%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM141+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.24s 0.45s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : COM141+1 : TPTP v9.0.0. Released v6.4.0.
% 0.14/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Jun 19 12:25:11 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.45 % SZS status Theorem
% 0.24/0.45 % SZS output start Proof
% 0.24/0.45 tff(vnoType_type, type, (
% 0.24/0.45 vnoType: $i)).
% 0.24/0.45 tff(vlookup_type, type, (
% 0.24/0.45 vlookup: ( $i * $i ) > $i)).
% 0.24/0.45 tff(tptp_fun_VC_53_type, type, (
% 0.24/0.45 tptp_fun_VC_53: $i)).
% 0.24/0.45 tff(tptp_fun_Vy_52_type, type, (
% 0.24/0.45 tptp_fun_Vy_52: $i)).
% 0.24/0.45 tff(tptp_fun_Vx_55_type, type, (
% 0.24/0.45 tptp_fun_Vx_55: $i)).
% 0.24/0.45 tff(vtcheck_type, type, (
% 0.24/0.45 vtcheck: ( $i * $i * $i ) > $o)).
% 0.24/0.45 tff(tptp_fun_VT_50_type, type, (
% 0.24/0.45 tptp_fun_VT_50: $i)).
% 0.24/0.45 tff(vabs_type, type, (
% 0.24/0.45 vabs: ( $i * $i * $i ) > $i)).
% 0.24/0.45 tff(veabs_type, type, (
% 0.24/0.45 veabs: $i)).
% 0.24/0.45 tff(tptp_fun_VS1_51_type, type, (
% 0.24/0.45 tptp_fun_VS1_51: $i)).
% 0.24/0.45 tff(vbind_type, type, (
% 0.24/0.45 vbind: ( $i * $i * $i ) > $i)).
% 0.24/0.45 tff(tptp_fun_VS_54_type, type, (
% 0.24/0.45 tptp_fun_VS_54: $i)).
% 0.24/0.45 tff(1,plain,
% 0.24/0.45 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(2,plain,
% 0.24/0.45 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(3,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-abs'')).
% 0.24/0.45 tff(4,plain,
% 0.24/0.45 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.24/0.45 tff(5,plain,
% 0.24/0.45 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.24/0.45 tff(6,plain,
% 0.24/0.45 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.24/0.45 tff(7,plain,
% 0.24/0.45 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.24/0.45 tff(8,plain,(
% 0.24/0.45 ~((~((vlookup(Vx!55, VC!53) = vnoType) & vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50))),
% 0.24/0.45 inference(skolemize,[status(sab)],[7])).
% 0.24/0.45 tff(9,plain,
% 0.24/0.45 ((vlookup(Vx!55, VC!53) = vnoType) & vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.24/0.45 inference(or_elim,[status(thm)],[8])).
% 0.24/0.45 tff(10,plain,
% 0.24/0.45 (vlookup(Vx!55, VC!53) = vnoType),
% 0.24/0.45 inference(and_elim,[status(thm)],[9])).
% 0.24/0.45 tff(11,plain,
% 0.24/0.45 (~vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.24/0.45 inference(or_elim,[status(thm)],[8])).
% 0.24/0.45 tff(12,plain,
% 0.24/0.45 (vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.24/0.45 inference(and_elim,[status(thm)],[9])).
% 0.24/0.45 tff(13,plain,
% 0.24/0.45 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : refl(((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(14,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.24/0.45 tff(15,plain,
% 0.24/0.45 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) <=> (~((Vx = Vy) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))), ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> (~(~((Vx = Vy) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))))), rewrite((~(~((Vx = Vy) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))) <=> ((Vx = Vy) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))), ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ((Vx = Vy) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))), (((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> (((Vx = Vy) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))), rewrite((((Vx = Vy) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))), (((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(16,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[15])).
% 0.24/0.45 tff(17,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(18,plain,
% 0.24/0.45 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : trans(monotonicity(rewrite((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) <=> ((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))), (((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> (((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))), rewrite((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), (((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(19,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[18])).
% 0.24/0.45 tff(20,axiom,(![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-abs-1'')).
% 0.24/0.45 tff(21,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.24/0.45 tff(22,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.24/0.45 tff(23,plain,(
% 0.24/0.45 ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.45 inference(skolemize,[status(sab)],[22])).
% 0.24/0.45 tff(24,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.24/0.45 tff(25,plain,
% 0.24/0.45 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.24/0.45 tff(26,plain,
% 0.24/0.45 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (Vx!55 = Vy!52))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (Vx!55 = Vy!52))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(27,plain,
% 0.24/0.45 (((Vx!55 = Vy!52) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50))) <=> (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (Vx!55 = Vy!52))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(28,plain,
% 0.24/0.45 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((Vx!55 = Vy!52) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (Vx!55 = Vy!52)))),
% 0.24/0.46 inference(monotonicity,[status(thm)],[27])).
% 0.24/0.46 tff(29,plain,
% 0.24/0.46 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((Vx!55 = Vy!52) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (Vx!55 = Vy!52))),
% 0.24/0.46 inference(transitivity,[status(thm)],[28, 26])).
% 0.24/0.46 tff(30,plain,
% 0.24/0.46 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((Vx!55 = Vy!52) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(31,plain,
% 0.24/0.46 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (Vx!55 = Vy!52)),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.24/0.46 tff(32,plain,
% 0.24/0.46 (Vx!55 = Vy!52),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[31, 25, 10, 12, 11])).
% 0.24/0.46 tff(33,plain,
% 0.24/0.46 (Vy!52 = Vx!55),
% 0.24/0.46 inference(symmetry,[status(thm)],[32])).
% 0.24/0.46 tff(34,plain,
% 0.24/0.46 (vlookup(Vy!52, VC!53) = vlookup(Vx!55, VC!53)),
% 0.24/0.46 inference(monotonicity,[status(thm)],[33])).
% 0.24/0.46 tff(35,plain,
% 0.24/0.46 (vlookup(Vy!52, VC!53) = vnoType),
% 0.24/0.46 inference(transitivity,[status(thm)],[34, 10])).
% 0.24/0.46 tff(36,plain,
% 0.24/0.46 (vbind(Vy!52, VS!54, VC!53) = vbind(Vx!55, VS!54, VC!53)),
% 0.24/0.46 inference(monotonicity,[status(thm)],[33])).
% 0.24/0.46 tff(37,plain,
% 0.24/0.46 (vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) <=> vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.24/0.46 inference(monotonicity,[status(thm)],[36])).
% 0.24/0.46 tff(38,plain,
% 0.24/0.46 (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) <=> vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.24/0.46 inference(symmetry,[status(thm)],[37])).
% 0.24/0.46 tff(39,plain,
% 0.24/0.46 ((~vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)) <=> (~vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50))),
% 0.24/0.46 inference(monotonicity,[status(thm)],[38])).
% 0.24/0.46 tff(40,plain,
% 0.24/0.46 (~vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[11, 39])).
% 0.24/0.46 tff(41,plain,
% 0.24/0.46 (^[VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : refl(((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType))) <=> ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(42,plain,
% 0.24/0.46 (![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType))) <=> ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[41])).
% 0.24/0.46 tff(43,plain,
% 0.24/0.46 (![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType))) <=> ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(44,plain,
% 0.24/0.46 (^[VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : rewrite((vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | (~(vlookup(Vy, VC) = vnoType))) <=> ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(45,plain,
% 0.24/0.46 (![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | (~(vlookup(Vy, VC) = vnoType))) <=> ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[44])).
% 0.24/0.46 tff(46,plain,
% 0.24/0.46 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | (~(vlookup(Vy, VC) = vnoType))) <=> ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.24/0.46 tff(47,plain,
% 0.24/0.46 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.24/0.46 tff(48,plain,
% 0.24/0.46 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(transitivity,[status(thm)],[47, 46])).
% 0.24/0.46 tff(49,plain,
% 0.24/0.46 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(transitivity,[status(thm)],[48, 45])).
% 0.24/0.46 tff(50,plain,
% 0.24/0.46 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : trans(monotonicity(rewrite((((Vx = Vy) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) <=> ((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))), (((((Vx = Vy) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> (((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))), rewrite((((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), (((((Vx = Vy) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(51,plain,
% 0.24/0.46 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((Vx = Vy) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[50])).
% 0.24/0.46 tff(52,plain,
% 0.24/0.46 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((Vx = Vy) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(transitivity,[status(thm)],[51, 49])).
% 0.24/0.46 tff(53,axiom,(![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((Vx = Vy) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-abs-2'')).
% 0.24/0.46 tff(54,plain,
% 0.24/0.46 (![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.24/0.46 tff(55,plain,
% 0.24/0.46 (![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[54, 43])).
% 0.24/0.46 tff(56,plain,(
% 0.24/0.46 ![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(skolemize,[status(sab)],[55])).
% 0.24/0.46 tff(57,plain,
% 0.24/0.46 (![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[56, 42])).
% 0.24/0.46 tff(58,plain,
% 0.24/0.46 (((~![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))) | ((~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vy!52, VC!53) = vnoType)))) <=> ((~![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vy!52, VC!53) = vnoType)))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(59,plain,
% 0.24/0.46 ((~![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))) | ((~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vy!52, VC!53) = vnoType)))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(60,plain,
% 0.24/0.46 ((~![VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~vtcheck(VC, vabs(Vy, VS1, veabs), VT)) | vtcheck(vbind(Vy, VS, VC), vabs(Vy, VS1, veabs), VT) | (~(vlookup(Vy, VC) = vnoType)))) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | vtcheck(vbind(Vy!52, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vy!52, VC!53) = vnoType))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.24/0.46 tff(61,plain,
% 0.24/0.47 ($false),
% 0.24/0.47 inference(unit_resolution,[status(thm)],[60, 57, 12, 40, 35])).
% 0.24/0.47 % SZS output end Proof
% 0.24/0.47 % E exiting
%------------------------------------------------------------------------------