TSTP Solution File: COM128+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM128+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 18:06:11 EDT 2022
% Result : Theorem 0.75s 0.72s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : COM128+1 : TPTP v8.1.0. Released v6.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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 15:07:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.75/0.72 % SZS status Theorem
% 0.75/0.72 % SZS output start Proof
% 0.75/0.72 tff(visFreeVar_type, type, (
% 0.75/0.72 visFreeVar: ( $i * $i ) > $o)).
% 0.75/0.72 tff(vapp_type, type, (
% 0.75/0.72 vapp: ( $i * $i ) > $i)).
% 0.75/0.72 tff(vvar_type, type, (
% 0.75/0.72 vvar: $i > $i)).
% 0.75/0.72 tff(tptp_fun_Vx_75_type, type, (
% 0.75/0.72 tptp_fun_Vx_75: $i)).
% 0.75/0.72 tff(tptp_fun_Ve1_76_type, type, (
% 0.75/0.72 tptp_fun_Ve1_76: $i)).
% 0.75/0.72 tff(tptp_fun_Ve_77_type, type, (
% 0.75/0.72 tptp_fun_Ve_77: $i)).
% 0.75/0.72 tff(tptp_fun_Vfresh_74_type, type, (
% 0.75/0.72 tptp_fun_Vfresh_74: $i)).
% 0.75/0.72 tff(vgensym_type, type, (
% 0.75/0.72 vgensym: $i > $i)).
% 0.75/0.72 tff(1,plain,
% 0.75/0.72 ((~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))) <=> (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))))))),
% 0.75/0.72 inference(rewrite,[status(thm)],[])).
% 0.75/0.72 tff(2,plain,
% 0.75/0.72 ((~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))) => (~(Vx = Vfresh)))) <=> (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))))))),
% 0.75/0.72 inference(rewrite,[status(thm)],[])).
% 0.75/0.72 tff(3,axiom,(~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))) => (~(Vx = Vfresh)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''fresh-unequal-var-3'')).
% 0.75/0.72 tff(4,plain,
% 0.75/0.72 (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))),
% 0.75/0.72 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.75/0.72 tff(5,plain,
% 0.75/0.72 (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))),
% 0.75/0.72 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.75/0.72 tff(6,plain,
% 0.75/0.72 (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))),
% 0.75/0.72 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.75/0.72 tff(7,plain,
% 0.75/0.72 (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))),
% 0.75/0.72 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.75/0.72 tff(8,plain,
% 0.75/0.72 (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))),
% 0.75/0.72 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.75/0.72 tff(9,plain,
% 0.75/0.72 (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))),
% 0.75/0.72 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.75/0.72 tff(10,plain,
% 0.75/0.72 (~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((~(Vx = Vfresh)) | (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))))))),
% 0.75/0.72 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.75/0.72 tff(11,plain,(
% 0.75/0.72 ~((~(Vx!75 = Vfresh!74)) | (~(Vfresh!74 = vgensym(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))),
% 0.75/0.72 inference(skolemize,[status(sab)],[10])).
% 0.75/0.72 tff(12,plain,
% 0.75/0.72 (Vx!75 = Vfresh!74),
% 0.75/0.72 inference(or_elim,[status(thm)],[11])).
% 0.75/0.72 tff(13,plain,
% 0.75/0.72 (Vfresh!74 = Vx!75),
% 0.75/0.72 inference(symmetry,[status(thm)],[12])).
% 0.75/0.72 tff(14,plain,
% 0.75/0.72 (vvar(Vfresh!74) = vvar(Vx!75)),
% 0.75/0.72 inference(monotonicity,[status(thm)],[13])).
% 0.75/0.72 tff(15,plain,
% 0.75/0.72 (vvar(Vx!75) = vvar(Vfresh!74)),
% 0.75/0.72 inference(symmetry,[status(thm)],[14])).
% 0.75/0.72 tff(16,plain,
% 0.75/0.72 (^[VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = Vv) & (VExp0 = vvar(Vx))) <=> (~((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))), ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) <=> (~(~((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))))), rewrite((~(~((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))))), ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))))), rewrite((((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))) <=> (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))), (((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> (((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))))), rewrite((((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx)))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))), (((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))))),
% 0.75/0.73 inference(bind,[status(th)],[])).
% 0.75/0.73 tff(17,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 0.75/0.73 inference(quant_intro,[status(thm)],[16])).
% 0.75/0.73 tff(18,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(19,plain,
% 0.75/0.73 (^[VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : trans(monotonicity(rewrite((((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))) <=> (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))), rewrite((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 0.75/0.73 inference(bind,[status(th)],[])).
% 0.75/0.73 tff(20,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 0.75/0.73 inference(quant_intro,[status(thm)],[19])).
% 0.75/0.73 tff(21,axiom,(![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','isFreeVar0')).
% 0.75/0.73 tff(22,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.75/0.73 tff(23,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.75/0.73 tff(24,plain,(
% 0.75/0.73 ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 0.75/0.73 inference(skolemize,[status(sab)],[23])).
% 0.75/0.73 tff(25,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.75/0.73 tff(26,plain,
% 0.75/0.73 (((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75)))) <=> ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(27,plain,
% 0.75/0.73 (($false | (~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75))) <=> ((~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(28,plain,
% 0.75/0.73 ((~(~visFreeVar(Vfresh!74, vvar(Vx!75)))) <=> visFreeVar(Vfresh!74, vvar(Vx!75))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(29,plain,
% 0.75/0.73 (((~visFreeVar(Vfresh!74, vvar(Vx!75))) | $false) <=> (~visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(30,plain,
% 0.75/0.73 ((~$true) <=> $false),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(31,plain,
% 0.75/0.73 (((~visFreeVar(Vfresh!74, vvar(Vx!75))) | $true) <=> $true),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(32,plain,
% 0.75/0.73 ((Vfresh!74 = Vfresh!74) <=> $true),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(33,plain,
% 0.75/0.73 (((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74)) <=> ((~visFreeVar(Vfresh!74, vvar(Vx!75))) | $true)),
% 0.75/0.73 inference(monotonicity,[status(thm)],[32])).
% 0.75/0.73 tff(34,plain,
% 0.75/0.73 (((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74)) <=> $true),
% 0.75/0.73 inference(transitivity,[status(thm)],[33, 31])).
% 0.75/0.73 tff(35,plain,
% 0.75/0.73 ((~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74))) <=> (~$true)),
% 0.75/0.73 inference(monotonicity,[status(thm)],[34])).
% 0.75/0.73 tff(36,plain,
% 0.75/0.73 ((~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74))) <=> $false),
% 0.75/0.73 inference(transitivity,[status(thm)],[35, 30])).
% 0.75/0.73 tff(37,plain,
% 0.75/0.73 ((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) <=> (~visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(38,plain,
% 0.75/0.73 (((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74)))) <=> ((~visFreeVar(Vfresh!74, vvar(Vx!75))) | $false)),
% 0.75/0.73 inference(monotonicity,[status(thm)],[37, 36])).
% 0.75/0.73 tff(39,plain,
% 0.75/0.73 (((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74)))) <=> (~visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(transitivity,[status(thm)],[38, 29])).
% 0.75/0.73 tff(40,plain,
% 0.75/0.73 ((~((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74))))) <=> (~(~visFreeVar(Vfresh!74, vvar(Vx!75))))),
% 0.75/0.73 inference(monotonicity,[status(thm)],[39])).
% 0.75/0.73 tff(41,plain,
% 0.75/0.73 ((~((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74))))) <=> visFreeVar(Vfresh!74, vvar(Vx!75))),
% 0.75/0.73 inference(transitivity,[status(thm)],[40, 28])).
% 0.75/0.73 tff(42,plain,
% 0.75/0.73 ((~(Vfresh!74 = Vfresh!74)) <=> (~$true)),
% 0.75/0.73 inference(monotonicity,[status(thm)],[32])).
% 0.75/0.73 tff(43,plain,
% 0.75/0.73 ((~(Vfresh!74 = Vfresh!74)) <=> $false),
% 0.75/0.73 inference(transitivity,[status(thm)],[42, 30])).
% 0.75/0.73 tff(44,plain,
% 0.75/0.73 (((~(Vfresh!74 = Vfresh!74)) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | (~((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74)))))) <=> ($false | (~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(monotonicity,[status(thm)],[43, 41])).
% 0.75/0.73 tff(45,plain,
% 0.75/0.73 (((~(Vfresh!74 = Vfresh!74)) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | (~((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74)))))) <=> ((~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(transitivity,[status(thm)],[44, 27])).
% 0.75/0.73 tff(46,plain,
% 0.75/0.73 (((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(Vfresh!74 = Vfresh!74)) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | (~((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74))))))) <=> ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75))))),
% 0.75/0.73 inference(monotonicity,[status(thm)],[45])).
% 0.75/0.73 tff(47,plain,
% 0.75/0.73 (((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(Vfresh!74 = Vfresh!74)) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | (~((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74))))))) <=> ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(transitivity,[status(thm)],[46, 26])).
% 0.75/0.73 tff(48,plain,
% 0.75/0.73 ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | ((~(Vfresh!74 = Vfresh!74)) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | (~((~((~(Vfresh!74 = Vfresh!74)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | (~((~visFreeVar(Vfresh!74, vvar(Vx!75))) | (Vfresh!74 = Vfresh!74))))))),
% 0.75/0.73 inference(quant_inst,[status(thm)],[])).
% 0.75/0.73 tff(49,plain,
% 0.75/0.73 ((~![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vvar(Vx))) | (~((~((~(Vx = Vv)) | visFreeVar(VVar0, VExp0))) | (~((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))) | (~(vvar(Vx!75) = vvar(Vfresh!74))) | visFreeVar(Vfresh!74, vvar(Vx!75))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.75/0.73 tff(50,plain,
% 0.75/0.73 (visFreeVar(Vfresh!74, vvar(Vx!75))),
% 0.75/0.73 inference(unit_resolution,[status(thm)],[49, 25, 15])).
% 0.75/0.73 tff(51,plain,
% 0.75/0.73 ((visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76))) | (~visFreeVar(Vfresh!74, vvar(Vx!75)))),
% 0.75/0.73 inference(tautology,[status(thm)],[])).
% 0.75/0.73 tff(52,plain,
% 0.75/0.73 (visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76))),
% 0.75/0.73 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.75/0.73 tff(53,plain,
% 0.75/0.73 (Vfresh!74 = vgensym(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))),
% 0.75/0.73 inference(or_elim,[status(thm)],[11])).
% 0.75/0.73 tff(54,plain,
% 0.75/0.73 (vgensym(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))) = Vfresh!74),
% 0.75/0.73 inference(symmetry,[status(thm)],[53])).
% 0.75/0.73 tff(55,assumption,(visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))), introduced(assumption)).
% 0.75/0.73 tff(56,plain,
% 0.75/0.73 (^[Vv: $i, Ve: $i] : refl(((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))) <=> ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))))),
% 0.75/0.73 inference(bind,[status(th)],[])).
% 0.75/0.73 tff(57,plain,
% 0.75/0.73 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))) <=> ![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.75/0.73 inference(quant_intro,[status(thm)],[56])).
% 0.75/0.73 tff(58,plain,
% 0.75/0.73 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))) <=> ![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(59,plain,
% 0.75/0.73 (^[Vv: $i, Ve: $i] : rewrite(((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))))),
% 0.75/0.73 inference(bind,[status(th)],[])).
% 0.75/0.73 tff(60,plain,
% 0.75/0.73 (![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.75/0.73 inference(quant_intro,[status(thm)],[59])).
% 0.75/0.73 tff(61,axiom,(![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''gensym-is-fresh'')).
% 0.75/0.73 tff(62,plain,
% 0.75/0.73 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.75/0.73 tff(63,plain,
% 0.75/0.73 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.75/0.73 tff(64,plain,(
% 0.75/0.73 ![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.75/0.73 inference(skolemize,[status(sab)],[63])).
% 0.75/0.73 tff(65,plain,
% 0.75/0.73 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.75/0.73 tff(66,plain,
% 0.75/0.73 (((~![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))) | ((~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~(vgensym(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))) = Vfresh!74)))) <=> ((~![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~(vgensym(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))) = Vfresh!74)))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(67,plain,
% 0.75/0.73 ((~![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))) | ((~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~(vgensym(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))) = Vfresh!74)))),
% 0.75/0.73 inference(quant_inst,[status(thm)],[])).
% 0.75/0.73 tff(68,plain,
% 0.75/0.73 ((~![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~(vgensym(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))) = Vfresh!74))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.75/0.73 tff(69,plain,
% 0.75/0.73 ($false),
% 0.75/0.73 inference(unit_resolution,[status(thm)],[68, 65, 55, 54])).
% 0.75/0.73 tff(70,plain,(~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.73 tff(71,plain,
% 0.75/0.73 ((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))),
% 0.75/0.73 inference(tautology,[status(thm)],[])).
% 0.75/0.73 tff(72,plain,
% 0.75/0.73 (~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))),
% 0.75/0.73 inference(unit_resolution,[status(thm)],[71, 70, 52])).
% 0.75/0.73 tff(73,plain,
% 0.75/0.73 (((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))) | ((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))),
% 0.75/0.73 inference(tautology,[status(thm)],[])).
% 0.75/0.73 tff(74,plain,
% 0.75/0.73 ((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))),
% 0.75/0.73 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.75/0.73 tff(75,plain,
% 0.75/0.73 (^[VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : refl(((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))))),
% 0.75/0.73 inference(bind,[status(th)],[])).
% 0.75/0.73 tff(76,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))),
% 0.75/0.73 inference(quant_intro,[status(thm)],[75])).
% 0.75/0.73 tff(77,plain,
% 0.75/0.73 (^[VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) <=> (~((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2)))))), ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) <=> (~(~((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2)))))))), rewrite((~(~((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2)))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))))), ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2)))))), trans(monotonicity(monotonicity(rewrite((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) <=> (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))), (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) <=> ((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)))), rewrite((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))) <=> (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))), ((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))) <=> (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))), rewrite((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))), ((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))), (((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> (((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2)))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))))), rewrite((((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2)))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))), (((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))))),
% 0.75/0.73 inference(bind,[status(th)],[])).
% 0.75/0.73 tff(78,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))),
% 0.75/0.73 inference(quant_intro,[status(thm)],[77])).
% 0.75/0.73 tff(79,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(80,plain,
% 0.75/0.73 (^[VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : trans(monotonicity(rewrite((((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))) <=> (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))), ((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))), rewrite((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))), ((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))),
% 0.75/0.73 inference(bind,[status(th)],[])).
% 0.75/0.73 tff(81,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))),
% 0.75/0.73 inference(quant_intro,[status(thm)],[80])).
% 0.75/0.73 tff(82,axiom,(![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','isFreeVar2')).
% 0.75/0.73 tff(83,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.75/0.73 tff(84,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.75/0.73 tff(85,plain,(
% 0.75/0.73 ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))),
% 0.75/0.73 inference(skolemize,[status(sab)],[84])).
% 0.75/0.73 tff(86,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.75/0.73 tff(87,plain,
% 0.75/0.73 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))),
% 0.75/0.73 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.75/0.73 tff(88,plain,
% 0.75/0.73 (((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))) <=> ((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(89,plain,
% 0.75/0.73 (($false | $false | (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))) <=> (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(90,plain,
% 0.75/0.73 ((~((~((~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))) <=> (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))),
% 0.75/0.73 inference(rewrite,[status(thm)],[])).
% 0.75/0.73 tff(91,plain,
% 0.75/0.73 ((vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))) <=> $true),
% 0.75/0.74 inference(rewrite,[status(thm)],[])).
% 0.75/0.74 tff(92,plain,
% 0.75/0.74 ((~(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) <=> (~$true)),
% 0.75/0.74 inference(monotonicity,[status(thm)],[91])).
% 0.75/0.74 tff(93,plain,
% 0.75/0.74 ((~(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) <=> $false),
% 0.75/0.74 inference(transitivity,[status(thm)],[92, 30])).
% 0.75/0.74 tff(94,plain,
% 0.75/0.74 (((~(Vfresh!74 = Vfresh!74)) | (~(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~((~((~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))) <=> ($false | $false | (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))))),
% 0.75/0.74 inference(monotonicity,[status(thm)],[43, 93, 90])).
% 0.75/0.74 tff(95,plain,
% 0.75/0.74 (((~(Vfresh!74 = Vfresh!74)) | (~(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~((~((~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))) <=> (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))),
% 0.75/0.74 inference(transitivity,[status(thm)],[94, 89])).
% 0.75/0.74 tff(96,plain,
% 0.75/0.74 (((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | ((~(Vfresh!74 = Vfresh!74)) | (~(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~((~((~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))))) <=> ((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))))),
% 0.75/0.74 inference(monotonicity,[status(thm)],[95])).
% 0.75/0.74 tff(97,plain,
% 0.75/0.74 (((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | ((~(Vfresh!74 = Vfresh!74)) | (~(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~((~((~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))))) <=> ((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))))),
% 0.75/0.74 inference(transitivity,[status(thm)],[96, 88])).
% 0.75/0.74 tff(98,plain,
% 0.75/0.74 ((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | ((~(Vfresh!74 = Vfresh!74)) | (~(vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)) = vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))) | (~((~((~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | visFreeVar(Vfresh!74, vvar(Vx!75)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75)))))))))),
% 0.75/0.74 inference(quant_inst,[status(thm)],[])).
% 0.75/0.74 tff(99,plain,
% 0.75/0.74 ((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | (~((~((~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)))) | visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))) | (~(visFreeVar(Vfresh!74, vvar(Vx!75)) | visFreeVar(Vfresh!74, vapp(Ve!77, Ve1!76)) | (~visFreeVar(Vfresh!74, vapp(vapp(Ve!77, Ve1!76), vvar(Vx!75))))))))),
% 0.75/0.74 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.75/0.74 tff(100,plain,
% 0.75/0.74 ($false),
% 0.75/0.74 inference(unit_resolution,[status(thm)],[99, 87, 74])).
% 0.75/0.74 % SZS output end Proof
%------------------------------------------------------------------------------