%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM149+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:01:08 AM UTC 2025
% Result : Theorem 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : COM149+1 : TPTP v9.0.0. Released v6.4.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 12:26:46 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 tff(vsomeType_type, type, (
% 0.22/0.43 vsomeType: $i > $i)).
% 0.22/0.43 tff(tptp_fun_VT_51_type, type, (
% 0.22/0.43 tptp_fun_VT_51: $i)).
% 0.22/0.43 tff(vnoType_type, type, (
% 0.22/0.43 vnoType: $i)).
% 0.22/0.43 tff(vlookup_type, type, (
% 0.22/0.43 vlookup: ( $i * $i ) > $i)).
% 0.22/0.43 tff(vempty_type, type, (
% 0.22/0.43 vempty: $i)).
% 0.22/0.43 tff(tptp_fun_Vx_42_type, type, (
% 0.22/0.43 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(vvar_type, type, (
% 0.22/0.43 vvar: $i > $i)).
% 0.22/0.43 tff(tptp_fun_Vx_50_type, type, (
% 0.22/0.43 tptp_fun_Vx_50: $i)).
% 0.22/0.43 tff(vtcheck_type, type, (
% 0.22/0.43 vtcheck: ( $i * $i * $i ) > $o)).
% 0.22/0.43 tff(tptp_fun_VS_47_type, type, (
% 0.22/0.43 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_Ve2_48_type, type, (
% 0.22/0.43 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(varrow_type, type, (
% 0.22/0.43 varrow: ( $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_Ve1_49_type, type, (
% 0.22/0.43 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(vapp_type, type, (
% 0.22/0.43 vapp: ( $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_VT2_43_type, type, (
% 0.22/0.43 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_Ve2_45_type, type, (
% 0.22/0.43 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(vbind_type, type, (
% 0.22/0.43 vbind: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_VT1_44_type, type, (
% 0.22/0.43 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_Vx_46_type, type, (
% 0.22/0.43 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(vabs_type, type, (
% 0.22/0.43 vabs: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(vsomeExp_type, type, (
% 0.22/0.43 vsomeExp: $i > $i)).
% 0.22/0.43 tff(vreduce_type, type, (
% 0.22/0.43 vreduce: $i > $i)).
% 0.22/0.43 tff(visValue_type, type, (
% 0.22/0.43 visValue: $i > $o)).
% 0.22/0.43 tff(1,assumption,(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)))), introduced(assumption)).
% 0.22/0.43 tff(2,plain,
% 0.22/0.43 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(3,plain,
% 0.22/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.43 tff(4,plain,
% 0.22/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(5,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 0.22/0.43 tff(6,plain,
% 0.22/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.22/0.43 tff(7,plain,(
% 0.22/0.43 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[6])).
% 0.22/0.43 tff(8,plain,
% 0.22/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.43 tff(9,plain,
% 0.22/0.43 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(10,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.22/0.44 tff(11,plain,(~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(12,plain,
% 0.22/0.44 (((~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), varrow(tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)), VT!51))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)), tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50))))) | (vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(13,plain,
% 0.22/0.44 ((~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), varrow(tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)), VT!51))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)), tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.22/0.44 tff(14,assumption,(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)))), introduced(assumption)).
% 0.22/0.44 tff(15,plain,
% 0.22/0.44 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(18,axiom,(![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-abs'')).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.44 tff(20,plain,(
% 0.22/0.44 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[19])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.22/0.44 tff(22,plain,
% 0.22/0.44 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(23,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.22/0.44 tff(24,plain,(~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (((~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))) | (~(VT!51 = varrow(tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), vempty), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(26,plain,
% 0.22/0.44 ((~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))) | (~(VT!51 = varrow(tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), vempty), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 (((vtcheck(vempty, vvar(Vx!50), VT!51) & (~visValue(vvar(Vx!50)))) & ![Veout: $i] : (~(vreduce(vvar(Vx!50)) = vsomeExp(Veout)))) <=> (vtcheck(vempty, vvar(Vx!50), VT!51) & (~visValue(vvar(Vx!50))) & ![Veout: $i] : (~(vreduce(vvar(Vx!50)) = vsomeExp(Veout))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(28,plain,
% 0.22/0.44 ((~![VT: $i, Vx: $i] : ((~(vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx))))) | ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout)))) <=> (~![VT: $i, Vx: $i] : ((~(vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx))))) | ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(29,plain,
% 0.22/0.44 ((~![VT: $i, Vx: $i] : ((vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx)))) => ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout)))) <=> (~![VT: $i, Vx: $i] : ((~(vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx))))) | ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(30,axiom,(~![VT: $i, Vx: $i] : ((vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx)))) => ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Progress-T-var'')).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (~![VT: $i, Vx: $i] : ((~(vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx))))) | ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (~![VT: $i, Vx: $i] : ((~(vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx))))) | ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 (~![VT: $i, Vx: $i] : ((~(vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx))))) | ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 (~![VT: $i, Vx: $i] : ((~(vtcheck(vempty, vvar(Vx), VT) & (~visValue(vvar(Vx))))) | ?[Veout: $i] : (vreduce(vvar(Vx)) = vsomeExp(Veout)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.22/0.44 tff(35,plain,
% 0.22/0.44 (vtcheck(vempty, vvar(Vx!50), VT!51) & (~visValue(vvar(Vx!50))) & ![Veout: $i] : (~(vreduce(vvar(Vx!50)) = vsomeExp(Veout)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.22/0.44 tff(36,plain,
% 0.22/0.44 (vtcheck(vempty, vvar(Vx!50), VT!51)),
% 0.22/0.44 inference(and_elim,[status(thm)],[35])).
% 0.22/0.44 tff(37,plain,
% 0.22/0.44 (^[Ve: $i, VT: $i, VC: $i] : refl(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(38,plain,
% 0.22/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.22/0.44 tff(39,plain,
% 0.22/0.44 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(rewrite(((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) <=> (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT)))))), rewrite(((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) <=> (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))))), rewrite(((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) <=> (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))), rewrite(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(40,plain,
% 0.22/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.22/0.44 tff(41,plain,
% 0.22/0.44 (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(42,plain,
% 0.22/0.44 (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[41])).
% 0.22/0.44 tff(43,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(44,plain,
% 0.22/0.44 (^[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)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(45,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.45 tff(46,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'')).
% 0.22/0.45 tff(47,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.22/0.45 tff(48,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.22/0.45 tff(49,plain,(
% 0.22/0.45 ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[48])).
% 0.22/0.45 tff(50,plain,
% 0.22/0.45 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.22/0.45 tff(51,plain,
% 0.22/0.45 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[51, 38])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(vempty, vvar(Vx!50), VT!51)) | (~((~(vvar(Vx!50) = vvar(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51))))) | (~((~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))) | (~(VT!51 = varrow(tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), vempty), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50)))))) | (~((~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), varrow(tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)), VT!51))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)), tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(vempty, vvar(Vx!50), VT!51)) | (~((~(vvar(Vx!50) = vvar(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51))))) | (~((~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))) | (~(VT!51 = varrow(tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), vempty), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50)))))) | (~((~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), varrow(tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)), VT!51))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)), tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(vempty, vvar(Vx!50), VT!51)) | (~((~(vvar(Vx!50) = vvar(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51))))) | (~((~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))) | (~(VT!51 = varrow(tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), vempty), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50)))))) | (~((~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), varrow(tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)), VT!51))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)), tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(vempty, vvar(Vx!50), VT!51)) | (~((~(vvar(Vx!50) = vvar(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51))))) | (~((~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))) | (~(VT!51 = varrow(tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), vempty), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50)))))) | (~((~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), varrow(tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)), VT!51))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)), tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.22/0.46 tff(56,plain,
% 0.22/0.46 ((~((~(vvar(Vx!50) = vvar(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51))))) | (~((~(vvar(Vx!50) = vabs(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50))))) | (~(VT!51 = varrow(tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT1_44(vempty, VT!51, vvar(Vx!50)), vempty), tptp_fun_Ve2_45(vempty, VT!51, vvar(Vx!50)), tptp_fun_VT2_43(vempty, VT!51, vvar(Vx!50)))))) | (~((~(vvar(Vx!50) = vapp(tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!51, vvar(Vx!50)), varrow(tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50)), VT!51))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!51, vvar(Vx!50)), tptp_fun_VS_47(vempty, VT!51, vvar(Vx!50))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[55, 52, 36])).
% 0.22/0.46 tff(57,plain,
% 0.22/0.46 (~((~(vvar(Vx!50) = vvar(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[56, 26, 13])).
% 0.22/0.46 tff(58,plain,
% 0.22/0.46 (((~(vvar(Vx!50) = vvar(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51)))) | (vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 (vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vsomeType(VT!51)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 (^[Vx: $i] : refl((vlookup(Vx, vempty) = vnoType) <=> (vlookup(Vx, vempty) = vnoType))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(61,plain,
% 0.22/0.46 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.46 inference(quant_intro,[status(thm)],[60])).
% 0.22/0.46 tff(62,plain,
% 0.22/0.46 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(63,plain,
% 0.22/0.46 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (vlookup(Vx, vempty) = vnoType) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty)))) <=> ![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty)))) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.46 inference(transitivity,[status(thm)],[64, 63])).
% 0.22/0.46 tff(66,plain,
% 0.22/0.46 (^[Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : trans(monotonicity(rewrite(((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType)) <=> ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vnoType))), ((((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> (((VVar0 = Vx) & (VCtx0 = vempty)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vnoType))))), rewrite((((VVar0 = Vx) & (VCtx0 = vempty)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vnoType))) <=> ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty))))), ((((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(67,plain,
% 0.22/0.47 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> ![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[66])).
% 0.22/0.47 tff(68,plain,
% 0.22/0.47 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.47 inference(transitivity,[status(thm)],[67, 65])).
% 0.22/0.47 tff(69,axiom,(![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','lookup0')).
% 0.22/0.47 tff(70,plain,
% 0.22/0.47 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.47 tff(71,plain,
% 0.22/0.47 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[70, 62])).
% 0.22/0.47 tff(72,plain,(
% 0.22/0.47 ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.47 inference(skolemize,[status(sab)],[71])).
% 0.22/0.47 tff(73,plain,
% 0.22/0.47 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[72, 61])).
% 0.22/0.47 tff(74,plain,
% 0.22/0.47 ((~![Vx: $i] : (vlookup(Vx, vempty) = vnoType)) | (vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vnoType)),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(75,plain,
% 0.22/0.47 (vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty) = vnoType),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.22/0.47 tff(76,plain,
% 0.22/0.47 (vnoType = vlookup(tptp_fun_Vx_42(vempty, VT!51, vvar(Vx!50)), vempty)),
% 0.22/0.47 inference(symmetry,[status(thm)],[75])).
% 0.22/0.47 tff(77,plain,
% 0.22/0.47 (vnoType = vsomeType(VT!51)),
% 0.22/0.47 inference(transitivity,[status(thm)],[76, 59])).
% 0.22/0.47 tff(78,plain,
% 0.22/0.47 (^[VTyp0: $i] : refl((~(vnoType = vsomeType(VTyp0))) <=> (~(vnoType = vsomeType(VTyp0))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(79,plain,
% 0.22/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[78])).
% 0.22/0.47 tff(80,plain,
% 0.22/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(81,axiom,(![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-noType-someType'')).
% 0.22/0.47 tff(82,plain,
% 0.22/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.47 tff(83,plain,(
% 0.22/0.47 ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.22/0.47 inference(skolemize,[status(sab)],[82])).
% 0.22/0.47 tff(84,plain,
% 0.22/0.47 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.22/0.47 tff(85,plain,
% 0.22/0.47 ((~![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))) | (~(vnoType = vsomeType(VT!51)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(86,plain,
% 0.22/0.47 (~(vnoType = vsomeType(VT!51))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.22/0.47 tff(87,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[86, 77])).
% 0.22/0.47 % SZS output end Proof
% 0.22/0.47 % E exiting
%------------------------------------------------------------------------------