TSTP Solution File: COM133+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM133+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 6 18:06:12 EDT 2022
% Result : Theorem 0.17s 0.41s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : COM133+1 : TPTP v8.1.0. Released v6.4.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Aug 30 14:54:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.17/0.41 % SZS status Theorem
% 0.17/0.41 % SZS output start Proof
% 0.17/0.41 tff(visFreeVar_type, type, (
% 0.17/0.41 visFreeVar: ( $i * $i ) > $o)).
% 0.17/0.41 tff(tptp_fun_Ve_77_type, type, (
% 0.17/0.41 tptp_fun_Ve_77: $i)).
% 0.17/0.41 tff(tptp_fun_Vy_76_type, type, (
% 0.17/0.41 tptp_fun_Vy_76: $i)).
% 0.17/0.41 tff(tptp_fun_Vx_78_type, type, (
% 0.17/0.41 tptp_fun_Vx_78: $i)).
% 0.17/0.41 tff(vtcheck_type, type, (
% 0.17/0.41 vtcheck: ( $i * $i * $i ) > $o)).
% 0.17/0.41 tff(tptp_fun_VT2_74_type, type, (
% 0.17/0.41 tptp_fun_VT2_74: $i)).
% 0.17/0.41 tff(vsubst_type, type, (
% 0.17/0.41 vsubst: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(vabs_type, type, (
% 0.17/0.41 vabs: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(veabs_type, type, (
% 0.17/0.41 veabs: $i)).
% 0.17/0.41 tff(tptp_fun_VS_75_type, type, (
% 0.17/0.41 tptp_fun_VS_75: $i)).
% 0.17/0.41 tff(tptp_fun_VC_79_type, type, (
% 0.17/0.41 tptp_fun_VC_79: $i)).
% 0.17/0.41 tff(vbind_type, type, (
% 0.17/0.41 vbind: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_VT_80_type, type, (
% 0.17/0.41 tptp_fun_VT_80: $i)).
% 0.17/0.41 tff(1,plain,
% 0.17/0.41 ((~![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(2,plain,
% 0.17/0.41 ((~![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(3,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'')).
% 0.17/0.41 tff(4,plain,
% 0.17/0.41 (~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.17/0.41 tff(5,plain,
% 0.17/0.41 (~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.17/0.41 tff(6,plain,
% 0.17/0.41 (~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.17/0.41 tff(7,plain,
% 0.17/0.41 (~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.17/0.41 tff(8,plain,
% 0.17/0.41 (~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.17/0.41 tff(9,plain,
% 0.17/0.41 (~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.17/0.41 tff(10,plain,
% 0.17/0.41 (~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.17/0.41 tff(11,plain,(
% 0.17/0.41 ~((~(vtcheck(VC!79, Ve!77, VT!80) & vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74))) | vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74))),
% 0.17/0.41 inference(skolemize,[status(sab)],[10])).
% 0.17/0.41 tff(12,plain,
% 0.17/0.41 (~vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74)),
% 0.17/0.41 inference(or_elim,[status(thm)],[11])).
% 0.17/0.41 tff(13,plain,
% 0.17/0.41 (vtcheck(VC!79, Ve!77, VT!80) & vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)),
% 0.17/0.41 inference(or_elim,[status(thm)],[11])).
% 0.17/0.41 tff(14,plain,
% 0.17/0.41 (vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)),
% 0.17/0.41 inference(and_elim,[status(thm)],[13])).
% 0.17/0.41 tff(15,plain,
% 0.17/0.41 (vtcheck(VC!79, Ve!77, VT!80)),
% 0.17/0.41 inference(and_elim,[status(thm)],[13])).
% 0.17/0.41 tff(16,plain,
% 0.17/0.41 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : refl((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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(17,plain,
% 0.17/0.41 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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))) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.17/0.41 tff(18,plain,
% 0.17/0.41 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : trans(monotonicity(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))) <=> (~(~((~(Vx = Vy)) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, Ve1), VT2))))))), 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))) <=> ((~(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)) <=> (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)))), (((~((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)) <=> (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)))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(19,plain,
% 0.17/0.41 (![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, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.17/0.41 tff(20,plain,
% 0.17/0.41 (![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, 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))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(21,plain,
% 0.17/0.42 (^[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))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(22,plain,
% 0.17/0.42 (![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))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.17/0.42 tff(23,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'')).
% 0.17/0.42 tff(24,plain,
% 0.17/0.42 (![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))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.17/0.42 tff(25,plain,
% 0.17/0.42 (![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))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.17/0.42 tff(26,plain,(
% 0.17/0.42 ![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))),
% 0.17/0.42 inference(skolemize,[status(sab)],[25])).
% 0.17/0.42 tff(27,plain,
% 0.17/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.17/0.42 tff(28,plain,
% 0.17/0.42 (![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.17/0.42 tff(29,plain,
% 0.17/0.42 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (~(Vx!78 = Vy!76)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (~(Vx!78 = Vy!76)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(30,plain,
% 0.17/0.42 ((vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~(Vx!78 = Vy!76)) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74))) <=> (vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (~(Vx!78 = Vy!76)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(31,plain,
% 0.17/0.42 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~(Vx!78 = Vy!76)) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (~(Vx!78 = Vy!76))))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[30])).
% 0.17/0.42 tff(32,plain,
% 0.17/0.42 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~(Vx!78 = Vy!76)) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (~(Vx!78 = Vy!76)))),
% 0.17/0.42 inference(transitivity,[status(thm)],[31, 29])).
% 0.17/0.42 tff(33,plain,
% 0.17/0.42 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~(Vx!78 = Vy!76)) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(34,plain,
% 0.17/0.42 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, Ve1: $i, VT2: $i] : (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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (~(Vx!78 = Vy!76))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.17/0.42 tff(35,plain,
% 0.17/0.42 (~(Vx!78 = Vy!76)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[34, 28, 15, 14, 12])).
% 0.17/0.42 tff(36,plain,
% 0.17/0.42 (^[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))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(37,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.17/0.42 tff(38,plain,
% 0.17/0.42 (^[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)))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(39,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.17/0.42 tff(40,plain,
% 0.17/0.42 (![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))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(41,plain,
% 0.17/0.42 (^[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))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(42,plain,
% 0.17/0.42 (![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))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.17/0.42 tff(43,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'')).
% 0.17/0.42 tff(44,plain,
% 0.17/0.42 (![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))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.17/0.42 tff(45,plain,
% 0.17/0.42 (![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))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.17/0.42 tff(46,plain,(
% 0.17/0.42 ![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))),
% 0.17/0.43 inference(skolemize,[status(sab)],[45])).
% 0.17/0.43 tff(47,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.17/0.43 tff(48,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.17/0.43 tff(49,plain,
% 0.17/0.43 (((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | visFreeVar(Vy!76, Ve!77))) <=> ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | visFreeVar(Vy!76, Ve!77))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(50,plain,
% 0.17/0.43 ((vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | visFreeVar(Vy!76, Ve!77) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74))) <=> (vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | visFreeVar(Vy!76, Ve!77))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(51,plain,
% 0.17/0.43 (((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | visFreeVar(Vy!76, Ve!77) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))) <=> ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | visFreeVar(Vy!76, Ve!77)))),
% 0.17/0.43 inference(monotonicity,[status(thm)],[50])).
% 0.17/0.43 tff(52,plain,
% 0.17/0.43 (((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | visFreeVar(Vy!76, Ve!77) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))) <=> ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | visFreeVar(Vy!76, Ve!77))),
% 0.17/0.43 inference(transitivity,[status(thm)],[51, 49])).
% 0.17/0.43 tff(53,plain,
% 0.17/0.43 ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | visFreeVar(Vy!76, Ve!77) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(54,plain,
% 0.17/0.43 ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | visFreeVar(Vy!76, Ve!77)),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.17/0.43 tff(55,plain,
% 0.17/0.43 (visFreeVar(Vy!76, Ve!77)),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[54, 48, 15, 14, 12, 35])).
% 0.17/0.43 tff(56,plain,
% 0.17/0.43 (^[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))))),
% 0.17/0.43 inference(bind,[status(th)],[])).
% 0.17/0.43 tff(57,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.17/0.43 tff(58,plain,
% 0.17/0.43 (^[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)))))),
% 0.17/0.43 inference(bind,[status(th)],[])).
% 0.17/0.43 tff(59,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.17/0.43 tff(60,plain,
% 0.17/0.43 (![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))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(61,plain,
% 0.17/0.43 (^[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))))),
% 0.17/0.43 inference(bind,[status(th)],[])).
% 0.17/0.43 tff(62,plain,
% 0.17/0.43 (![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))),
% 0.17/0.44 inference(quant_intro,[status(thm)],[61])).
% 0.17/0.44 tff(63,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'')).
% 0.17/0.44 tff(64,plain,
% 0.17/0.44 (![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))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.17/0.44 tff(65,plain,
% 0.17/0.44 (![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))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.17/0.44 tff(66,plain,(
% 0.17/0.44 ![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))),
% 0.17/0.44 inference(skolemize,[status(sab)],[65])).
% 0.17/0.44 tff(67,plain,
% 0.17/0.44 (![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)))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.17/0.44 tff(68,plain,
% 0.17/0.44 (![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)))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.17/0.44 tff(69,plain,
% 0.17/0.44 (((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | (~visFreeVar(Vy!76, Ve!77)))) <=> ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | (~visFreeVar(Vy!76, Ve!77)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(70,plain,
% 0.17/0.44 ((vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~visFreeVar(Vy!76, Ve!77)) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74))) <=> (vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | (~visFreeVar(Vy!76, Ve!77)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(71,plain,
% 0.17/0.44 (((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~visFreeVar(Vy!76, Ve!77)) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))) <=> ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | (~visFreeVar(Vy!76, Ve!77))))),
% 0.17/0.45 inference(monotonicity,[status(thm)],[70])).
% 0.17/0.45 tff(72,plain,
% 0.17/0.45 (((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~visFreeVar(Vy!76, Ve!77)) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))) <=> ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | (~visFreeVar(Vy!76, Ve!77)))),
% 0.17/0.45 inference(transitivity,[status(thm)],[71, 69])).
% 0.17/0.45 tff(73,plain,
% 0.17/0.45 ((~![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!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~visFreeVar(Vy!76, Ve!77)) | (Vx!78 = Vy!76) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)))),
% 0.17/0.45 inference(quant_inst,[status(thm)],[])).
% 0.17/0.45 tff(74,plain,
% 0.17/0.45 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2) | (~visFreeVar(Vy, Ve)) | (Vx = Vy) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)))) | vtcheck(VC!79, vsubst(Vx!78, Ve!77, vabs(Vy!76, VS!75, veabs)), VT2!74) | (~vtcheck(VC!79, Ve!77, VT!80)) | (~vtcheck(vbind(Vx!78, VT!80, VC!79), vabs(Vy!76, VS!75, veabs), VT2!74)) | (Vx!78 = Vy!76) | (~visFreeVar(Vy!76, Ve!77))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.17/0.45 tff(75,plain,
% 0.17/0.45 ($false),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[74, 68, 15, 14, 12, 35, 55])).
% 0.17/0.45 % SZS output end Proof
%------------------------------------------------------------------------------