%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM133+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM133+1 : TPTP v9.0.0. Released v6.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 12:25:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(vtcheck_type, type, (
% 0.19/0.41 vtcheck: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_VT2_50_type, type, (
% 0.19/0.41 tptp_fun_VT2_50: $i)).
% 0.19/0.41 tff(vsubst_type, type, (
% 0.19/0.41 vsubst: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(vabs_type, type, (
% 0.19/0.41 vabs: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(veabs_type, type, (
% 0.19/0.41 veabs: $i)).
% 0.19/0.41 tff(tptp_fun_VS_51_type, type, (
% 0.19/0.41 tptp_fun_VS_51: $i)).
% 0.19/0.41 tff(tptp_fun_Vy_52_type, type, (
% 0.19/0.41 tptp_fun_Vy_52: $i)).
% 0.19/0.41 tff(tptp_fun_Ve_53_type, type, (
% 0.19/0.41 tptp_fun_Ve_53: $i)).
% 0.19/0.41 tff(tptp_fun_VC_55_type, type, (
% 0.19/0.41 tptp_fun_VC_55: $i)).
% 0.19/0.41 tff(tptp_fun_Vx_54_type, type, (
% 0.19/0.41 tptp_fun_Vx_54: $i)).
% 0.19/0.41 tff(visFreeVar_type, type, (
% 0.19/0.41 visFreeVar: ( $i * $i ) > $o)).
% 0.19/0.41 tff(vbind_type, type, (
% 0.19/0.41 vbind: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_VT_56_type, type, (
% 0.19/0.41 tptp_fun_VT_56: $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[Ve: $i, Vy: $i, VT: $i, Ve1: $i] : refl((vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1)) <=> (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1)) <=> ![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1)) <=> ![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1)) <=> ![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))))) <=> ![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))))) <=> ![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[5, 4])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (^[Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : trans(monotonicity(rewrite((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) <=> ((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))), trans(monotonicity(rewrite(((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1))) <=> ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vabs(Vy, VT, Ve1)))), (((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1)))) <=> ((Vx = Vy) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vabs(Vy, VT, Ve1)))))), rewrite(((Vx = Vy) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vabs(Vy, VT, Ve1)))) <=> ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)))), (((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1)))) <=> ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1))))) <=> (((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))) => ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)))))), rewrite((((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))) => ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)))) <=> ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1))))) <=> ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1))))) <=> ![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : ((RESULT = vabs(Vy, VT, Ve1)) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1))))) <=> ![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[8, 6])).
% 0.19/0.41 tff(10,axiom,(![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Ve1: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, Ve1)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','subst3')).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.19/0.41 tff(13,plain,(
% 0.19/0.41 ![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(skolemize,[status(sab)],[12])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 ((~![Ve: $i, Vy: $i, VT: $i, Ve1: $i] : (vsubst(Vy, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, Ve1))) | (vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, veabs))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, veabs)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) <=> vtcheck(VC!55, vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (vtcheck(VC!55, vabs(Vy!52, VS!51, veabs), VT2!50) <=> vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)),
% 0.19/0.41 inference(symmetry,[status(thm)],[17])).
% 0.19/0.41 tff(19,assumption,(~(Vx!54 = Vy!52)), introduced(assumption)).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))) <=> (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))) <=> (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(22,axiom,(~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-subst-abs'')).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.19/0.42 tff(27,plain,(
% 0.19/0.42 ~((~(vtcheck(VC!55, Ve!53, VT!56) & vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50))),
% 0.19/0.42 inference(skolemize,[status(sab)],[26])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (~vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)),
% 0.19/0.42 inference(or_elim,[status(thm)],[27])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (vtcheck(VC!55, Ve!53, VT!56) & vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.19/0.42 inference(or_elim,[status(thm)],[27])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.19/0.42 inference(and_elim,[status(thm)],[29])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (vtcheck(VC!55, Ve!53, VT!56)),
% 0.19/0.42 inference(and_elim,[status(thm)],[29])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : refl((vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> (~(visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))), ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> (~(~(visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))))), rewrite((~(~(visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))) <=> (visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> (visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))), (((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ((visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))), rewrite(((visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), (((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) <=> ((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT))), (((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), rewrite((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> ((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))), (((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> ((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), ((((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))), rewrite((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))), ((((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.42 tff(39,axiom,(![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-subst-abs-2'')).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.42 tff(42,plain,(
% 0.19/0.42 ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.42 inference(skolemize,[status(sab)],[41])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 ((vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50))) <=> (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52))),
% 0.19/0.42 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | visFreeVar(Vy, Ve) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 44, 31, 30, 28])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (visFreeVar(Vy!52, Ve!53)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[51, 19])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : refl((vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> (~((~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))), ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> (~(~((~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))))), rewrite((~(~((~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))) <=> ((~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) <=> ((~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))))), (((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> (((~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))), rewrite((((~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), (((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~(Vx = Vy)) & visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) <=> ((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT))), (((((~(Vx = Vy)) & visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> (((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), rewrite((((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> ((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))), (((((~(Vx = Vy)) & visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) <=> ((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))), ((((((~(Vx = Vy)) & visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> (((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))), rewrite((((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))), ((((((~(Vx = Vy)) & visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (((((~(Vx = Vy)) & visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.43 tff(60,axiom,(![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (((((~(Vx = Vy)) & visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-subst-abs-3'')).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.43 tff(63,plain,(
% 0.19/0.43 ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & visFreeVar(Vy, Ve) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.19/0.43 inference(skolemize,[status(sab)],[62])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (Vx!54 = Vy!52) | (~visFreeVar(Vy!52, Ve!53)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (Vx!54 = Vy!52) | (~visFreeVar(Vy!52, Ve!53)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 ((vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~visFreeVar(Vy!52, Ve!53)) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50))) <=> (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (Vx!54 = Vy!52) | (~visFreeVar(Vy!52, Ve!53)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~visFreeVar(Vy!52, Ve!53)) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (Vx!54 = Vy!52) | (~visFreeVar(Vy!52, Ve!53))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~visFreeVar(Vy!52, Ve!53)) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (Vx!54 = Vy!52) | (~visFreeVar(Vy!52, Ve!53)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[68, 66])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~visFreeVar(Vy!52, Ve!53)) | (Vx!54 = Vy!52) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(VC!55, Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (Vx!54 = Vy!52) | (~visFreeVar(Vy!52, Ve!53))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 ((Vx!54 = Vy!52) | (~visFreeVar(Vy!52, Ve!53))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[71, 65, 31, 30, 28])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[72, 52, 19])).
% 0.19/0.44 tff(74,plain,(Vx!54 = Vy!52), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, veabs)),
% 0.19/0.44 inference(transitivity,[status(thm)],[75, 16])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) <=> vtcheck(VC!55, vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) <=> vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)),
% 0.19/0.44 inference(transitivity,[status(thm)],[77, 18])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 ((~vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)) <=> (~vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (~vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[28, 79])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (Vy!52 = Vx!54),
% 0.19/0.44 inference(symmetry,[status(thm)],[74])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (vbind(Vy!52, VT!56, VC!55) = vbind(Vx!54, VT!56, VC!55)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50) <=> vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50) <=> vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.19/0.44 inference(symmetry,[status(thm)],[83])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[30, 84])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (^[VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : refl((vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT))) <=> (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT))) <=> ![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT))) <=> ![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT))) <=> ![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : ((~((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : ((~((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)) <=> ![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[90, 89])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : trans(monotonicity(rewrite((((Vx = Vy) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) <=> ((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2))), (((((Vx = Vy) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)) <=> (((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)))), rewrite((((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)) <=> ((~((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2))), (((((Vx = Vy) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)) <=> ((~((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : ((((Vx = Vy) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : ((~((Vx = Vy) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : ((((Vx = Vy) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2)) <=> ![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.44 tff(95,axiom,(![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : ((((Vx = Vy) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, Ve1)), VT2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-subst-abs-1'')).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[96, 88])).
% 0.19/0.44 tff(98,plain,(
% 0.19/0.44 ![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[97])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[98, 87])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | ((~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))) <=> ((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 ((vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~vtcheck(VC!55, Ve!53, VT!56))) <=> ((~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~vtcheck(VC!55, Ve!53, VT!56)))) <=> ((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | ((~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~vtcheck(VC!55, Ve!53, VT!56)))) <=> ((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 ((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~vtcheck(VC!55, Ve!53, VT!56)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 ((~![VT: $i, VC: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (vtcheck(VC, vsubst(Vy, Ve, vabs(Vy, VS, Ve1)), VT2) | (~vtcheck(vbind(Vy, VT, VC), vabs(Vy, VS, Ve1), VT2)) | (~vtcheck(VC, Ve, VT)))) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (vtcheck(VC!55, vsubst(Vy!52, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) | (~vtcheck(vbind(Vy!52, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[105, 99, 31])).
% 0.19/0.45 tff(107,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[106, 85, 80])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------