TSTP Solution File: COM125+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM125+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 18:06:10 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COM125+1 : TPTP v8.1.0. Released v6.4.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:52:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(tptp_fun_Vy_76_type, type, (
% 0.20/0.42 tptp_fun_Vy_76: $i)).
% 0.20/0.42 tff(tptp_fun_Vx_79_type, type, (
% 0.20/0.42 tptp_fun_Vx_79: $i)).
% 0.20/0.42 tff(vtcheck_type, type, (
% 0.20/0.42 vtcheck: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_VT_74_type, type, (
% 0.20/0.42 tptp_fun_VT_74: $i)).
% 0.20/0.42 tff(vabs_type, type, (
% 0.20/0.42 vabs: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(veabs_type, type, (
% 0.20/0.42 veabs: $i)).
% 0.20/0.42 tff(tptp_fun_VS1_75_type, type, (
% 0.20/0.42 tptp_fun_VS1_75: $i)).
% 0.20/0.42 tff(vbind_type, type, (
% 0.20/0.42 vbind: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_VC_77_type, type, (
% 0.20/0.42 tptp_fun_VC_77: $i)).
% 0.20/0.42 tff(tptp_fun_VS_78_type, type, (
% 0.20/0.42 tptp_fun_VS_78: $i)).
% 0.20/0.42 tff(visFreeVar_type, type, (
% 0.20/0.42 visFreeVar: ( $i * $i ) > $o)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(3,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak-FreeVar-abs'')).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.42 tff(11,plain,(
% 0.20/0.42 ~((~((~visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))) & vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74))),
% 0.20/0.42 inference(skolemize,[status(sab)],[10])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74)),
% 0.20/0.42 inference(or_elim,[status(thm)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))) & vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)),
% 0.20/0.42 inference(or_elim,[status(thm)],[11])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)),
% 0.20/0.42 inference(and_elim,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (~visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs))),
% 0.20/0.42 inference(and_elim,[status(thm)],[13])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : refl(((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) <=> (~((Vx = Vy) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))), ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> (~(~((Vx = Vy) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))))), rewrite((~(~((Vx = Vy) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))) <=> ((Vx = Vy) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))), ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ((Vx = Vy) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))), (((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> (((Vx = Vy) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))), rewrite((((Vx = Vy) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))), (((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : trans(monotonicity(rewrite((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) <=> ((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))), (((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> (((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))), rewrite((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), (((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.43 tff(23,axiom,(![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak-FreeVar-abs-1'')).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.43 tff(26,plain,(
% 0.20/0.43 ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.43 inference(skolemize,[status(sab)],[25])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | (visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (Vx!79 = Vy!76))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (Vx!79 = Vy!76))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (((Vx!79 = Vy!76) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74))) <=> (visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (Vx!79 = Vy!76))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((Vx!79 = Vy!76) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | (visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (Vx!79 = Vy!76)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((Vx!79 = Vy!76) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (Vx!79 = Vy!76))),
% 0.20/0.43 inference(transitivity,[status(thm)],[31, 29])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((Vx!79 = Vy!76) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((Vx = Vy) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (Vx!79 = Vy!76)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (Vx!79 = Vy!76),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[34, 28, 15, 14, 12])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : refl(((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) <=> (~((~(Vx = Vy)) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))), ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> (~(~((~(Vx = Vy)) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))))), rewrite((~(~((~(Vx = Vy)) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))) <=> ((~(Vx = Vy)) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))), ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> ((~(Vx = Vy)) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))))), (((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> (((~(Vx = Vy)) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))), rewrite((((~(Vx = Vy)) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))), (((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (^[Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : trans(monotonicity(rewrite((((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) <=> ((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))), (((((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> (((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))), rewrite((((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), (((((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) <=> ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.44 tff(43,axiom,(![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak-FreeVar-abs-2'')).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.44 tff(46,plain,(
% 0.20/0.44 ![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((Vx = Vy) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.20/0.44 inference(skolemize,[status(sab)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | (visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~(Vx!79 = Vy!76)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~(Vx!79 = Vy!76)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (((~(Vx!79 = Vy!76)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74))) <=> (visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~(Vx!79 = Vy!76)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((~(Vx!79 = Vy!76)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | (visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~(Vx!79 = Vy!76))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((~(Vx!79 = Vy!76)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~(Vx!79 = Vy!76)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | ((~(Vx!79 = Vy!76)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~(Vx = Vy)) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT) | visFreeVar(Vx, vabs(Vy, VS1, veabs)) | (~vtcheck(VC, vabs(Vy, VS1, veabs), VT)))) | visFreeVar(Vx!79, vabs(Vy!76, VS1!75, veabs)) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) | (~vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~(Vx!79 = Vy!76))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[54, 48, 15, 14, 12, 35])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------