%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM130+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:01:06 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM130+1 : TPTP v9.0.0. Released v6.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:24:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(visFreeVar_type, type, (
% 0.19/0.40 visFreeVar: ( $i * $i ) > $o)).
% 0.19/0.40 tff(vabs_type, type, (
% 0.19/0.40 vabs: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Ve1_51_type, type, (
% 0.19/0.40 tptp_fun_Ve1_51: $i)).
% 0.19/0.40 tff(tptp_fun_VS_52_type, type, (
% 0.19/0.40 tptp_fun_VS_52: $i)).
% 0.19/0.40 tff(tptp_fun_Vy_53_type, type, (
% 0.19/0.40 tptp_fun_Vy_53: $i)).
% 0.19/0.40 tff(vtcheck_type, type, (
% 0.19/0.40 vtcheck: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_VT2_50_type, type, (
% 0.19/0.40 tptp_fun_VT2_50: $i)).
% 0.19/0.40 tff(tptp_fun_VC_55_type, type, (
% 0.19/0.40 tptp_fun_VC_55: $i)).
% 0.19/0.40 tff(vsubst_type, type, (
% 0.19/0.40 vsubst: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Ve_54_type, type, (
% 0.19/0.40 tptp_fun_Ve_54: $i)).
% 0.19/0.40 tff(tptp_fun_VT_56_type, type, (
% 0.19/0.40 tptp_fun_VT_56: $i)).
% 0.19/0.40 tff(vbind_type, type, (
% 0.19/0.40 vbind: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(transitivity,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (^[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!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)) = vabs(Vy!53, VS!52, Ve1!51))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (vsubst(Vy!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)) = vabs(Vy!53, VS!52, Ve1!51)),
% 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!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)), VT2!50) <=> vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), 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, vsubst(Vy!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)), VT2!50)) <=> (~vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ((~(vtcheck(VC!55, vsubst(Vy!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | (~vtcheck(VC!55, Ve!54, VT!56)))) <=> (~(vtcheck(VC!55, vsubst(Vy!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | (~vtcheck(VC!55, Ve!54, VT!56))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ((~![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))))),
% 0.19/0.41 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, 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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,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'')).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (~![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (~![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (~![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (~![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.19/0.41 tff(27,plain,(
% 0.19/0.41 ~(vtcheck(VC!55, vsubst(Vy!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | (~vtcheck(VC!55, Ve!54, VT!56)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (~(vtcheck(VC!55, vsubst(Vy!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | (~vtcheck(VC!55, Ve!54, VT!56)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (~vtcheck(VC!55, vsubst(Vy!53, Ve!54, vabs(Vy!53, VS!52, Ve1!51)), VT2!50)),
% 0.19/0.41 inference(or_elim,[status(thm)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (~vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 18])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)),
% 0.19/0.41 inference(or_elim,[status(thm)],[28])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : refl((visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))) <=> (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> (~(visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))), ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) <=> (~(~(visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))))), rewrite((~(~(visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))) <=> (visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))), ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) <=> (visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))), (((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> ((visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)))), rewrite(((visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))), (((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : rewrite((((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) => vtcheck(VC, Ve, VT)) <=> ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) => vtcheck(VC, Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.41 tff(39,axiom,(![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) => vtcheck(VC, Ve, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Strong'')).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.41 tff(42,plain,(
% 0.19/0.41 ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.19/0.41 inference(skolemize,[status(sab)],[41])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | ((~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50))) <=> ((~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | ((~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50))),
% 0.19/0.41 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (~vtcheck(vbind(Vy!53, VT!56, VC!55), vabs(Vy!53, VS!52, Ve1!51), VT2!50)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)) | vtcheck(VC!55, vabs(Vy!53, VS!52, Ve1!51), VT2!50)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[50, 44, 31])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 30])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[VT: $i, Vx: $i, Vv: $i, Ve: $i] : refl((~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))) <=> (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (^[VT: $i, Vx: $i, Vv: $i, Ve: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vv)) & visFreeVar(Vv, Ve)) <=> (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))), ((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> (~(~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))), rewrite((~(~((Vx = Vv) | (~visFreeVar(Vv, Ve))))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve)))), ((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve))))), (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) <=> (((Vx = Vv) | (~visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))))), rewrite((((Vx = Vv) | (~visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))), (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve))))), rewrite(((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))), ((((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))), rewrite((((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))) <=> (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))), ((((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[59, 58])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (^[VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : trans(monotonicity(rewrite(((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))), ((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))))), rewrite((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))), ((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.42 tff(64,axiom,(![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isFreeVar1')).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[65, 57])).
% 0.19/0.42 tff(67,plain,(
% 0.19/0.42 ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 56])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.43 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[68, 54])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)))) <=> ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 ((~((~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)))) | (~((~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))) | (~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51)))))))) <=> (~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)))) | (~((~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))) | (~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51))))))))) <=> ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)))) | (~((~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))) | (~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51))))))))) <=> ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[72, 70])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51)) | visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)))) | (~((~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51))) | (~((Vy!53 = Vy!53) | (~visFreeVar(Vy!53, Ve1!51))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~visFreeVar(Vy!53, vabs(Vy!53, VS!52, Ve1!51)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[75, 69, 52])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------