%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : COM137+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n027.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 18:06:13 EDT 2022

% Result   : Theorem 1.05s 0.90s
% Output   : Proof 1.09s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : COM137+1 : TPTP v8.1.0. Released v6.4.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue Aug 30 15:16:46 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 1.05/0.90  % SZS status Theorem
% 1.05/0.90  % SZS output start Proof
% 1.05/0.90  tff(vtcheck_type, type, (
% 1.05/0.90     vtcheck: ( $i * $i * $i ) > $o)).
% 1.05/0.90  tff(varrow_type, type, (
% 1.05/0.90     varrow: ( $i * $i ) > $i)).
% 1.05/0.90  tff(tptp_fun_VT_74_type, type, (
% 1.05/0.90     tptp_fun_VT_74: $i)).
% 1.05/0.90  tff(tptp_fun_VS_71_type, type, (
% 1.05/0.90     tptp_fun_VS_71: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(vapp_type, type, (
% 1.05/0.90     vapp: ( $i * $i ) > $i)).
% 1.05/0.90  tff(ve2app_type, type, (
% 1.05/0.90     ve2app: $i)).
% 1.05/0.90  tff(ve1app_type, type, (
% 1.05/0.90     ve1app: $i)).
% 1.05/0.90  tff(vbind_type, type, (
% 1.05/0.90     vbind: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(tptp_fun_VC_75_type, type, (
% 1.05/0.90     tptp_fun_VC_75: $i)).
% 1.05/0.90  tff(tptp_fun_VS_76_type, type, (
% 1.05/0.90     tptp_fun_VS_76: $i)).
% 1.05/0.90  tff(tptp_fun_Vx_77_type, type, (
% 1.05/0.90     tptp_fun_Vx_77: $i)).
% 1.05/0.90  tff(visFreeVar_type, type, (
% 1.05/0.90     visFreeVar: ( $i * $i ) > $o)).
% 1.05/0.90  tff(tptp_fun_Ve2_72_type, type, (
% 1.05/0.90     tptp_fun_Ve2_72: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(tptp_fun_Ve1_73_type, type, (
% 1.05/0.90     tptp_fun_Ve1_73: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(vsomeType_type, type, (
% 1.05/0.90     vsomeType: $i > $i)).
% 1.05/0.90  tff(vlookup_type, type, (
% 1.05/0.90     vlookup: ( $i * $i ) > $i)).
% 1.05/0.90  tff(tptp_fun_Vx_66_type, type, (
% 1.05/0.90     tptp_fun_Vx_66: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(vvar_type, type, (
% 1.05/0.90     vvar: $i > $i)).
% 1.05/0.90  tff(tptp_fun_VT2_67_type, type, (
% 1.05/0.90     tptp_fun_VT2_67: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(tptp_fun_Ve2_69_type, type, (
% 1.05/0.90     tptp_fun_Ve2_69: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(tptp_fun_VT1_68_type, type, (
% 1.05/0.90     tptp_fun_VT1_68: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(tptp_fun_Vx_70_type, type, (
% 1.05/0.90     tptp_fun_Vx_70: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(vabs_type, type, (
% 1.05/0.90     vabs: ( $i * $i * $i ) > $i)).
% 1.05/0.90  tff(1,assumption,((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))), introduced(assumption)).
% 1.05/0.90  tff(2,plain,
% 1.05/0.90      ((vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) <=> (vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.90      inference(commutativity,[status(thm)],[])).
% 1.05/0.90  tff(3,plain,
% 1.05/0.90      ((~(vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) <=> (~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.05/0.90      inference(monotonicity,[status(thm)],[2])).
% 1.05/0.90  tff(4,assumption,(vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)), introduced(assumption)).
% 1.05/0.90  tff(5,plain,
% 1.05/0.90      (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 1.05/0.90      inference(bind,[status(th)],[])).
% 1.05/0.90  tff(6,plain,
% 1.05/0.90      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.05/0.90      inference(quant_intro,[status(thm)],[5])).
% 1.05/0.90  tff(7,plain,
% 1.05/0.90      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.05/0.90      inference(rewrite,[status(thm)],[])).
% 1.05/0.90  tff(8,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 1.05/0.90  tff(9,plain,
% 1.05/0.90      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[8, 7])).
% 1.05/0.90  tff(10,plain,(
% 1.05/0.90      ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.05/0.90      inference(skolemize,[status(sab)],[9])).
% 1.05/0.90  tff(11,plain,
% 1.05/0.90      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[10, 6])).
% 1.05/0.90  tff(12,plain,
% 1.05/0.90      ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)))),
% 1.05/0.90      inference(quant_inst,[status(thm)],[])).
% 1.05/0.90  tff(13,plain,
% 1.05/0.90      ($false),
% 1.05/0.90      inference(unit_resolution,[status(thm)],[12, 11, 4])).
% 1.05/0.90  tff(14,plain,(~(vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))), inference(lemma,lemma(discharge,[]))).
% 1.05/0.90  tff(15,plain,
% 1.05/0.90      (~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[14, 3])).
% 1.05/0.90  tff(16,plain,
% 1.05/0.90      (((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74)))) | (vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.90      inference(tautology,[status(thm)],[])).
% 1.05/0.90  tff(17,plain,
% 1.05/0.90      ((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74)))),
% 1.05/0.90      inference(unit_resolution,[status(thm)],[16, 15])).
% 1.05/0.90  tff(18,plain,
% 1.05/0.90      ((vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) <=> (vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.90      inference(commutativity,[status(thm)],[])).
% 1.05/0.90  tff(19,plain,
% 1.05/0.90      ((~(vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) <=> (~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.05/0.90      inference(monotonicity,[status(thm)],[18])).
% 1.05/0.90  tff(20,assumption,(vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)), introduced(assumption)).
% 1.05/0.90  tff(21,plain,
% 1.05/0.90      (^[VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : refl((~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))))),
% 1.05/0.90      inference(bind,[status(th)],[])).
% 1.05/0.90  tff(22,plain,
% 1.05/0.90      (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 1.05/0.90      inference(quant_intro,[status(thm)],[21])).
% 1.05/0.90  tff(23,plain,
% 1.05/0.90      (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 1.05/0.90      inference(rewrite,[status(thm)],[])).
% 1.05/0.90  tff(24,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-abs-app'')).
% 1.05/0.90  tff(25,plain,
% 1.05/0.90      (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[24, 23])).
% 1.05/0.90  tff(26,plain,(
% 1.05/0.90      ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 1.05/0.90      inference(skolemize,[status(sab)],[25])).
% 1.05/0.90  tff(27,plain,
% 1.05/0.90      (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[26, 22])).
% 1.05/0.90  tff(28,plain,
% 1.05/0.90      ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)))),
% 1.05/0.90      inference(quant_inst,[status(thm)],[])).
% 1.05/0.90  tff(29,plain,
% 1.05/0.90      ($false),
% 1.05/0.90      inference(unit_resolution,[status(thm)],[28, 27, 20])).
% 1.05/0.90  tff(30,plain,(~(vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))), inference(lemma,lemma(discharge,[]))).
% 1.05/0.90  tff(31,plain,
% 1.05/0.90      (~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[30, 19])).
% 1.05/0.90  tff(32,plain,
% 1.05/0.90      (((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.90      inference(tautology,[status(thm)],[])).
% 1.05/0.90  tff(33,plain,
% 1.05/0.90      ((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.90      inference(unit_resolution,[status(thm)],[32, 31])).
% 1.05/0.90  tff(34,plain,
% 1.05/0.90      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT)))),
% 1.05/0.90      inference(rewrite,[status(thm)],[])).
% 1.05/0.90  tff(35,plain,
% 1.05/0.90      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT)) => vtcheck(VC, vapp(ve1app, ve2app), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT)))),
% 1.05/0.90      inference(rewrite,[status(thm)],[])).
% 1.05/0.90  tff(36,axiom,(~![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT)) => vtcheck(VC, vapp(ve1app, ve2app), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Strong-app'')).
% 1.05/0.90  tff(37,plain,
% 1.05/0.90      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[36, 35])).
% 1.05/0.90  tff(38,plain,
% 1.05/0.90      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[37, 34])).
% 1.05/0.90  tff(39,plain,
% 1.05/0.90      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[38, 34])).
% 1.05/0.90  tff(40,plain,
% 1.05/0.90      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[39, 34])).
% 1.05/0.90  tff(41,plain,
% 1.05/0.90      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[40, 34])).
% 1.05/0.90  tff(42,plain,
% 1.05/0.90      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[41, 34])).
% 1.05/0.90  tff(43,plain,
% 1.05/0.90      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) | vtcheck(VC, vapp(ve1app, ve2app), VT))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[42, 34])).
% 1.05/0.90  tff(44,plain,(
% 1.05/0.90      ~((~((~visFreeVar(Vx!77, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74))) | vtcheck(VC!75, vapp(ve1app, ve2app), VT!74))),
% 1.05/0.90      inference(skolemize,[status(sab)],[43])).
% 1.05/0.90  tff(45,plain,
% 1.05/0.90      ((~visFreeVar(Vx!77, vapp(ve1app, ve2app))) & vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74)),
% 1.05/0.90      inference(or_elim,[status(thm)],[44])).
% 1.05/0.90  tff(46,plain,
% 1.05/0.90      (vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74)),
% 1.05/0.90      inference(and_elim,[status(thm)],[45])).
% 1.05/0.90  tff(47,plain,
% 1.05/0.90      (^[Ve: $i, VT: $i, VC: $i] : refl(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))))),
% 1.05/0.90      inference(bind,[status(th)],[])).
% 1.05/0.90  tff(48,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 1.05/0.90      inference(quant_intro,[status(thm)],[47])).
% 1.05/0.90  tff(49,plain,
% 1.05/0.90      (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(rewrite(((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) <=> (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT)))))), rewrite(((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) <=> (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))))), rewrite(((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) <=> (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))))), rewrite(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))))),
% 1.05/0.90      inference(bind,[status(th)],[])).
% 1.05/0.90  tff(50,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 1.05/0.90      inference(quant_intro,[status(thm)],[49])).
% 1.05/0.90  tff(51,plain,
% 1.05/0.90      (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))),
% 1.05/0.90      inference(bind,[status(th)],[])).
% 1.05/0.90  tff(52,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))),
% 1.05/0.90      inference(quant_intro,[status(thm)],[51])).
% 1.05/0.90  tff(53,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 1.05/0.90      inference(rewrite,[status(thm)],[])).
% 1.05/0.90  tff(54,plain,
% 1.05/0.90      (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 1.05/0.90      inference(bind,[status(th)],[])).
% 1.05/0.90  tff(55,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 1.05/0.90      inference(quant_intro,[status(thm)],[54])).
% 1.05/0.90  tff(56,axiom,(![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 1.05/0.90  tff(57,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[56, 55])).
% 1.05/0.90  tff(58,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 1.05/0.90      inference(modus_ponens,[status(thm)],[57, 53])).
% 1.05/0.90  tff(59,plain,(
% 1.05/0.90      ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 1.05/0.90      inference(skolemize,[status(sab)],[58])).
% 1.05/0.90  tff(60,plain,
% 1.05/0.90      (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[59, 52])).
% 1.05/0.91  tff(61,plain,
% 1.05/0.91      (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[60, 50])).
% 1.05/0.91  tff(62,plain,
% 1.05/0.91      (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[61, 48])).
% 1.05/0.91  tff(63,plain,
% 1.05/0.91      (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))),
% 1.05/0.91      inference(rewrite,[status(thm)],[])).
% 1.05/0.91  tff(64,plain,
% 1.05/0.91      ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))),
% 1.05/0.91      inference(quant_inst,[status(thm)],[])).
% 1.05/0.91  tff(65,plain,
% 1.05/0.91      ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[64, 63])).
% 1.05/0.91  tff(66,plain,
% 1.05/0.91      ((~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)), tptp_fun_Ve2_69(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))),
% 1.05/0.91      inference(unit_resolution,[status(thm)],[65, 62, 46])).
% 1.05/0.91  tff(67,plain,
% 1.05/0.91      ((~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), vbind(Vx!77, VS!76, VC!75)) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))),
% 1.05/0.91      inference(unit_resolution,[status(thm)],[66, 33])).
% 1.05/0.91  tff(68,plain,
% 1.05/0.91      (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.05/0.91      inference(unit_resolution,[status(thm)],[67, 17])).
% 1.05/0.91  tff(69,plain,
% 1.05/0.91      (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.05/0.91      inference(tautology,[status(thm)],[])).
% 1.05/0.91  tff(70,plain,
% 1.05/0.91      (vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))),
% 1.05/0.91      inference(unit_resolution,[status(thm)],[69, 68])).
% 1.05/0.91  tff(71,plain,
% 1.05/0.91      (vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)),
% 1.05/0.91      inference(symmetry,[status(thm)],[70])).
% 1.05/0.91  tff(72,plain,
% 1.05/0.91      (^[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))))))))),
% 1.05/0.91      inference(bind,[status(th)],[])).
% 1.05/0.91  tff(73,plain,
% 1.05/0.91      (![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)))))))),
% 1.05/0.91      inference(quant_intro,[status(thm)],[72])).
% 1.05/0.91  tff(74,plain,
% 1.05/0.91      (^[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)))))))))),
% 1.05/0.91      inference(bind,[status(th)],[])).
% 1.05/0.91  tff(75,plain,
% 1.05/0.91      (![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)))))))),
% 1.05/0.91      inference(quant_intro,[status(thm)],[74])).
% 1.05/0.91  tff(76,plain,
% 1.05/0.91      (![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)))))),
% 1.05/0.91      inference(rewrite,[status(thm)],[])).
% 1.05/0.91  tff(77,plain,
% 1.05/0.91      (^[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)))))))),
% 1.05/0.91      inference(bind,[status(th)],[])).
% 1.05/0.91  tff(78,plain,
% 1.05/0.91      (![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)))))),
% 1.05/0.91      inference(quant_intro,[status(thm)],[77])).
% 1.05/0.91  tff(79,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')).
% 1.05/0.91  tff(80,plain,
% 1.05/0.91      (![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)))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[79, 78])).
% 1.05/0.91  tff(81,plain,
% 1.05/0.91      (![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)))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[80, 76])).
% 1.05/0.91  tff(82,plain,(
% 1.05/0.91      ![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)))))),
% 1.05/0.91      inference(skolemize,[status(sab)],[81])).
% 1.05/0.91  tff(83,plain,
% 1.05/0.91      (![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)))))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[82, 75])).
% 1.05/0.91  tff(84,plain,
% 1.05/0.91      (![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)))))))),
% 1.05/0.91      inference(modus_ponens,[status(thm)],[83, 73])).
% 1.05/0.91  tff(85,plain,
% 1.05/0.91      (((~![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)))))))) | ((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))) <=> ((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))),
% 1.05/0.91      inference(rewrite,[status(thm)],[])).
% 1.05/0.91  tff(86,plain,
% 1.05/0.91      (($false | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))))) <=> ((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))),
% 1.05/0.92      inference(rewrite,[status(thm)],[])).
% 1.05/0.92  tff(87,plain,
% 1.05/0.92      ((~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))) <=> (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))))),
% 1.05/0.92      inference(rewrite,[status(thm)],[])).
% 1.05/0.92  tff(88,plain,
% 1.05/0.92      ((~$true) <=> $false),
% 1.05/0.92      inference(rewrite,[status(thm)],[])).
% 1.05/0.92  tff(89,plain,
% 1.05/0.92      ((Vx!77 = Vx!77) <=> $true),
% 1.05/0.92      inference(rewrite,[status(thm)],[])).
% 1.05/0.92  tff(90,plain,
% 1.05/0.92      ((~(Vx!77 = Vx!77)) <=> (~$true)),
% 1.05/0.92      inference(monotonicity,[status(thm)],[89])).
% 1.05/0.92  tff(91,plain,
% 1.05/0.92      ((~(Vx!77 = Vx!77)) <=> $false),
% 1.05/0.92      inference(transitivity,[status(thm)],[90, 88])).
% 1.05/0.92  tff(92,plain,
% 1.05/0.92      (((~(Vx!77 = Vx!77)) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))))) <=> ($false | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))),
% 1.05/0.92      inference(monotonicity,[status(thm)],[91, 87])).
% 1.05/0.92  tff(93,plain,
% 1.05/0.92      (((~(Vx!77 = Vx!77)) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))))) <=> ((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))),
% 1.05/0.92      inference(transitivity,[status(thm)],[92, 86])).
% 1.05/0.92  tff(94,plain,
% 1.05/0.92      (((~![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)))))))) | ((~(Vx!77 = Vx!77)) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))) <=> ((~![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)))))))) | ((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))))))),
% 1.05/0.92      inference(monotonicity,[status(thm)],[93])).
% 1.05/0.92  tff(95,plain,
% 1.05/0.92      (((~![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)))))))) | ((~(Vx!77 = Vx!77)) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))) <=> ((~![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)))))))) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))),
% 1.08/0.92      inference(transitivity,[status(thm)],[94, 85])).
% 1.08/0.92  tff(96,plain,
% 1.08/0.92      ((~![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)))))))) | ((~(Vx!77 = Vx!77)) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))))),
% 1.08/0.92      inference(quant_inst,[status(thm)],[])).
% 1.08/0.92  tff(97,plain,
% 1.08/0.92      ((~![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~(VVar0 = Vv)) | (~(VExp0 = vapp(Ve1, Ve2))) | (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))))),
% 1.08/0.92      inference(modus_ponens,[status(thm)],[96, 95])).
% 1.08/0.92  tff(98,plain,
% 1.08/0.92      ($false),
% 1.08/0.92      inference(unit_resolution,[status(thm)],[97, 84, 71, 1])).
% 1.08/0.92  tff(99,plain,(~((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))))))), inference(lemma,lemma(discharge,[]))).
% 1.08/0.92  tff(100,plain,
% 1.08/0.92      (((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve2app) | visFreeVar(Vx!77, ve1app) | (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))))) | ((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.08/0.92      inference(tautology,[status(thm)],[])).
% 1.08/0.92  tff(101,plain,
% 1.08/0.92      ((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.08/0.92      inference(unit_resolution,[status(thm)],[100, 99])).
% 1.08/0.92  tff(102,plain,
% 1.08/0.92      (visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))) <=> visFreeVar(Vx!77, vapp(ve1app, ve2app))),
% 1.08/0.92      inference(monotonicity,[status(thm)],[71])).
% 1.08/0.92  tff(103,plain,
% 1.08/0.92      (visFreeVar(Vx!77, vapp(ve1app, ve2app)) <=> visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.08/0.92      inference(symmetry,[status(thm)],[102])).
% 1.08/0.92  tff(104,plain,
% 1.08/0.92      ((~visFreeVar(Vx!77, vapp(ve1app, ve2app))) <=> (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.08/0.92      inference(monotonicity,[status(thm)],[103])).
% 1.08/0.92  tff(105,plain,
% 1.08/0.92      (~visFreeVar(Vx!77, vapp(ve1app, ve2app))),
% 1.08/0.92      inference(and_elim,[status(thm)],[45])).
% 1.08/0.92  tff(106,plain,
% 1.08/0.92      (~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.08/0.92      inference(modus_ponens,[status(thm)],[105, 104])).
% 1.08/0.92  tff(107,assumption,(visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))), introduced(assumption)).
% 1.08/0.92  tff(108,plain,
% 1.08/0.92      ($false),
% 1.08/0.92      inference(unit_resolution,[status(thm)],[107, 106])).
% 1.08/0.92  tff(109,plain,(~visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))), inference(lemma,lemma(discharge,[]))).
% 1.08/0.92  tff(110,plain,
% 1.08/0.92      ((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.08/0.92      inference(tautology,[status(thm)],[])).
% 1.08/0.92  tff(111,plain,
% 1.08/0.92      ((~((~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))) | visFreeVar(Vx!77, vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) | (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app)))),
% 1.08/0.92      inference(unit_resolution,[status(thm)],[110, 109])).
% 1.08/0.92  tff(112,plain,
% 1.08/0.92      (~(visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app))),
% 1.08/0.92      inference(unit_resolution,[status(thm)],[111, 101])).
% 1.08/0.92  tff(113,plain,
% 1.08/0.92      ((visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app)) | (~visFreeVar(Vx!77, ve1app))),
% 1.08/0.92      inference(tautology,[status(thm)],[])).
% 1.08/0.92  tff(114,plain,
% 1.08/0.92      (~visFreeVar(Vx!77, ve1app)),
% 1.08/0.92      inference(unit_resolution,[status(thm)],[113, 112])).
% 1.08/0.92  tff(115,plain,
% 1.08/0.92      (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : refl((~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))))),
% 1.08/0.92      inference(bind,[status(th)],[])).
% 1.08/0.92  tff(116,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 1.08/0.92      inference(quant_intro,[status(thm)],[115])).
% 1.08/0.92  tff(117,plain,
% 1.08/0.92      (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : trans(monotonicity(rewrite(((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), trans(monotonicity(trans(monotonicity(rewrite(((VExp0 = VExp2) & (VExp1 = VExp3)) <=> (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> (~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), rewrite((~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> (((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), rewrite((((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), rewrite((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))))),
% 1.08/0.92      inference(bind,[status(th)],[])).
% 1.08/0.92  tff(118,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 1.08/0.92      inference(quant_intro,[status(thm)],[117])).
% 1.08/0.92  tff(119,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 1.08/0.92      inference(rewrite,[status(thm)],[])).
% 1.08/0.92  tff(120,plain,
% 1.08/0.92      (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : rewrite((((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))))),
% 1.08/0.92      inference(bind,[status(th)],[])).
% 1.08/0.92  tff(121,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 1.08/0.92      inference(quant_intro,[status(thm)],[120])).
% 1.08/0.92  tff(122,axiom,(![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''EQ-app'')).
% 1.08/0.92  tff(123,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 1.08/0.92      inference(modus_ponens,[status(thm)],[122, 121])).
% 1.08/0.92  tff(124,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 1.08/0.92      inference(modus_ponens,[status(thm)],[123, 119])).
% 1.08/0.92  tff(125,plain,(
% 1.08/0.92      ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 1.08/0.92      inference(skolemize,[status(sab)],[124])).
% 1.08/0.92  tff(126,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 1.08/0.92      inference(modus_ponens,[status(thm)],[125, 118])).
% 1.08/0.92  tff(127,plain,
% 1.08/0.92      (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 1.08/0.92      inference(modus_ponens,[status(thm)],[126, 116])).
% 1.08/0.92  tff(128,plain,
% 1.08/0.92      ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app))))))),
% 1.08/0.93      inference(quant_inst,[status(thm)],[])).
% 1.08/0.93  tff(129,plain,
% 1.08/0.93      (~((~((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))))),
% 1.08/0.93      inference(unit_resolution,[status(thm)],[128, 127])).
% 1.08/0.93  tff(130,plain,
% 1.08/0.93      (((~((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app))))) | ((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))))),
% 1.08/0.93      inference(tautology,[status(thm)],[])).
% 1.08/0.93  tff(131,plain,
% 1.08/0.93      ((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app))))),
% 1.08/0.93      inference(unit_resolution,[status(thm)],[130, 129])).
% 1.08/0.93  tff(132,plain,
% 1.08/0.93      ((~((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app))))),
% 1.08/0.93      inference(tautology,[status(thm)],[])).
% 1.08/0.93  tff(133,plain,
% 1.08/0.93      ((~((~(vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app))))),
% 1.08/0.93      inference(unit_resolution,[status(thm)],[132, 71])).
% 1.08/0.93  tff(134,plain,
% 1.08/0.93      (~((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)))),
% 1.08/0.93      inference(unit_resolution,[status(thm)],[133, 131])).
% 1.08/0.93  tff(135,plain,
% 1.08/0.93      (((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app))) | (tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)),
% 1.08/0.93      inference(tautology,[status(thm)],[])).
% 1.08/0.93  tff(136,plain,
% 1.08/0.93      (tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app),
% 1.08/0.93      inference(unit_resolution,[status(thm)],[135, 134])).
% 1.08/0.93  tff(137,plain,
% 1.08/0.93      (ve1app = tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))),
% 1.08/0.93      inference(symmetry,[status(thm)],[136])).
% 1.08/0.93  tff(138,plain,
% 1.08/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) <=> vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))),
% 1.08/0.93      inference(monotonicity,[status(thm)],[137])).
% 1.08/0.93  tff(139,plain,
% 1.08/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) <=> vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))),
% 1.08/0.93      inference(symmetry,[status(thm)],[138])).
% 1.08/0.93  tff(140,plain,
% 1.08/0.93      (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))),
% 1.08/0.93      inference(tautology,[status(thm)],[])).
% 1.08/0.93  tff(141,plain,
% 1.08/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))),
% 1.08/0.93      inference(unit_resolution,[status(thm)],[140, 68])).
% 1.08/0.93  tff(142,plain,
% 1.08/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))),
% 1.08/0.93      inference(modus_ponens,[status(thm)],[141, 139])).
% 1.08/0.93  tff(143,plain,
% 1.08/0.93      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))),
% 1.08/0.93      inference(bind,[status(th)],[])).
% 1.08/0.93  tff(144,plain,
% 1.08/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 1.08/0.93      inference(quant_intro,[status(thm)],[143])).
% 1.08/0.93  tff(145,plain,
% 1.08/0.93      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> (~(visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))), ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> (~(~(visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))))), rewrite((~(~(visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))) <=> (visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))), ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) <=> (visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))))), (((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> ((visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)))), rewrite(((visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))), (((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))))),
% 1.09/0.93      inference(bind,[status(th)],[])).
% 1.09/0.93  tff(146,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 1.09/0.93      inference(quant_intro,[status(thm)],[145])).
% 1.09/0.93  tff(147,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 1.09/0.93      inference(rewrite,[status(thm)],[])).
% 1.09/0.93  tff(148,plain,
% 1.09/0.93      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) => vtcheck(VC, ve1app, VT)) <=> ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT)))),
% 1.09/0.93      inference(bind,[status(th)],[])).
% 1.09/0.93  tff(149,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) => vtcheck(VC, ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 1.09/0.93      inference(quant_intro,[status(thm)],[148])).
% 1.09/0.93  tff(150,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT)) => vtcheck(VC, ve1app, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Strong-app-IH1'')).
% 1.09/0.93  tff(151,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[150, 149])).
% 1.09/0.93  tff(152,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[151, 147])).
% 1.09/0.93  tff(153,plain,(
% 1.09/0.93      ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve1app)) & vtcheck(vbind(Vx, VS, VC), ve1app, VT))) | vtcheck(VC, ve1app, VT))),
% 1.09/0.93      inference(skolemize,[status(sab)],[152])).
% 1.09/0.93  tff(154,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[153, 146])).
% 1.09/0.93  tff(155,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[154, 144])).
% 1.09/0.93  tff(156,plain,
% 1.09/0.93      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | (vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) | visFreeVar(Vx!77, ve1app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) | visFreeVar(Vx!77, ve1app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))))),
% 1.09/0.93      inference(rewrite,[status(thm)],[])).
% 1.09/0.93  tff(157,plain,
% 1.09/0.93      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | (vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) | visFreeVar(Vx!77, ve1app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))))),
% 1.09/0.93      inference(quant_inst,[status(thm)],[])).
% 1.09/0.93  tff(158,plain,
% 1.09/0.93      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve1app, VT) | visFreeVar(Vx, ve1app) | (~vtcheck(vbind(Vx, VS, VC), ve1app, VT)))) | vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) | visFreeVar(Vx!77, ve1app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[157, 156])).
% 1.09/0.93  tff(159,plain,
% 1.09/0.93      (vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) | visFreeVar(Vx!77, ve1app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)))),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[158, 155])).
% 1.09/0.93  tff(160,plain,
% 1.09/0.93      (vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74)) | visFreeVar(Vx!77, ve1app)),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[159, 142])).
% 1.09/0.93  tff(161,plain,
% 1.09/0.93      (vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[160, 114])).
% 1.09/0.93  tff(162,plain,
% 1.09/0.93      ((visFreeVar(Vx!77, ve1app) | visFreeVar(Vx!77, ve2app)) | (~visFreeVar(Vx!77, ve2app))),
% 1.09/0.93      inference(tautology,[status(thm)],[])).
% 1.09/0.93  tff(163,plain,
% 1.09/0.93      (~visFreeVar(Vx!77, ve2app)),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[162, 112])).
% 1.09/0.93  tff(164,plain,
% 1.09/0.93      (((~(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app))) | (tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app)),
% 1.09/0.93      inference(tautology,[status(thm)],[])).
% 1.09/0.93  tff(165,plain,
% 1.09/0.93      (tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)) = ve2app),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[164, 134])).
% 1.09/0.93  tff(166,plain,
% 1.09/0.93      (ve2app = tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))),
% 1.09/0.93      inference(symmetry,[status(thm)],[165])).
% 1.09/0.93  tff(167,plain,
% 1.09/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) <=> vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))),
% 1.09/0.93      inference(monotonicity,[status(thm)],[166])).
% 1.09/0.93  tff(168,plain,
% 1.09/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) <=> vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))),
% 1.09/0.93      inference(symmetry,[status(thm)],[167])).
% 1.09/0.93  tff(169,plain,
% 1.09/0.93      (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve1_73(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))) | vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))),
% 1.09/0.93      inference(tautology,[status(thm)],[])).
% 1.09/0.93  tff(170,plain,
% 1.09/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), tptp_fun_Ve2_72(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[169, 68])).
% 1.09/0.93  tff(171,plain,
% 1.09/0.93      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[170, 168])).
% 1.09/0.93  tff(172,plain,
% 1.09/0.93      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))),
% 1.09/0.93      inference(bind,[status(th)],[])).
% 1.09/0.93  tff(173,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 1.09/0.93      inference(quant_intro,[status(thm)],[172])).
% 1.09/0.93  tff(174,plain,
% 1.09/0.93      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> (~(visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))), ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> (~(~(visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))))), rewrite((~(~(visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))) <=> (visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))), ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) <=> (visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))))), (((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> ((visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)))), rewrite(((visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))), (((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))))),
% 1.09/0.93      inference(bind,[status(th)],[])).
% 1.09/0.93  tff(175,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 1.09/0.93      inference(quant_intro,[status(thm)],[174])).
% 1.09/0.93  tff(176,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 1.09/0.93      inference(rewrite,[status(thm)],[])).
% 1.09/0.93  tff(177,plain,
% 1.09/0.93      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) => vtcheck(VC, ve2app, VT)) <=> ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT)))),
% 1.09/0.93      inference(bind,[status(th)],[])).
% 1.09/0.93  tff(178,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) => vtcheck(VC, ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 1.09/0.93      inference(quant_intro,[status(thm)],[177])).
% 1.09/0.93  tff(179,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT)) => vtcheck(VC, ve2app, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Strong-app-IH2'')).
% 1.09/0.93  tff(180,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[179, 178])).
% 1.09/0.93  tff(181,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[180, 176])).
% 1.09/0.93  tff(182,plain,(
% 1.09/0.93      ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, ve2app)) & vtcheck(vbind(Vx, VS, VC), ve2app, VT))) | vtcheck(VC, ve2app, VT))),
% 1.09/0.93      inference(skolemize,[status(sab)],[181])).
% 1.09/0.93  tff(183,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[182, 175])).
% 1.09/0.93  tff(184,plain,
% 1.09/0.93      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[183, 173])).
% 1.09/0.93  tff(185,plain,
% 1.09/0.93      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | (vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) | visFreeVar(Vx!77, ve2app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) | visFreeVar(Vx!77, ve2app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.09/0.93      inference(rewrite,[status(thm)],[])).
% 1.09/0.93  tff(186,plain,
% 1.09/0.93      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | (vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) | visFreeVar(Vx!77, ve2app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.09/0.93      inference(quant_inst,[status(thm)],[])).
% 1.09/0.93  tff(187,plain,
% 1.09/0.93      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, ve2app, VT) | visFreeVar(Vx, ve2app) | (~vtcheck(vbind(Vx, VS, VC), ve2app, VT)))) | vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) | visFreeVar(Vx!77, ve2app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.09/0.93      inference(modus_ponens,[status(thm)],[186, 185])).
% 1.09/0.93  tff(188,plain,
% 1.09/0.93      (vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) | visFreeVar(Vx!77, ve2app) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[187, 184])).
% 1.09/0.93  tff(189,plain,
% 1.09/0.93      (vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))) | visFreeVar(Vx!77, ve2app)),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[188, 171])).
% 1.09/0.93  tff(190,plain,
% 1.09/0.93      (vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))),
% 1.09/0.93      inference(unit_resolution,[status(thm)],[189, 163])).
% 1.09/0.93  tff(191,assumption,(vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))), introduced(assumption)).
% 1.09/0.93  tff(192,assumption,(vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))), introduced(assumption)).
% 1.09/0.93  tff(193,plain,
% 1.09/0.93      (~vtcheck(VC!75, vapp(ve1app, ve2app), VT!74)),
% 1.09/0.94      inference(or_elim,[status(thm)],[44])).
% 1.09/0.94  tff(194,plain,
% 1.09/0.94      (^[VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : refl((vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) <=> (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))),
% 1.09/0.94      inference(bind,[status(th)],[])).
% 1.09/0.94  tff(195,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 1.09/0.94      inference(quant_intro,[status(thm)],[194])).
% 1.09/0.94  tff(196,plain,
% 1.09/0.94      (^[VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) <=> (~((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))), ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (~(~((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))))), rewrite((~(~((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))) <=> ((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))), ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> ((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))))), (((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> (((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)))), rewrite((((~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))), (((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))))),
% 1.09/0.94      inference(bind,[status(th)],[])).
% 1.09/0.94  tff(197,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 1.09/0.94      inference(quant_intro,[status(thm)],[196])).
% 1.09/0.94  tff(198,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 1.09/0.94      inference(rewrite,[status(thm)],[])).
% 1.09/0.94  tff(199,plain,
% 1.09/0.94      (^[VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : rewrite(((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) => vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT)))),
% 1.09/0.94      inference(bind,[status(th)],[])).
% 1.09/0.94  tff(200,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) => vtcheck(VC, vapp(Ve1, Ve2), VT)) <=> ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 1.09/0.94      inference(quant_intro,[status(thm)],[199])).
% 1.09/0.94  tff(201,axiom,(![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) => vtcheck(VC, vapp(Ve1, Ve2), VT))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''T-app'')).
% 1.09/0.94  tff(202,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[201, 200])).
% 1.09/0.94  tff(203,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[202, 198])).
% 1.09/0.94  tff(204,plain,(
% 1.09/0.94      ![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : ((~(vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) | vtcheck(VC, vapp(Ve1, Ve2), VT))),
% 1.09/0.94      inference(skolemize,[status(sab)],[203])).
% 1.09/0.94  tff(205,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[204, 197])).
% 1.09/0.94  tff(206,plain,
% 1.09/0.94      (![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[205, 195])).
% 1.09/0.94  tff(207,plain,
% 1.09/0.94      (((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (vtcheck(VC!75, vapp(ve1app, ve2app), VT!74) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))) <=> ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | vtcheck(VC!75, vapp(ve1app, ve2app), VT!74) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.09/0.94      inference(rewrite,[status(thm)],[])).
% 1.09/0.94  tff(208,plain,
% 1.09/0.94      ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | (vtcheck(VC!75, vapp(ve1app, ve2app), VT!74) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)))))),
% 1.09/0.94      inference(quant_inst,[status(thm)],[])).
% 1.09/0.94  tff(209,plain,
% 1.09/0.94      ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | vtcheck(VC!75, vapp(ve1app, ve2app), VT!74) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))),
% 1.09/0.94      inference(modus_ponens,[status(thm)],[208, 207])).
% 1.09/0.94  tff(210,plain,
% 1.09/0.94      ($false),
% 1.09/0.94      inference(unit_resolution,[status(thm)],[209, 206, 193, 192, 191])).
% 1.09/0.94  tff(211,plain,((~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(vbind(Vx!77, VS!76, VC!75), VT!74, vapp(ve1app, ve2app))))), inference(lemma,lemma(discharge,[]))).
% 1.09/0.94  tff(212,plain,
% 1.09/0.94      ($false),
% 1.09/0.94      inference(unit_resolution,[status(thm)],[211, 190, 161])).
% 1.09/0.94  % SZS output end Proof
%------------------------------------------------------------------------------