49 tff(109,plain,
% 0.22/0.49 (vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) <=> vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.49 inference(symmetry,[status(thm)],[108])).
% 0.22/0.49 tff(110,plain,
% 0.22/0.49 (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(111,plain,
% 0.22/0.49 (vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[110, 1])).
% 0.22/0.49 tff(112,plain,
% 0.22/0.49 (vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[111, 109])).
% 0.22/0.49 tff(113,plain,
% 0.22/0.49 ((visFreeVar(Vx!53, ve1app) | visFreeVar(Vx!53, ve2app)) | (~visFreeVar(Vx!53, ve1app))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(114,plain,
% 0.22/0.49 (~visFreeVar(Vx!53, ve1app)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[113, 78])).
% 0.22/0.49 tff(115,plain,
% 0.22/0.49 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(116,plain,
% 0.22/0.49 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.49 tff(117,plain,
% 0.22/0.49 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> (~(visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))), ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> (~(~(visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))))), rewrite((~(~(visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))) <=> (visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))), ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> (visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))), (((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> ((visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)))), rewrite(((visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))), (((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(118,plain,
% 0.22/0.50 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[117])).
% 0.22/0.50 tff(119,plain,
% 0.22/0.50 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(120,plain,
% 0.22/0.50 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) => vtcheck(VC, ve1app, VT)) <=> ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(121,plain,
% 0.22/0.50 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) => vtcheck(VC, ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[120])).
% 0.22/0.50 tff(122,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) => vtcheck(VC, ve1app, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Strong-app-IH1'')).
% 0.22/0.50 tff(123,plain,
% 0.22/0.50 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.22/0.50 tff(124,plain,
% 0.22/0.50 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.22/0.50 tff(125,plain,(
% 0.22/0.50 ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 0.22/0.50 inference(skolemize,[status(sab)],[124])).
% 0.22/0.50 tff(126,plain,
% 0.22/0.50 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.22/0.50 tff(127,plain,
% 0.22/0.50 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.22/0.50 tff(128,plain,
% 0.22/0.50 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | (visFreeVar(Vx!53, ve1app) | vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | visFreeVar(Vx!53, ve1app) | vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(129,plain,
% 0.22/0.50 ((vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | visFreeVar(Vx!53, ve1app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)))) <=> (visFreeVar(Vx!53, ve1app) | vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(130,plain,
% 0.22/0.50 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | (vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | visFreeVar(Vx!53, ve1app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | (visFreeVar(Vx!53, ve1app) | vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[129])).
% 0.22/0.50 tff(131,plain,
% 0.22/0.50 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | (vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | visFreeVar(Vx!53, ve1app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | visFreeVar(Vx!53, ve1app) | vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[130, 128])).
% 0.22/0.50 tff(132,plain,
% 0.22/0.50 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | (vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | visFreeVar(Vx!53, ve1app) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(133,plain,
% 0.22/0.50 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | visFreeVar(Vx!53, ve1app) | vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.22/0.50 tff(134,plain,
% 0.22/0.50 (vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[133, 127, 114])).
% 0.22/0.50 tff(135,plain,
% 0.22/0.50 (vtcheck(VC!51, ve1app, varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[134, 112])).
% 0.22/0.50 tff(136,plain,
% 0.22/0.50 (vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[135, 106])).
% 0.22/0.50 tff(137,plain,
% 0.22/0.50 (^[VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : refl((vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) <=> (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(138,plain,
% 0.22/0.50 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[137])).
% 0.22/0.50 tff(139,plain,
% 0.22/0.50 (^[VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) <=> (~((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))), ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (~(~((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))))), rewrite((~(~((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))) <=> ((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))), ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> ((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))), (((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> (((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)))), rewrite((((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))), (((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(140,plain,
% 0.22/0.50 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[139])).
% 0.22/0.50 tff(141,plain,
% 0.22/0.50 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(142,plain,
% 0.22/0.50 (^[VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : rewrite(((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) => vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(143,plain,
% 0.22/0.50 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) => vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[142])).
% 0.22/0.50 tff(144,axiom,(![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) => vtcheck(VC, vapp(Ve1, Ve2), VT))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-app'')).
% 0.22/0.50 tff(145,plain,
% 0.22/0.50 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.22/0.50 tff(146,plain,
% 0.22/0.50 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.22/0.50 tff(147,plain,(
% 0.22/0.50 ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 0.22/0.51 inference(skolemize,[status(sab)],[146])).
% 0.22/0.51 tff(148,plain,
% 0.22/0.51 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.22/0.51 tff(149,plain,
% 0.22/0.51 (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[148, 138])).
% 0.22/0.51 tff(150,plain,
% 0.22/0.51 (((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | ((~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50))) <=> ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(151,plain,
% 0.22/0.51 ((vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) <=> ((~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(152,plain,
% 0.22/0.51 (((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) <=> ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | ((~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[151])).
% 0.22/0.51 tff(153,plain,
% 0.22/0.51 (((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) <=> ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50))),
% 0.22/0.51 inference(transitivity,[status(thm)],[152, 150])).
% 0.22/0.51 tff(154,plain,
% 0.22/0.51 ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(155,plain,
% 0.22/0.51 ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.51 tff(156,plain,
% 0.22/0.51 ((~vtcheck(VC!51, tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))) | (~vtcheck(VC!51, tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | vtcheck(VC!51, vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))), VT!50)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[155, 149])).
% 0.22/0.51 tff(157,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[156, 136, 102, 17])).
% 0.22/0.51 tff(158,plain,((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(159,plain,
% 0.22/0.51 ((vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) <=> (vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))),
% 0.22/0.51 inference(commutativity,[status(thm)],[])).
% 0.22/0.51 tff(160,plain,
% 0.22/0.51 ((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) <=> (~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[159])).
% 0.22/0.51 tff(161,assumption,(vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)), introduced(assumption)).
% 0.22/0.51 tff(162,plain,
% 0.22/0.51 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(163,plain,
% 0.22/0.51 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[162])).
% 0.22/0.51 tff(164,plain,
% 0.22/0.51 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(165,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 0.22/0.51 tff(166,plain,
% 0.22/0.51 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.22/0.51 tff(167,plain,(
% 0.22/0.51 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.51 inference(skolemize,[status(sab)],[166])).
% 0.22/0.51 tff(168,plain,
% 0.22/0.51 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.22/0.51 tff(169,plain,
% 0.22/0.51 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(170,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[169, 168, 161])).
% 0.22/0.51 tff(171,plain,(~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(172,plain,
% 0.22/0.51 (~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[171, 160])).
% 0.22/0.51 tff(173,plain,
% 0.22/0.51 (((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)) = vsomeType(VT!50)))) | (vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(174,plain,
% 0.22/0.51 ((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)) = vsomeType(VT!50)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.22/0.51 tff(175,plain,
% 0.22/0.51 (vtcheck(vbind(Vx!53, VS!52, VC!51), vapp(ve1app, ve2app), VT!50)),
% 0.22/0.51 inference(and_elim,[status(thm)],[74])).
% 0.22/0.51 tff(176,plain,
% 0.22/0.51 (^[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)))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(177,plain,
% 0.22/0.51 (![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)))))) <=> ![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))))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[176])).
% 0.22/0.51 tff(178,plain,
% 0.22/0.51 (^[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))))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(179,plain,
% 0.22/0.52 (![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))))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[178])).
% 0.22/0.52 tff(180,plain,
% 0.22/0.52 (^[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)))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(181,plain,
% 0.22/0.52 (![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))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[180])).
% 0.22/0.52 tff(182,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(183,plain,
% 0.22/0.52 (^[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)))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(184,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[183])).
% 0.22/0.52 tff(185,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'')).
% 0.22/0.52 tff(186,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.22/0.52 tff(187,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.22/0.52 tff(188,plain,(
% 0.22/0.52 ![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)))),
% 0.22/0.52 inference(skolemize,[status(sab)],[187])).
% 0.22/0.52 tff(189,plain,
% 0.22/0.52 (![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))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.22/0.52 tff(190,plain,
% 0.22/0.52 (![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))))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[189, 179])).
% 0.22/0.52 tff(191,plain,
% 0.22/0.52 (![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))))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[190, 177])).
% 0.22/0.52 tff(192,plain,
% 0.22/0.52 (((~![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(vbind(Vx!53, VS!52, VC!51), vapp(ve1app, ve2app), VT!50)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)) = vsomeType(VT!50))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))))) <=> ((~![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(vbind(Vx!53, VS!52, VC!51), vapp(ve1app, ve2app), VT!50)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)) = vsomeType(VT!50))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(193,plain,
% 0.22/0.52 ((~![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(vbind(Vx!53, VS!52, VC!51), vapp(ve1app, ve2app), VT!50)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)) = vsomeType(VT!50))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(194,plain,
% 0.22/0.52 ((~![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(vbind(Vx!53, VS!52, VC!51), vapp(ve1app, ve2app), VT!50)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)) = vsomeType(VT!50))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.22/0.53 tff(195,plain,
% 0.22/0.53 ((~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)) = vsomeType(VT!50))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve1_49(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), VT!50))) | (~vtcheck(vbind(Vx!53, VS!52, VC!51), tptp_fun_Ve2_48(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VS_47(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[194, 191, 175])).
% 0.22/0.53 tff(196,plain,
% 0.22/0.53 (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[195, 174, 158])).
% 0.22/0.53 tff(197,plain,
% 0.22/0.53 (((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), vbind(Vx!53, VS!52, VC!51)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT2_43(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))) | (vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(198,plain,
% 0.22/0.53 (vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.22/0.53 tff(199,plain,
% 0.22/0.53 (vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)),
% 0.22/0.53 inference(symmetry,[status(thm)],[198])).
% 0.22/0.53 tff(200,plain,
% 0.22/0.53 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : refl((~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(201,plain,
% 0.22/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[200])).
% 0.22/0.53 tff(202,plain,
% 0.22/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(203,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-abs-app'')).
% 0.22/0.53 tff(204,plain,
% 0.22/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.22/0.53 tff(205,plain,(
% 0.22/0.53 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.22/0.53 inference(skolemize,[status(sab)],[204])).
% 0.22/0.53 tff(206,plain,
% 0.22/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.22/0.53 tff(207,plain,
% 0.22/0.53 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(tptp_fun_Vx_46(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_VT1_44(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app)), tptp_fun_Ve2_45(vbind(Vx!53, VS!52, VC!51), VT!50, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(208,plain,
% 0.22/0.53 ($false),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[207, 206, 199])).
% 0.22/0.53 % SZS output end Proof
% 0.22/0.54 % E exiting
%------------------------------------------------------------------------------