%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM139+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:01:07 AM UTC 2025
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM139+1 : TPTP v9.0.0. Released v6.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 12:26:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(tptp_fun_Vy_3_type, type, (
% 0.21/0.42 tptp_fun_Vy_3: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Vx_55_type, type, (
% 0.21/0.42 tptp_fun_Vx_55: $i)).
% 0.21/0.42 tff(vbind_type, type, (
% 0.21/0.42 vbind: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_VC_53_type, type, (
% 0.21/0.42 tptp_fun_VC_53: $i)).
% 0.21/0.42 tff(tptp_fun_VS_54_type, type, (
% 0.21/0.42 tptp_fun_VS_54: $i)).
% 0.21/0.42 tff(tptp_fun_VC_2_type, type, (
% 0.21/0.42 tptp_fun_VC_2: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_VTy_4_type, type, (
% 0.21/0.42 tptp_fun_VTy_4: ( $i * $i ) > $i)).
% 0.21/0.42 tff(vlookup_type, type, (
% 0.21/0.42 vlookup: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_VC_1_type, type, (
% 0.21/0.42 tptp_fun_VC_1: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_VTy_0_type, type, (
% 0.21/0.42 tptp_fun_VTy_0: ( $i * $i ) > $i)).
% 0.21/0.42 tff(vsomeType_type, type, (
% 0.21/0.42 vsomeType: $i > $i)).
% 0.21/0.42 tff(vtcheck_type, type, (
% 0.21/0.42 vtcheck: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_VT2_43_type, type, (
% 0.21/0.42 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(vabs_type, type, (
% 0.21/0.42 vabs: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(veabs_type, type, (
% 0.21/0.42 veabs: $i)).
% 0.21/0.42 tff(tptp_fun_VS1_51_type, type, (
% 0.21/0.42 tptp_fun_VS1_51: $i)).
% 0.21/0.42 tff(tptp_fun_Vy_52_type, type, (
% 0.21/0.42 tptp_fun_Vy_52: $i)).
% 0.21/0.42 tff(tptp_fun_VT_50_type, type, (
% 0.21/0.42 tptp_fun_VT_50: $i)).
% 0.21/0.42 tff(tptp_fun_Ve2_45_type, type, (
% 0.21/0.42 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_VT1_44_type, type, (
% 0.21/0.42 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Vx_46_type, type, (
% 0.21/0.42 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(varrow_type, type, (
% 0.21/0.42 varrow: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Vx_42_type, type, (
% 0.21/0.42 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(vvar_type, type, (
% 0.21/0.42 vvar: $i > $i)).
% 0.21/0.42 tff(tptp_fun_VS_47_type, type, (
% 0.21/0.42 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Ve2_48_type, type, (
% 0.21/0.42 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Ve1_49_type, type, (
% 0.21/0.42 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(vapp_type, type, (
% 0.21/0.42 vapp: ( $i * $i ) > $i)).
% 0.21/0.42 tff(vnoType_type, type, (
% 0.21/0.42 vnoType: $i)).
% 0.21/0.42 tff(vempty_type, type, (
% 0.21/0.42 vempty: $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 ((vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) <=> (vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.42 inference(commutativity,[status(thm)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 ((~(vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) <=> (~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.42 tff(3,assumption,(vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)), introduced(assumption)).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(7,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'')).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.42 tff(9,plain,(
% 0.21/0.42 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[11, 10, 3])).
% 0.21/0.43 tff(13,plain,(~(vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50)))) | (vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 ((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.43 tff(17,assumption,(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))), introduced(assumption)).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(21,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'')).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.43 tff(23,plain,(
% 0.21/0.43 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[22])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[25, 24, 17])).
% 0.21/0.43 tff(27,plain,(~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(VC!53, tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(VC!53, tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 ((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(VC!53, tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(VC!53, tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-abs-1'')).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.21/0.43 tff(37,plain,(
% 0.21/0.43 ~((~((~(Vx!55 = Vy!52)) & (vlookup(Vx!55, VC!53) = vnoType) & vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50))),
% 0.21/0.43 inference(skolemize,[status(sab)],[36])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 ((~(Vx!55 = Vy!52)) & (vlookup(Vx!55, VC!53) = vnoType) & vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.21/0.43 inference(or_elim,[status(thm)],[37])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.21/0.43 inference(and_elim,[status(thm)],[38])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (^[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)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (^[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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.44 tff(49,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'')).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.44 tff(52,plain,(
% 0.21/0.44 ![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)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[51])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[54, 41])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (((~![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))))))) | ((~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(VC!53, tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(VC!53, tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))))) <=> ((~![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(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(VC!53, tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(VC!53, tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 ((~![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))))))) | ((~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(VC!53, tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(VC!53, tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 ((~![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(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(VC!53, tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(VC!53, tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 ((~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(VC!53, tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(VC!53, tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[58, 55, 39])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 ((~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[59, 29])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[60, 16])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (vlookup(Vx!55, VC!53) = vnoType),
% 0.21/0.45 inference(and_elim,[status(thm)],[38])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (~(Vx!55 = Vy!52)),
% 0.21/0.45 inference(and_elim,[status(thm)],[38])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : refl(((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : rewrite(((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.45 inference(transitivity,[status(thm)],[70, 69])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[71, 68])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (^[VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite(((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))) <=> ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))), (((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))) <=> ((~(Vx = Vy)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))))), rewrite(((~(Vx = Vy)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))), (((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[74, 72])).
% 0.21/0.45 tff(76,axiom,(![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','lookup2')).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[77, 66])).
% 0.21/0.45 tff(79,plain,(
% 0.21/0.45 ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[78])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[79, 65])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | ((Vx!55 = Vy!52) | (vlookup(Vx!55, vbind(Vy!52, VS1!51, VC!53)) = vlookup(Vx!55, VC!53)))) <=> ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | (Vx!55 = Vy!52) | (vlookup(Vx!55, vbind(Vy!52, VS1!51, VC!53)) = vlookup(Vx!55, VC!53)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | ((Vx!55 = Vy!52) | (vlookup(Vx!55, vbind(Vy!52, VS1!51, VC!53)) = vlookup(Vx!55, VC!53)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | (Vx!55 = Vy!52) | (vlookup(Vx!55, vbind(Vy!52, VS1!51, VC!53)) = vlookup(Vx!55, VC!53))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (vlookup(Vx!55, vbind(Vy!52, VS1!51, VC!53)) = vlookup(Vx!55, VC!53)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[83, 80, 63])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : refl((~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : trans(monotonicity(rewrite(((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1)) <=> (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> (~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), rewrite((~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> (((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))), rewrite((((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), rewrite((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : rewrite((((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.45 tff(92,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-abs'')).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.21/0.45 tff(95,plain,(
% 0.21/0.45 ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[94])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))) | (~((~((~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) | (~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 (~((~((~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) | (~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 (((~((~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) | (~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))) | ((~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 ((~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.21/0.46 tff(102,assumption,(~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))), introduced(assumption)).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)),
% 0.21/0.46 inference(symmetry,[status(thm)],[104])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 ((~((~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 ((~((~(vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (~((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[107, 101])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))) | (tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (VS1!51 = tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.21/0.46 inference(symmetry,[status(thm)],[110])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))) | (tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 (tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[112, 108])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (Vy!52 = tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.21/0.46 inference(symmetry,[status(thm)],[113])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 (vbind(Vy!52, VS1!51, VC!53) = vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[114, 111])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 (vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53) = vbind(Vy!52, VS1!51, VC!53)),
% 0.21/0.46 inference(symmetry,[status(thm)],[115])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vlookup(Vx!55, vbind(Vy!52, VS1!51, VC!53))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 (vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vnoType),
% 0.21/0.46 inference(transitivity,[status(thm)],[117, 84, 62])).
% 0.21/0.46 tff(119,plain,
% 0.21/0.46 (((~(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))) | (tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 (tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[119, 108])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 (veabs = tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.21/0.46 inference(symmetry,[status(thm)],[120])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 (vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[121])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 (vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[122])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 (((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 (vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[124, 102])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 (vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[125, 123])).
% 0.21/0.46 tff(127,plain,
% 0.21/0.46 (vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 (vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[128])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 ((~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> (~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.46 tff(131,assumption,(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), introduced(assumption)).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 (vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)) = vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[114, 111, 131])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[132, 121])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[133])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.47 ((~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> (~vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[134])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[136, 102])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = VT!50),
% 0.21/0.47 inference(symmetry,[status(thm)],[137])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)) = vbind(Vx!55, VS!54, VC!53)),
% 0.21/0.47 inference(symmetry,[status(thm)],[131])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[139, 105, 138])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) <=> vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(symmetry,[status(thm)],[140])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 ((~vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)) <=> (~vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (~vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.21/0.47 inference(or_elim,[status(thm)],[37])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (~vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (^[VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : refl(((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[145])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (^[VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : rewrite((vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[148])).
% 0.21/0.47 tff(150,axiom,(![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-abs'')).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.21/0.47 tff(153,plain,(
% 0.21/0.47 ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[152])).
% 0.21/0.47 tff(154,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.21/0.47 tff(155,plain,
% 0.21/0.47 (((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | ((~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | ((~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 ((~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)), vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[158, 144])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 (~vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[159, 135])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : refl((vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[161])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) <=> (~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))), ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> (~(~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))))), rewrite((~(~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))) <=> ((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))), ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))), (((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)))), rewrite((((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))), (((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[163])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : rewrite((((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(167,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[166])).
% 0.21/0.47 tff(168,axiom,(![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-Context-Swap'')).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.47 tff(170,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.21/0.47 tff(171,plain,(
% 0.21/0.47 ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 0.21/0.47 inference(skolemize,[status(sab)],[170])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[172, 162])).
% 0.21/0.47 tff(174,plain,
% 0.21/0.47 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | ((Vx!55 = Vy!52) | vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!55 = Vy!52) | vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(175,plain,
% 0.21/0.47 ((vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (Vx!55 = Vy!52) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) <=> ((Vx!55 = Vy!52) | vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (Vx!55 = Vy!52) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | ((Vx!55 = Vy!52) | vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[175])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (Vx!55 = Vy!52) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!55 = Vy!52) | vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[176, 174])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (Vx!55 = Vy!52) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!55 = Vy!52) | vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 (vtcheck(vbind(Vy!52, VS1!51, vbind(Vx!55, VS!54, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[179, 173, 63])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 (~vtcheck(vbind(Vx!55, VS!54, vbind(Vy!52, VS1!51, VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[180, 160])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[181, 130])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[183])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) <=> (~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) <=> (~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))))), rewrite((~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))), rewrite((((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[185])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[188])).
% 0.21/0.48 tff(190,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-abs-IH'')).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.21/0.48 tff(193,plain,(
% 0.21/0.48 ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.21/0.48 inference(skolemize,[status(sab)],[192])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[194, 184])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~(vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vnoType)) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~(vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vnoType)) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~(vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vnoType)) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~(vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vnoType)) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~(vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vnoType)) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[198, 195])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (~(vlookup(Vx!55, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)) = vnoType)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[199, 182, 126])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[200, 118])).
% 0.21/0.48 tff(202,plain,(((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[202, 61])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 (((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 ((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 ((vsomeType(VS!54) = vnoType) <=> (vnoType = vsomeType(VS!54))),
% 0.21/0.48 inference(commutativity,[status(thm)],[])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 (^[VC: $i, Vy: $i, VTy: $i] : refl((vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[207])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(transitivity,[status(thm)],[211, 210])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 (^[VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : trans(monotonicity(trans(monotonicity(rewrite(((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))) <=> ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vsomeType(VTy)))), (((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy)))) <=> ((Vx = Vy) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vsomeType(VTy)))))), rewrite(((Vx = Vy) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vsomeType(VTy)))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)))), (((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy)))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> ![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[213])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(transitivity,[status(thm)],[214, 212])).
% 0.21/0.48 tff(216,axiom,(![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','lookup1')).
% 0.21/0.48 tff(217,plain,
% 0.21/0.48 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.21/0.48 tff(218,plain,
% 0.21/0.48 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[217, 209])).
% 0.21/0.48 tff(219,plain,(
% 0.21/0.48 ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(skolemize,[status(sab)],[218])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[219, 208])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 ((~![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))) | (vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(VS!54))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(VS!54)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.21/0.48 tff(223,plain,
% 0.21/0.48 ((vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType) <=> (vsomeType(VS!54) = vnoType)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[222])).
% 0.21/0.48 tff(224,plain,
% 0.21/0.48 ((vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType) <=> (vnoType = vsomeType(VS!54))),
% 0.21/0.48 inference(transitivity,[status(thm)],[223, 206])).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 ((vnoType = vsomeType(VS!54)) <=> (vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)),
% 0.21/0.48 inference(symmetry,[status(thm)],[224])).
% 0.21/0.48 tff(226,plain,
% 0.21/0.48 ((~(vnoType = vsomeType(VS!54))) <=> (~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[225])).
% 0.21/0.48 tff(227,plain,
% 0.21/0.48 (^[VTyp0: $i] : refl((~(vnoType = vsomeType(VTyp0))) <=> (~(vnoType = vsomeType(VTyp0))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(228,plain,
% 0.21/0.48 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[227])).
% 0.21/0.48 tff(229,plain,
% 0.21/0.48 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(230,axiom,(![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-noType-someType'')).
% 0.21/0.48 tff(231,plain,
% 0.21/0.48 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.21/0.48 tff(232,plain,(
% 0.21/0.48 ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[231])).
% 0.21/0.48 tff(233,plain,
% 0.21/0.48 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.21/0.48 tff(234,plain,
% 0.21/0.48 ((~![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))) | (~(vnoType = vsomeType(VS!54)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(235,plain,
% 0.21/0.48 (~(vnoType = vsomeType(VS!54))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.21/0.48 tff(236,plain,
% 0.21/0.48 (~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[235, 226])).
% 0.21/0.48 tff(237,plain,
% 0.21/0.48 (((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty))) | (vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(238,plain,
% 0.21/0.48 ((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.21/0.48 tff(239,plain,
% 0.21/0.48 (^[VVar0: $i, VCtx0: $i] : refl(((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))) <=> ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(240,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))) <=> ![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[239])).
% 0.21/0.48 tff(241,plain,
% 0.21/0.48 (^[VVar0: $i, VCtx0: $i] : rewrite((((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))) <=> ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(242,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i] : (((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))) <=> ![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[241])).
% 0.21/0.48 tff(243,plain,
% 0.21/0.48 (^[VVar0: $i, VCtx0: $i] : rewrite((((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))) <=> (((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(244,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i] : (((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0))))) <=> ![VVar0: $i, VCtx0: $i] : (((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[243])).
% 0.21/0.48 tff(245,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i] : (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))) <=> ![VVar0: $i, VCtx0: $i] : (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(246,plain,
% 0.21/0.48 (^[VVar0: $i, VCtx0: $i] : rewrite((?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC)))) <=> (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(247,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i] : (?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC)))) <=> ![VVar0: $i, VCtx0: $i] : (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[246])).
% 0.21/0.48 tff(248,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC)))) <=> ![VVar0: $i, VCtx0: $i] : (?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))))),
% 0.21/0.48 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.48 tff(249,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (((RESULT = vnoType) & (VCtx0 = vempty)) | (~(vlookup(VVar0, VCtx0) = RESULT)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))))),
% 0.21/0.48 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.48 tff(250,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (((RESULT = vnoType) & (VCtx0 = vempty)) | (~(vlookup(VVar0, VCtx0) = RESULT)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))) <=> ![VVar0: $i, VCtx0: $i] : (?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[249, 248])).
% 0.21/0.48 tff(251,plain,
% 0.21/0.48 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (((RESULT = vnoType) & (VCtx0 = vempty)) | (~(vlookup(VVar0, VCtx0) = RESULT)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))) <=> ![VVar0: $i, VCtx0: $i] : (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[250, 247])).
% 0.21/0.48 tff(252,plain,
% 0.21/0.48 (^[VVar0: $i, VCtx0: $i, RESULT: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) <=> (((RESULT = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))))), trans(quant_intro(proof_bind(^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : trans(monotonicity(rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)))), (((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))), (((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))))), (?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))), trans(der(?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) <=> ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))), elim_unused(?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))) <=> ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))), (?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) <=> ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))), (?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))), (((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))) <=> ((((RESULT = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC)))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))))), rewrite(((((RESULT = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC)))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))) <=> (((RESULT = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))), (((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))) <=> (((RESULT = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy)))))), (((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> ((vlookup(VVar0, VCtx0) = RESULT) => (((RESULT = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))))), rewrite(((vlookup(VVar0, VCtx0) = RESULT) => (((RESULT = vnoType) & (VCtx0 = vempty)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))) <=> (((RESULT = vnoType) & (VCtx0 = vempty)) | (~(vlookup(VVar0, VCtx0) = RESULT)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))), (((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> (((RESULT = vnoType) & (VCtx0 = vempty)) | (~(vlookup(VVar0, VCtx0) = RESULT)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(253,plain,
% 0.21/0.49 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : (((RESULT = vnoType) & (VCtx0 = vempty)) | (~(vlookup(VVar0, VCtx0) = RESULT)) | ?[VC: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ?[VTy: $i, Vy: $i, VC: $i] : ((RESULT = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[252])).
% 0.21/0.49 tff(254,plain,
% 0.21/0.49 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> ![VVar0: $i, VCtx0: $i] : (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[253, 251])).
% 0.21/0.49 tff(255,axiom,(![VVar0: $i, VCtx0: $i, RESULT: $i] : ((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''lookup-INV'')).
% 0.21/0.49 tff(256,plain,
% 0.21/0.49 (![VVar0: $i, VCtx0: $i] : (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.21/0.49 tff(257,plain,
% 0.21/0.49 (![VVar0: $i, VCtx0: $i] : (?[VC: $i, VTy: $i] : ((vlookup(VVar0, VCtx0) = vsomeType(VTy)) & (VCtx0 = vbind(VVar0, VTy, VC))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ?[VTy: $i, Vy: $i, VC: $i] : ((vlookup(VVar0, VCtx0) = vlookup(VVar0, VC)) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(VVar0 = Vy))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[256, 245])).
% 0.21/0.49 tff(258,plain,(
% 0.21/0.49 ![VVar0: $i, VCtx0: $i] : (((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[257])).
% 0.21/0.49 tff(259,plain,
% 0.21/0.49 (![VVar0: $i, VCtx0: $i] : (((vlookup(VVar0, VCtx0) = vnoType) & (VCtx0 = vempty)) | ((vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0))) & (VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))) | ((vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0))) & (VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0))) & (~(VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[258, 244])).
% 0.21/0.49 tff(260,plain,
% 0.21/0.49 (![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[259, 242])).
% 0.21/0.49 tff(261,plain,
% 0.21/0.49 (![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[260, 240])).
% 0.21/0.49 tff(262,plain,
% 0.21/0.49 (((~![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))) | ((~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty)))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) <=> ((~![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty)))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(263,plain,
% 0.21/0.49 ((~![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))) | ((~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty)))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(264,plain,
% 0.21/0.49 ((~![VVar0: $i, VCtx0: $i] : ((~((~(vlookup(VVar0, VCtx0) = vnoType)) | (~(VCtx0 = vempty)))) | (~((~(vlookup(VVar0, VCtx0) = vsomeType(tptp_fun_VTy_0(VCtx0, VVar0)))) | (~(VCtx0 = vbind(VVar0, tptp_fun_VTy_0(VCtx0, VVar0), tptp_fun_VC_1(VCtx0, VVar0)))))) | (~((~(vlookup(VVar0, VCtx0) = vlookup(VVar0, tptp_fun_VC_2(VCtx0, VVar0)))) | (~(VCtx0 = vbind(tptp_fun_Vy_3(VCtx0, VVar0), tptp_fun_VTy_4(VCtx0, VVar0), tptp_fun_VC_2(VCtx0, VVar0)))) | (VVar0 = tptp_fun_Vy_3(VCtx0, VVar0)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty)))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.21/0.49 tff(265,plain,
% 0.21/0.49 ((~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty)))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[264, 261])).
% 0.21/0.49 tff(266,plain,
% 0.21/0.49 ((~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, tptp_fun_VTy_0(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_1(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[265, 238])).
% 0.21/0.49 tff(267,plain,
% 0.21/0.49 (~((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[266, 205])).
% 0.21/0.49 tff(268,plain,
% 0.21/0.49 (((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(269,plain,
% 0.21/0.49 (~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.21/0.49 tff(270,plain,
% 0.21/0.49 (((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vlookup(Vx!55, tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(271,plain,
% 0.21/0.49 (vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[270, 267])).
% 0.21/0.49 tff(272,assumption,((~((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))), introduced(assumption)).
% 0.21/0.49 tff(273,plain,
% 0.21/0.49 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : refl((~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(274,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[273])).
% 0.21/0.49 tff(275,plain,
% 0.21/0.49 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : trans(monotonicity(rewrite(((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> ((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))), trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1)) <=> (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> (~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))), rewrite((~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> (((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))), rewrite((((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), ((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) & ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))), rewrite((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) & ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))), ((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(276,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[275])).
% 0.21/0.49 tff(277,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(278,plain,
% 0.21/0.49 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : rewrite((((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(279,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[278])).
% 0.21/0.49 tff(280,axiom,(![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-bind'')).
% 0.21/0.49 tff(281,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.21/0.49 tff(282,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[281, 277])).
% 0.21/0.49 tff(283,plain,(
% 0.21/0.49 ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[282])).
% 0.21/0.49 tff(284,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[283, 276])).
% 0.21/0.49 tff(285,plain,
% 0.21/0.49 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[284, 274])).
% 0.21/0.49 tff(286,plain,
% 0.21/0.49 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(287,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[286, 285, 272])).
% 0.21/0.49 tff(288,plain,(~((~((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(289,plain,
% 0.21/0.50 (((~((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | ((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(290,plain,
% 0.21/0.50 ((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.21/0.50 tff(291,plain,
% 0.21/0.50 ((~((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(292,plain,
% 0.21/0.50 ((~(vbind(Vx!55, VS!54, VC!53) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.21/0.50 tff(293,plain,
% 0.21/0.50 (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[292, 271])).
% 0.21/0.50 tff(294,plain,
% 0.21/0.50 (((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VC!53 = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(295,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[294, 293, 269])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------