%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : COM142+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n024.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 18:06:14 EDT 2022

% Result   : Theorem 0.19s 0.46s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COM142+1 : TPTP v8.1.0. Released v6.4.0.
% 0.06/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 30 15:09:49 EDT 2022
% 0.13/0.34  % 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.
% 0.19/0.46  % SZS status Theorem
% 0.19/0.46  % SZS output start Proof
% 0.19/0.46  tff(vapp_type, type, (
% 0.19/0.46     vapp: ( $i * $i ) > $i)).
% 0.19/0.46  tff(ve2app_type, type, (
% 0.19/0.46     ve2app: $i)).
% 0.19/0.46  tff(ve1app_type, type, (
% 0.19/0.46     ve1app: $i)).
% 0.19/0.46  tff(vvar_type, type, (
% 0.19/0.46     vvar: $i > $i)).
% 0.19/0.46  tff(tptp_fun_Vx_66_type, type, (
% 0.19/0.46     tptp_fun_Vx_66: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(tptp_fun_VT_74_type, type, (
% 0.19/0.46     tptp_fun_VT_74: $i)).
% 0.19/0.46  tff(tptp_fun_VC_75_type, type, (
% 0.19/0.46     tptp_fun_VC_75: $i)).
% 0.19/0.46  tff(vsomeType_type, type, (
% 0.19/0.46     vsomeType: $i > $i)).
% 0.19/0.46  tff(vlookup_type, type, (
% 0.19/0.46     vlookup: ( $i * $i ) > $i)).
% 0.19/0.46  tff(vtcheck_type, type, (
% 0.19/0.46     vtcheck: ( $i * $i * $i ) > $o)).
% 0.19/0.46  tff(tptp_fun_VS_71_type, type, (
% 0.19/0.46     tptp_fun_VS_71: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(tptp_fun_Ve2_72_type, type, (
% 0.19/0.46     tptp_fun_Ve2_72: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(varrow_type, type, (
% 0.19/0.46     varrow: ( $i * $i ) > $i)).
% 0.19/0.46  tff(tptp_fun_Ve1_73_type, type, (
% 0.19/0.46     tptp_fun_Ve1_73: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(vbind_type, type, (
% 0.19/0.46     vbind: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(tptp_fun_VS_76_type, type, (
% 0.19/0.46     tptp_fun_VS_76: $i)).
% 0.19/0.46  tff(tptp_fun_Vx_77_type, type, (
% 0.19/0.46     tptp_fun_Vx_77: $i)).
% 0.19/0.46  tff(vnoType_type, type, (
% 0.19/0.46     vnoType: $i)).
% 0.19/0.46  tff(tptp_fun_VT2_67_type, type, (
% 0.19/0.46     tptp_fun_VT2_67: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(tptp_fun_Ve2_69_type, type, (
% 0.19/0.46     tptp_fun_Ve2_69: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(tptp_fun_VT1_68_type, type, (
% 0.19/0.46     tptp_fun_VT1_68: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(tptp_fun_Vx_70_type, type, (
% 0.19/0.46     tptp_fun_Vx_70: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(vabs_type, type, (
% 0.19/0.46     vabs: ( $i * $i * $i ) > $i)).
% 0.19/0.46  tff(1,plain,
% 0.19/0.46      (^[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)))))))),
% 0.19/0.46      inference(bind,[status(th)],[])).
% 0.19/0.46  tff(2,plain,
% 0.19/0.46      (![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))))))),
% 0.19/0.46      inference(quant_intro,[status(thm)],[1])).
% 0.19/0.46  tff(3,plain,
% 0.19/0.46      (^[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))))))))),
% 0.19/0.46      inference(bind,[status(th)],[])).
% 0.19/0.46  tff(4,plain,
% 0.19/0.46      (![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))))))),
% 0.19/0.46      inference(quant_intro,[status(thm)],[3])).
% 0.19/0.46  tff(5,plain,
% 0.19/0.46      (![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))))),
% 0.19/0.46      inference(rewrite,[status(thm)],[])).
% 0.19/0.46  tff(6,plain,
% 0.19/0.46      (^[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)))))),
% 0.19/0.46      inference(bind,[status(th)],[])).
% 0.19/0.46  tff(7,plain,
% 0.19/0.46      (![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))))),
% 0.19/0.46      inference(quant_intro,[status(thm)],[6])).
% 0.19/0.46  tff(8,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/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-app'')).
% 0.19/0.46  tff(9,plain,
% 0.19/0.46      (![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))))),
% 0.19/0.46      inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.46  tff(10,plain,
% 0.19/0.46      (![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))))),
% 0.19/0.46      inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.46  tff(11,plain,(
% 0.19/0.46      ![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))))),
% 0.19/0.46      inference(skolemize,[status(sab)],[10])).
% 0.19/0.46  tff(12,plain,
% 0.19/0.46      (![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))))))),
% 0.19/0.46      inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.46  tff(13,plain,
% 0.19/0.46      (![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))))))),
% 0.19/0.46      inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.46  tff(14,plain,
% 0.19/0.46      ((~![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(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app))))))),
% 0.19/0.46      inference(quant_inst,[status(thm)],[])).
% 0.19/0.46  tff(15,plain,
% 0.19/0.46      (~((~((~(vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))))),
% 0.19/0.46      inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.46  tff(16,plain,
% 0.19/0.46      (((~((~(vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) | (~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app))))) | ((~(vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))))),
% 0.19/0.46      inference(tautology,[status(thm)],[])).
% 0.19/0.46  tff(17,plain,
% 0.19/0.46      ((~(vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app))))),
% 0.19/0.46      inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.46  tff(18,assumption,(~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))), introduced(assumption)).
% 0.19/0.46  tff(19,plain,
% 0.19/0.46      (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))) | (vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.47      inference(tautology,[status(thm)],[])).
% 0.19/0.47  tff(20,plain,
% 0.19/0.47      (vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)))),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.47  tff(21,plain,
% 0.19/0.47      (vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)),
% 0.19/0.47      inference(symmetry,[status(thm)],[20])).
% 0.19/0.47  tff(22,plain,
% 0.19/0.47      ((~((~(vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~(vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app))))),
% 0.19/0.47      inference(tautology,[status(thm)],[])).
% 0.19/0.47  tff(23,plain,
% 0.19/0.47      ((~((~(vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))))) | (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app))))),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.47  tff(24,plain,
% 0.19/0.47      (~((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)))),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[23, 17])).
% 0.19/0.47  tff(25,plain,
% 0.19/0.47      (((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app))) | (tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)),
% 0.19/0.47      inference(tautology,[status(thm)],[])).
% 0.19/0.47  tff(26,plain,
% 0.19/0.47      (tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.47  tff(27,plain,
% 0.19/0.47      (vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) <=> vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))),
% 0.19/0.47      inference(monotonicity,[status(thm)],[26])).
% 0.19/0.47  tff(28,plain,
% 0.19/0.47      (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))) | vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))),
% 0.19/0.47      inference(tautology,[status(thm)],[])).
% 0.19/0.47  tff(29,plain,
% 0.19/0.47      (vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[28, 18])).
% 0.19/0.47  tff(30,plain,
% 0.19/0.47      (vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[29, 27])).
% 0.19/0.47  tff(31,plain,
% 0.19/0.47      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT)))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(32,plain,
% 0.19/0.47      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT)) => vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT)))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(33,axiom,(~![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT)) => vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-app'')).
% 0.19/0.47  tff(34,plain,
% 0.19/0.47      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.47  tff(35,plain,
% 0.19/0.47      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[34, 31])).
% 0.19/0.47  tff(36,plain,
% 0.19/0.47      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.47  tff(37,plain,
% 0.19/0.47      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[36, 31])).
% 0.19/0.47  tff(38,plain,
% 0.19/0.47      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[37, 31])).
% 0.19/0.47  tff(39,plain,
% 0.19/0.47      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.47  tff(40,plain,
% 0.19/0.47      (~![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, vapp(ve1app, ve2app), VT))) | vtcheck(vbind(Vx, VS, VC), vapp(ve1app, ve2app), VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[39, 31])).
% 0.19/0.47  tff(41,plain,(
% 0.19/0.47      ~((~((vlookup(Vx!77, VC!75) = vnoType) & vtcheck(VC!75, vapp(ve1app, ve2app), VT!74))) | vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74))),
% 0.19/0.47      inference(skolemize,[status(sab)],[40])).
% 0.19/0.47  tff(42,plain,
% 0.19/0.47      ((vlookup(Vx!77, VC!75) = vnoType) & vtcheck(VC!75, vapp(ve1app, ve2app), VT!74)),
% 0.19/0.47      inference(or_elim,[status(thm)],[41])).
% 0.19/0.47  tff(43,plain,
% 0.19/0.47      (vlookup(Vx!77, VC!75) = vnoType),
% 0.19/0.47      inference(and_elim,[status(thm)],[42])).
% 0.19/0.47  tff(44,plain,
% 0.19/0.47      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))) <=> (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(45,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[44])).
% 0.19/0.47  tff(46,plain,
% 0.19/0.47      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT)) <=> (~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) <=> (~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))))))), rewrite((~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> (((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT)))), rewrite((((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(47,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[46])).
% 0.19/0.47  tff(48,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(49,plain,
% 0.19/0.47      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT)) => vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT)))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(50,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT)) => vtcheck(vbind(Vx, VS, VC), ve1app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[49])).
% 0.19/0.47  tff(51,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT)) => vtcheck(vbind(Vx, VS, VC), ve1app, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-app-IH1'')).
% 0.19/0.47  tff(52,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.47  tff(53,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.47  tff(54,plain,(
% 0.19/0.47      ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve1app, VT))) | vtcheck(vbind(Vx, VS, VC), ve1app, VT))),
% 0.19/0.47      inference(skolemize,[status(sab)],[53])).
% 0.19/0.47  tff(55,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.47  tff(56,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[55, 45])).
% 0.19/0.47  tff(57,plain,
% 0.19/0.47      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | ((~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(58,plain,
% 0.19/0.47      ((vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)))) <=> ((~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(59,plain,
% 0.19/0.47      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | (vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | ((~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)))))),
% 0.19/0.47      inference(monotonicity,[status(thm)],[58])).
% 0.19/0.47  tff(60,plain,
% 0.19/0.47      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | (vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))))),
% 0.19/0.47      inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.47  tff(61,plain,
% 0.19/0.47      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | (vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))))),
% 0.19/0.47      inference(quant_inst,[status(thm)],[])).
% 0.19/0.47  tff(62,plain,
% 0.19/0.47      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve1app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve1app, VT)))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.47  tff(63,plain,
% 0.19/0.47      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)) | (~vtcheck(VC!75, ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74)))),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[62, 56, 43])).
% 0.19/0.47  tff(64,plain,
% 0.19/0.47      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[63, 30])).
% 0.19/0.47  tff(65,plain,
% 0.19/0.47      (((~(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)) = ve1app)) | (~(tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app))) | (tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app)),
% 0.19/0.47      inference(tautology,[status(thm)],[])).
% 0.19/0.47  tff(66,plain,
% 0.19/0.47      (tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)) = ve2app),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[65, 24])).
% 0.19/0.47  tff(67,plain,
% 0.19/0.47      (vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) <=> vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))),
% 0.19/0.47      inference(monotonicity,[status(thm)],[66])).
% 0.19/0.47  tff(68,plain,
% 0.19/0.47      (((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))) | vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))),
% 0.19/0.47      inference(tautology,[status(thm)],[])).
% 0.19/0.47  tff(69,plain,
% 0.19/0.47      (vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[68, 18])).
% 0.19/0.47  tff(70,plain,
% 0.19/0.47      (vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[69, 67])).
% 0.19/0.47  tff(71,plain,
% 0.19/0.47      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))) <=> (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(72,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[71])).
% 0.19/0.47  tff(73,plain,
% 0.19/0.47      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT)) <=> (~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) <=> (~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))))))), rewrite((~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> (((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT)))), rewrite((((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(74,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[73])).
% 0.19/0.47  tff(75,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(76,plain,
% 0.19/0.47      (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT)) => vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT)))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(77,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT)) => vtcheck(vbind(Vx, VS, VC), ve2app, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[76])).
% 0.19/0.47  tff(78,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT)) => vtcheck(vbind(Vx, VS, VC), ve2app, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-app-IH2'')).
% 0.19/0.47  tff(79,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.47  tff(80,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.47  tff(81,plain,(
% 0.19/0.47      ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, ve2app, VT))) | vtcheck(vbind(Vx, VS, VC), ve2app, VT))),
% 0.19/0.47      inference(skolemize,[status(sab)],[80])).
% 0.19/0.47  tff(82,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[81, 74])).
% 0.19/0.47  tff(83,plain,
% 0.19/0.47      (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[82, 72])).
% 0.19/0.47  tff(84,plain,
% 0.19/0.47      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | ((~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(85,plain,
% 0.19/0.47      ((vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))) <=> ((~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(86,plain,
% 0.19/0.47      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | (vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | ((~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))))),
% 0.19/0.47      inference(monotonicity,[status(thm)],[85])).
% 0.19/0.47  tff(87,plain,
% 0.19/0.47      (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | (vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))),
% 0.19/0.48      inference(transitivity,[status(thm)],[86, 84])).
% 0.19/0.48  tff(88,plain,
% 0.19/0.48      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | (vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))),
% 0.19/0.48      inference(quant_inst,[status(thm)],[])).
% 0.19/0.48  tff(89,plain,
% 0.19/0.48      ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), ve2app, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, ve2app, VT)))) | (~(vlookup(Vx!77, VC!75) = vnoType)) | vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.48  tff(90,plain,
% 0.19/0.48      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))) | (~vtcheck(VC!75, ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[89, 83, 43])).
% 0.19/0.48  tff(91,plain,
% 0.19/0.48      (vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[90, 70])).
% 0.19/0.48  tff(92,plain,
% 0.19/0.48      (~vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74)),
% 0.19/0.48      inference(or_elim,[status(thm)],[41])).
% 0.19/0.48  tff(93,plain,
% 0.19/0.48      (^[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))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(94,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[93])).
% 0.19/0.48  tff(95,plain,
% 0.19/0.48      (^[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)))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(96,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[95])).
% 0.19/0.48  tff(97,plain,
% 0.19/0.48      (![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))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(98,plain,
% 0.19/0.48      (^[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)))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(99,plain,
% 0.19/0.48      (![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))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[98])).
% 0.19/0.48  tff(100,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/sandbox/benchmark/Axioms/COM001+0.ax',''T-app'')).
% 0.19/0.48  tff(101,plain,
% 0.19/0.48      (![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))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.48  tff(102,plain,
% 0.19/0.48      (![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))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.48  tff(103,plain,(
% 0.19/0.48      ![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))),
% 0.19/0.48      inference(skolemize,[status(sab)],[102])).
% 0.19/0.48  tff(104,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[103, 96])).
% 0.19/0.48  tff(105,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[104, 94])).
% 0.19/0.48  tff(106,plain,
% 0.19/0.48      (((~![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(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(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(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(107,plain,
% 0.19/0.48      ((~![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(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))),
% 0.19/0.48      inference(quant_inst,[status(thm)],[])).
% 0.19/0.48  tff(108,plain,
% 0.19/0.48      ((~![VS: $i, VC: $i, Ve1: $i, Ve2: $i, VT: $i] : (vtcheck(VC, vapp(Ve1, Ve2), VT) | (~vtcheck(VC, Ve1, varrow(VS, VT))) | (~vtcheck(VC, Ve2, VS)))) | vtcheck(vbind(Vx!77, VS!76, VC!75), vapp(ve1app, ve2app), VT!74) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve1app, varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(vbind(Vx!77, VS!76, VC!75), ve2app, tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.48  tff(109,plain,
% 0.19/0.48      ($false),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[108, 105, 92, 91, 64])).
% 0.19/0.48  tff(110,plain,((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48  tff(111,plain,
% 0.19/0.48      ((vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)) <=> (vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.48      inference(commutativity,[status(thm)],[])).
% 0.19/0.48  tff(112,plain,
% 0.19/0.48      ((~(vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))) <=> (~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)))))),
% 0.19/0.48      inference(monotonicity,[status(thm)],[111])).
% 0.19/0.48  tff(113,assumption,(vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)), introduced(assumption)).
% 0.19/0.48  tff(114,plain,
% 0.19/0.48      (^[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))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(115,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[114])).
% 0.19/0.48  tff(116,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(117,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-abs-app'')).
% 0.19/0.48  tff(118,plain,
% 0.19/0.48      (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.48  tff(119,plain,(
% 0.19/0.48      ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.19/0.48      inference(skolemize,[status(sab)],[118])).
% 0.19/0.48  tff(120,plain,
% 0.19/0.48      (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[119, 115])).
% 0.19/0.48  tff(121,plain,
% 0.19/0.48      ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)))),
% 0.19/0.48      inference(quant_inst,[status(thm)],[])).
% 0.19/0.48  tff(122,plain,
% 0.19/0.48      ($false),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[121, 120, 113])).
% 0.19/0.48  tff(123,plain,(~(vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48  tff(124,plain,
% 0.19/0.48      (~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[123, 112])).
% 0.19/0.48  tff(125,plain,
% 0.19/0.48      (((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.48      inference(tautology,[status(thm)],[])).
% 0.19/0.48  tff(126,plain,
% 0.19/0.48      ((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.48  tff(127,plain,
% 0.19/0.48      (vtcheck(VC!75, vapp(ve1app, ve2app), VT!74)),
% 0.19/0.48      inference(and_elim,[status(thm)],[42])).
% 0.19/0.48  tff(128,plain,
% 0.19/0.48      (^[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)))))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(129,plain,
% 0.19/0.48      (![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))))))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[128])).
% 0.19/0.48  tff(130,plain,
% 0.19/0.48      (^[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))))))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(131,plain,
% 0.19/0.48      (![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))))))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[130])).
% 0.19/0.48  tff(132,plain,
% 0.19/0.48      (^[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)))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(133,plain,
% 0.19/0.48      (![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))))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[132])).
% 0.19/0.48  tff(134,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(135,plain,
% 0.19/0.48      (^[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)))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(136,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[135])).
% 0.19/0.48  tff(137,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/sandbox/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 0.19/0.48  tff(138,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.48  tff(139,plain,
% 0.19/0.48      (![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)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[138, 134])).
% 0.19/0.48  tff(140,plain,(
% 0.19/0.48      ![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)))),
% 0.19/0.48      inference(skolemize,[status(sab)],[139])).
% 0.19/0.48  tff(141,plain,
% 0.19/0.48      (![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))))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[140, 133])).
% 0.19/0.48  tff(142,plain,
% 0.19/0.48      (![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))))))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[141, 131])).
% 0.19/0.48  tff(143,plain,
% 0.19/0.48      (![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))))))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[142, 129])).
% 0.19/0.48  tff(144,plain,
% 0.19/0.48      (((~![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(VC!75, vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(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(VC!75, vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(145,plain,
% 0.19/0.49      ((~![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(VC!75, vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)))))))),
% 0.19/0.49      inference(quant_inst,[status(thm)],[])).
% 0.19/0.49  tff(146,plain,
% 0.19/0.49      ((~![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(VC!75, vapp(ve1app, ve2app), VT!74)) | (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.49  tff(147,plain,
% 0.19/0.49      ((~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75) = vsomeType(VT!74))))) | (~((~(vapp(ve1app, ve2app) = vabs(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT1_68(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75), tptp_fun_Ve2_69(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VT2_67(VC!75, VT!74, vapp(ve1app, ve2app)))))) | (~((~(vapp(ve1app, ve2app) = vapp(tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~vtcheck(VC!75, tptp_fun_Ve1_73(VC!75, VT!74, vapp(ve1app, ve2app)), varrow(tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app)), VT!74))) | (~vtcheck(VC!75, tptp_fun_Ve2_72(VC!75, VT!74, vapp(ve1app, ve2app)), tptp_fun_VS_71(VC!75, VT!74, vapp(ve1app, ve2app))))))),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[146, 143, 127])).
% 0.19/0.49  tff(148,plain,
% 0.19/0.49      (~((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75) = vsomeType(VT!74))))),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[147, 126, 110])).
% 0.19/0.49  tff(149,plain,
% 0.19/0.49      (((~(vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))) | (~(vlookup(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)), VC!75) = vsomeType(VT!74)))) | (vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))))),
% 0.19/0.49      inference(tautology,[status(thm)],[])).
% 0.19/0.49  tff(150,plain,
% 0.19/0.49      (vapp(ve1app, ve2app) = vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app)))),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[149, 148])).
% 0.19/0.49  tff(151,plain,
% 0.19/0.49      (vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)),
% 0.19/0.49      inference(symmetry,[status(thm)],[150])).
% 0.19/0.49  tff(152,plain,
% 0.19/0.49      (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 0.19/0.49      inference(bind,[status(th)],[])).
% 0.19/0.49  tff(153,plain,
% 0.19/0.49      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.49      inference(quant_intro,[status(thm)],[152])).
% 0.19/0.49  tff(154,plain,
% 0.19/0.49      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(155,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 0.19/0.49  tff(156,plain,
% 0.19/0.49      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.49  tff(157,plain,(
% 0.19/0.49      ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.49      inference(skolemize,[status(sab)],[156])).
% 0.19/0.49  tff(158,plain,
% 0.19/0.49      (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[157, 153])).
% 0.19/0.49  tff(159,plain,
% 0.19/0.49      ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_66(VC!75, VT!74, vapp(ve1app, ve2app))) = vapp(ve1app, ve2app)))),
% 0.19/0.49      inference(quant_inst,[status(thm)],[])).
% 0.19/0.49  tff(160,plain,
% 0.19/0.49      ($false),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[159, 158, 151])).
% 0.19/0.49  % SZS output end Proof
%------------------------------------------------------------------------------