%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM123+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:01:05 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM123+1 : TPTP v9.0.0. Released v6.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 12:24:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(vabs_type, type, (
% 0.19/0.43 vabs: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(veabs_type, type, (
% 0.19/0.43 veabs: $i)).
% 0.19/0.43 tff(tptp_fun_VS1_51_type, type, (
% 0.19/0.43 tptp_fun_VS1_51: $i)).
% 0.19/0.43 tff(tptp_fun_Vy_52_type, type, (
% 0.19/0.43 tptp_fun_Vy_52: $i)).
% 0.19/0.43 tff(vvar_type, type, (
% 0.19/0.43 vvar: $i > $i)).
% 0.19/0.43 tff(tptp_fun_Vx_42_type, type, (
% 0.19/0.43 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VT_50_type, type, (
% 0.19/0.43 tptp_fun_VT_50: $i)).
% 0.19/0.43 tff(tptp_fun_VC_53_type, type, (
% 0.19/0.43 tptp_fun_VC_53: $i)).
% 0.19/0.43 tff(vsomeType_type, type, (
% 0.19/0.43 vsomeType: $i > $i)).
% 0.19/0.43 tff(vlookup_type, type, (
% 0.19/0.43 vlookup: ( $i * $i ) > $i)).
% 0.19/0.43 tff(vtcheck_type, type, (
% 0.19/0.43 vtcheck: ( $i * $i * $i ) > $o)).
% 0.19/0.43 tff(tptp_fun_VS_47_type, type, (
% 0.19/0.43 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Ve2_48_type, type, (
% 0.19/0.43 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(varrow_type, type, (
% 0.19/0.43 varrow: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Ve1_49_type, type, (
% 0.19/0.43 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(vapp_type, type, (
% 0.19/0.43 vapp: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VT2_43_type, type, (
% 0.19/0.43 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Ve2_45_type, type, (
% 0.19/0.43 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(vbind_type, type, (
% 0.19/0.43 vbind: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VT1_44_type, type, (
% 0.19/0.43 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Vx_46_type, type, (
% 0.19/0.43 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VS_54_type, type, (
% 0.19/0.43 tptp_fun_VS_54: $i)).
% 0.19/0.43 tff(tptp_fun_Vx_55_type, type, (
% 0.19/0.43 tptp_fun_Vx_55: $i)).
% 0.19/0.43 tff(tptp_fun_VC_1_type, type, (
% 0.19/0.43 tptp_fun_VC_1: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VTy_0_type, type, (
% 0.19/0.43 tptp_fun_VTy_0: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_Vy_3_type, type, (
% 0.19/0.43 tptp_fun_Vy_3: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VC_2_type, type, (
% 0.19/0.43 tptp_fun_VC_2: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_VTy_4_type, type, (
% 0.19/0.43 tptp_fun_VTy_4: ( $i * $i ) > $i)).
% 0.19/0.43 tff(vempty_type, type, (
% 0.19/0.43 vempty: $i)).
% 0.19/0.43 tff(vnoType_type, type, (
% 0.19/0.43 vnoType: $i)).
% 0.19/0.43 tff(visFreeVar_type, type, (
% 0.19/0.43 visFreeVar: ( $i * $i ) > $o)).
% 0.19/0.43 tff(1,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)).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(5,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-abs-app'')).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.43 tff(7,plain,(
% 0.19/0.43 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[6])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.43 tff(11,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,[]))).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (((~(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))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((~(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))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (^[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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.44 tff(21,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/sandbox2/benchmark/Axioms/COM001+0.ax',''EQ-abs'')).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.44 tff(24,plain,(
% 0.19/0.44 ![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))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[23])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((~![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))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (~((~((~(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)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (((~((~(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)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 ((~(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))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.44 tff(31,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)).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (((~(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))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (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)),
% 0.19/0.44 inference(symmetry,[status(thm)],[33])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((~((~(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))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((~((~(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))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (~((~(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)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[36, 30])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (((~(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)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (veabs = tptp_fun_Ve2_45(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.19/0.44 inference(symmetry,[status(thm)],[39])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(symmetry,[status(thm)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (((~(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)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[43, 31])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[44, 42])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (((~(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)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[46, 37])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (VS1!51 = tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.19/0.44 inference(symmetry,[status(thm)],[47])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (((~(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)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[49, 37])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (Vy!52 = tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.19/0.44 inference(symmetry,[status(thm)],[50])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (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)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[51, 48])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (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)),
% 0.19/0.44 inference(symmetry,[status(thm)],[52])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (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))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (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)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (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)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[55])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 ((~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))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 ((vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) <=> (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)) = vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))))),
% 0.19/0.45 inference(commutativity,[status(thm)],[])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 ((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)) = vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))) <=> (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[58])).
% 0.19/0.45 tff(60,assumption,(~((~(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)))), introduced(assumption)).
% 0.19/0.45 tff(61,assumption,(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))), introduced(assumption)).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 ((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))) <=> (vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (((~(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)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (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))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[64, 60])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (((~(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)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[67, 60])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (((~(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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 ((~(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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.45 tff(71,assumption,((~((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))), introduced(assumption)).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (^[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)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (![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))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (^[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))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (![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))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.45 tff(79,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/sandbox2/benchmark/Axioms/COM001+0.ax',''EQ-bind'')).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.45 tff(82,plain,(
% 0.19/0.45 ![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))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[81])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![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))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (![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))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (((~![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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))) <=> ((~![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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 ((~((~((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) <=> (~((~((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 (((~![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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))) <=> ((~![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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (((~![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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))) <=> ((~![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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 ((~![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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = vbind(tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55), tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[90, 84, 71])).
% 0.19/0.46 tff(92,plain,(~((~((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (((~((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(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, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))) | ((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 ((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 ((~((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 ((~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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))) | (~(vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (~(vbind(Vx!55, VS!54, vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))) = 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)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[96, 70])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[97, 66])).
% 0.19/0.46 tff(99,plain,(((~(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))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[99, 60])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (((~(vlookup(Vx!55, VC!53) = vlookup(Vx!55, tptp_fun_VC_2(VC!53, Vx!55)))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(VC!53, Vx!55))) | (VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 ((~(vlookup(Vx!55, VC!53) = vlookup(Vx!55, tptp_fun_VC_2(VC!53, Vx!55)))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(VC!53, Vx!55))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & 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)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & 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)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(105,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs)))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak-FreeVar-abs-1'')).
% 0.19/0.46 tff(106,plain,
% 0.19/0.46 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[106, 103])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.19/0.47 tff(110,plain,(
% 0.19/0.47 ~((~((~(Vx!55 = Vy!52)) & (~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) & 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))),
% 0.19/0.47 inference(skolemize,[status(sab)],[109])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (~vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.19/0.47 inference(or_elim,[status(thm)],[110])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 ((~(Vx!55 = Vy!52)) & (~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) & vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.19/0.47 inference(or_elim,[status(thm)],[110])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.19/0.47 inference(and_elim,[status(thm)],[112])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))) <=> (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT)) <=> (~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) <=> (~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))))))), rewrite((~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> (((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)))), rewrite((((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : rewrite((((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT)) => vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT)) => vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.47 tff(121,axiom,(![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT)) => vtcheck(vbind(Vx, VS, VC), Ve, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak'')).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.19/0.47 tff(124,plain,(
% 0.19/0.47 ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.19/0.47 inference(skolemize,[status(sab)],[123])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~(vlookup(Vx!55, VC!53) = vnoType)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~(vlookup(Vx!55, VC!53) = vnoType)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 ((vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(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) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~(vlookup(Vx!55, VC!53) = vnoType)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~(vlookup(Vx!55, VC!53) = vnoType))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~(vlookup(Vx!55, VC!53) = vnoType)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~(vlookup(Vx!55, VC!53) = vnoType)) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, Ve, VT)))) | vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50) | (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) | (~(vlookup(Vx!55, VC!53) = vnoType))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (~(vlookup(Vx!55, VC!53) = vnoType)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[132, 126, 113, 111])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (((~(vlookup(Vx!55, VC!53) = vnoType)) | (~(VC!53 = vempty))) | (vlookup(Vx!55, VC!53) = vnoType)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 ((~(vlookup(Vx!55, VC!53) = vnoType)) | (~(VC!53 = vempty))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[146, 145])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[147, 144])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[150, 148])).
% 0.19/0.47 tff(152,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/sandbox2/benchmark/Axioms/COM001+0.ax',''lookup-INV'')).
% 0.19/0.48 tff(153,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.48 tff(154,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[153, 142])).
% 0.19/0.48 tff(155,plain,(
% 0.19/0.48 ![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)))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[154])).
% 0.19/0.48 tff(156,plain,
% 0.19/0.48 (![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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[155, 141])).
% 0.19/0.48 tff(157,plain,
% 0.19/0.48 (![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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[156, 139])).
% 0.19/0.48 tff(158,plain,
% 0.19/0.48 (![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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[157, 137])).
% 0.19/0.48 tff(159,plain,
% 0.19/0.48 (((~![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)))))) | ((~((~(vlookup(Vx!55, VC!53) = vnoType)) | (~(VC!53 = vempty)))) | (~((~(vlookup(Vx!55, VC!53) = vsomeType(tptp_fun_VTy_0(VC!53, Vx!55)))) | (~(VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))))) | (~((~(vlookup(Vx!55, VC!53) = vlookup(Vx!55, tptp_fun_VC_2(VC!53, Vx!55)))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(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, VC!53) = vnoType)) | (~(VC!53 = vempty)))) | (~((~(vlookup(Vx!55, VC!53) = vsomeType(tptp_fun_VTy_0(VC!53, Vx!55)))) | (~(VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))))) | (~((~(vlookup(Vx!55, VC!53) = vlookup(Vx!55, tptp_fun_VC_2(VC!53, Vx!55)))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(VC!53, Vx!55)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(160,plain,
% 0.19/0.48 ((~![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)))))) | ((~((~(vlookup(Vx!55, VC!53) = vnoType)) | (~(VC!53 = vempty)))) | (~((~(vlookup(Vx!55, VC!53) = vsomeType(tptp_fun_VTy_0(VC!53, Vx!55)))) | (~(VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))))) | (~((~(vlookup(Vx!55, VC!53) = vlookup(Vx!55, tptp_fun_VC_2(VC!53, Vx!55)))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(VC!53, Vx!55)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(161,plain,
% 0.19/0.48 ((~![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)))))) | (~((~(vlookup(Vx!55, VC!53) = vnoType)) | (~(VC!53 = vempty)))) | (~((~(vlookup(Vx!55, VC!53) = vsomeType(tptp_fun_VTy_0(VC!53, Vx!55)))) | (~(VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))))) | (~((~(vlookup(Vx!55, VC!53) = vlookup(Vx!55, tptp_fun_VC_2(VC!53, Vx!55)))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(VC!53, Vx!55))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.48 tff(162,plain,
% 0.19/0.48 ((~((~(vlookup(Vx!55, VC!53) = vsomeType(tptp_fun_VTy_0(VC!53, Vx!55)))) | (~(VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))))) | (~((~(vlookup(Vx!55, VC!53) = vlookup(Vx!55, tptp_fun_VC_2(VC!53, Vx!55)))) | (~(VC!53 = vbind(tptp_fun_Vy_3(VC!53, Vx!55), tptp_fun_VTy_4(VC!53, Vx!55), tptp_fun_VC_2(VC!53, Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(VC!53, Vx!55))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[161, 158, 135])).
% 0.19/0.48 tff(163,plain,
% 0.19/0.48 (~((~(vlookup(Vx!55, VC!53) = vsomeType(tptp_fun_VTy_0(VC!53, Vx!55)))) | (~(VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[162, 102])).
% 0.19/0.48 tff(164,plain,
% 0.19/0.48 (((~(vlookup(Vx!55, VC!53) = vsomeType(tptp_fun_VTy_0(VC!53, Vx!55)))) | (~(VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))))) | (VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(165,plain,
% 0.19/0.48 (VC!53 = vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.19/0.48 tff(166,plain,
% 0.19/0.48 (vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = VC!53),
% 0.19/0.48 inference(symmetry,[status(thm)],[165])).
% 0.19/0.48 tff(167,plain,
% 0.19/0.48 (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = vbind(Vx!55, VS!54, VC!53)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[166])).
% 0.19/0.48 tff(168,plain,
% 0.19/0.48 (vbind(Vx!55, VS!54, VC!53) = vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))),
% 0.19/0.48 inference(symmetry,[status(thm)],[167])).
% 0.19/0.48 tff(169,plain,
% 0.19/0.48 (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)) = vbind(Vx!55, VS!54, VC!53)),
% 0.19/0.48 inference(symmetry,[status(thm)],[65])).
% 0.19/0.48 tff(170,plain,
% 0.19/0.48 (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)) = vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[169, 168])).
% 0.19/0.48 tff(171,plain,
% 0.19/0.48 (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[170, 59])).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 (((~![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))))))) | (~((~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))))) <=> ((~![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))))))) | (~((~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(173,plain,
% 0.19/0.48 ((~((~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(174,plain,
% 0.19/0.48 (((~![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, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))) <=> ((~![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))))))) | (~((~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[173])).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 (((~![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, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))) <=> ((~![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))))))) | (~((~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[174, 172])).
% 0.19/0.49 tff(176,plain,
% 0.19/0.49 ((~![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, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~((vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(177,plain,
% 0.19/0.49 ((~![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))))))) | (~((~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.49 tff(178,plain,
% 0.19/0.49 (~((~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[177, 84])).
% 0.19/0.49 tff(179,plain,
% 0.19/0.49 (((~((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))) | (~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))))))) | ((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(180,plain,
% 0.19/0.49 ((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.19/0.49 tff(181,plain,
% 0.19/0.49 (((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))) | (Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(182,plain,
% 0.19/0.49 ((~(Vx!55 = tptp_fun_Vy_3(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[181, 68])).
% 0.19/0.49 tff(183,plain,
% 0.19/0.49 ((~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(184,plain,
% 0.19/0.49 ((~((~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55)) = tptp_fun_VC_2(vbind(Vx!55, VS!54, VC!53), Vx!55))) | (~(VS!54 = tptp_fun_VTy_4(vbind(Vx!55, VS!54, VC!53), Vx!55))))))) | (~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.19/0.49 tff(185,plain,
% 0.19/0.49 (~(vbind(Vx!55, VS!54, vbind(Vx!55, tptp_fun_VTy_0(VC!53, Vx!55), tptp_fun_VC_1(VC!53, Vx!55))) = 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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[184, 180])).
% 0.19/0.49 tff(186,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[185, 171])).
% 0.19/0.49 tff(187,plain,((~(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))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(188,plain,
% 0.19/0.49 ((vsomeType(VS!54) = vnoType) <=> (vnoType = vsomeType(VS!54))),
% 0.19/0.49 inference(commutativity,[status(thm)],[])).
% 0.19/0.49 tff(189,plain,
% 0.19/0.49 (^[VC: $i, Vy: $i, VTy: $i] : refl((vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(190,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[189])).
% 0.19/0.49 tff(191,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(192,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.49 tff(193,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.49 tff(194,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(transitivity,[status(thm)],[193, 192])).
% 0.19/0.49 tff(195,plain,
% 0.19/0.49 (^[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)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(196,plain,
% 0.19/0.49 (![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)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[195])).
% 0.19/0.49 tff(197,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(transitivity,[status(thm)],[196, 194])).
% 0.19/0.49 tff(198,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/sandbox2/benchmark/Axioms/COM001+0.ax','lookup1')).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.49 tff(200,plain,
% 0.19/0.49 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[199, 191])).
% 0.19/0.49 tff(201,plain,(
% 0.19/0.49 ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.19/0.49 inference(skolemize,[status(sab)],[200])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[201, 190])).
% 0.19/0.49 tff(203,plain,
% 0.19/0.49 ((~![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))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 (vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vsomeType(VS!54)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.19/0.49 tff(205,plain,
% 0.19/0.49 ((vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType) <=> (vsomeType(VS!54) = vnoType)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[204])).
% 0.19/0.49 tff(206,plain,
% 0.19/0.49 ((vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType) <=> (vnoType = vsomeType(VS!54))),
% 0.19/0.49 inference(transitivity,[status(thm)],[205, 188])).
% 0.19/0.49 tff(207,plain,
% 0.19/0.49 ((vnoType = vsomeType(VS!54)) <=> (vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)),
% 0.19/0.49 inference(symmetry,[status(thm)],[206])).
% 0.19/0.49 tff(208,plain,
% 0.19/0.49 ((~(vnoType = vsomeType(VS!54))) <=> (~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[207])).
% 0.19/0.49 tff(209,plain,
% 0.19/0.49 (^[VTyp0: $i] : refl((~(vnoType = vsomeType(VTyp0))) <=> (~(vnoType = vsomeType(VTyp0))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[209])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(212,axiom,(![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-noType-someType'')).
% 0.19/0.49 tff(213,plain,
% 0.19/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.19/0.49 tff(214,plain,(
% 0.19/0.49 ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[213])).
% 0.19/0.49 tff(215,plain,
% 0.19/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.19/0.49 tff(216,plain,
% 0.19/0.49 ((~![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))) | (~(vnoType = vsomeType(VS!54)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 (~(vnoType = vsomeType(VS!54))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.19/0.49 tff(218,plain,
% 0.19/0.49 (~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[217, 208])).
% 0.19/0.49 tff(219,plain,
% 0.19/0.49 (((~(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)) = vnoType)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(220,plain,
% 0.19/0.49 ((~(vlookup(Vx!55, vbind(Vx!55, VS!54, VC!53)) = vnoType)) | (~(vbind(Vx!55, VS!54, VC!53) = vempty))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.19/0.49 tff(221,plain,
% 0.19/0.49 (((~![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)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(222,plain,
% 0.19/0.50 ((~![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)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(223,plain,
% 0.19/0.50 ((~![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))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.50 tff(224,plain,
% 0.19/0.50 ((~((~(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))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[223, 158])).
% 0.19/0.50 tff(225,plain,
% 0.19/0.50 ((~((~(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))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[224, 220])).
% 0.19/0.50 tff(226,plain,
% 0.19/0.50 (~((~(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)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[225, 187])).
% 0.19/0.50 tff(227,plain,
% 0.19/0.50 (((~(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)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(228,plain,
% 0.19/0.50 (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))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.19/0.50 tff(229,plain,
% 0.19/0.50 (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)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[51, 48, 228])).
% 0.19/0.50 tff(230,plain,
% 0.19/0.50 (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)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[229, 40])).
% 0.19/0.50 tff(231,plain,
% 0.19/0.50 (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)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[230])).
% 0.19/0.50 tff(232,plain,
% 0.19/0.50 ((~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))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[231])).
% 0.19/0.50 tff(233,plain,
% 0.19/0.50 (((~(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))))) | (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))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(234,plain,
% 0.19/0.50 (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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[233, 31])).
% 0.19/0.50 tff(235,plain,
% 0.19/0.50 (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))) = VT!50),
% 0.19/0.50 inference(symmetry,[status(thm)],[234])).
% 0.19/0.50 tff(236,plain,
% 0.19/0.50 (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)),
% 0.19/0.50 inference(symmetry,[status(thm)],[228])).
% 0.19/0.50 tff(237,plain,
% 0.19/0.50 (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)))) <=> vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[236, 34, 235])).
% 0.19/0.50 tff(238,plain,
% 0.19/0.50 (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))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[237])).
% 0.19/0.50 tff(239,plain,
% 0.19/0.50 ((~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)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[238])).
% 0.19/0.50 tff(240,plain,
% 0.19/0.50 (~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))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[111, 239])).
% 0.19/0.50 tff(241,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(242,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[241])).
% 0.19/0.50 tff(243,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(244,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(245,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[244])).
% 0.19/0.50 tff(246,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/sandbox2/benchmark/Axioms/COM001+0.ax',''T-abs'')).
% 0.19/0.50 tff(247,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.19/0.50 tff(248,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.19/0.50 tff(249,plain,(
% 0.19/0.50 ![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)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[248])).
% 0.19/0.50 tff(250,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.19/0.50 tff(251,plain,
% 0.19/0.50 (((~![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)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(252,plain,
% 0.19/0.50 ((~![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)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(253,plain,
% 0.19/0.51 ((~![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))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.19/0.51 tff(254,plain,
% 0.19/0.51 ((~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))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[253, 250])).
% 0.19/0.51 tff(255,plain,
% 0.19/0.51 (~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)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[254, 240])).
% 0.19/0.51 tff(256,plain,
% 0.19/0.51 (~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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[255, 232])).
% 0.19/0.51 tff(257,plain,
% 0.19/0.51 (~(Vx!55 = Vy!52)),
% 0.19/0.51 inference(and_elim,[status(thm)],[112])).
% 0.19/0.51 tff(258,plain,
% 0.19/0.51 (^[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))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(259,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[258])).
% 0.19/0.51 tff(260,plain,
% 0.19/0.51 (^[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)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(261,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[260])).
% 0.19/0.51 tff(262,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(263,plain,
% 0.19/0.51 (^[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)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(264,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[263])).
% 0.19/0.51 tff(265,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/sandbox2/benchmark/Axioms/COM001+0.ax',''T-Context-Swap'')).
% 0.19/0.51 tff(266,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.19/0.51 tff(267,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.19/0.51 tff(268,plain,(
% 0.19/0.51 ![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))),
% 0.19/0.51 inference(skolemize,[status(sab)],[267])).
% 0.19/0.51 tff(269,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.19/0.51 tff(270,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[269, 259])).
% 0.19/0.51 tff(271,plain,
% 0.19/0.51 (((~![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)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(272,plain,
% 0.19/0.51 ((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)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(273,plain,
% 0.19/0.51 (((~![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))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[272])).
% 0.19/0.51 tff(274,plain,
% 0.19/0.51 (((~![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)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[273, 271])).
% 0.19/0.51 tff(275,plain,
% 0.19/0.51 ((~![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)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(276,plain,
% 0.19/0.51 ((~![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))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.51 tff(277,plain,
% 0.19/0.51 (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))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[276, 270, 257])).
% 0.19/0.51 tff(278,plain,
% 0.19/0.51 (~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)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[277, 256])).
% 0.19/0.51 tff(279,plain,
% 0.19/0.51 (~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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[278, 57])).
% 0.19/0.51 tff(280,plain,
% 0.19/0.51 (^[VT: $i, Vx: $i, Vv: $i, Ve: $i] : refl((~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))) <=> (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(281,plain,
% 0.19/0.51 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[280])).
% 0.19/0.51 tff(282,plain,
% 0.19/0.51 (^[VT: $i, Vx: $i, Vv: $i, Ve: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vv)) & visFreeVar(Vv, Ve)) <=> (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))), ((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> (~(~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))), rewrite((~(~((Vx = Vv) | (~visFreeVar(Vv, Ve))))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve)))), ((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve))))), (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) <=> (((Vx = Vv) | (~visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))))), rewrite((((Vx = Vv) | (~visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))), (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) <=> ((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve))))), rewrite(((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))) <=> ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))), ((((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))))), rewrite((((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve)))))) <=> (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))), ((((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(283,plain,
% 0.19/0.51 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[282])).
% 0.19/0.51 tff(284,plain,
% 0.19/0.51 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(285,plain,
% 0.19/0.51 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.51 tff(286,plain,
% 0.19/0.51 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.51 tff(287,plain,
% 0.19/0.51 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[286, 285])).
% 0.19/0.51 tff(288,plain,
% 0.19/0.51 (^[VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : trans(monotonicity(rewrite(((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))) <=> (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))), ((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))))), rewrite((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))), ((((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(289,plain,
% 0.19/0.51 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : ((~((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve)))) | (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[288])).
% 0.19/0.51 tff(290,plain,
% 0.19/0.51 (![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))) <=> ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[289, 287])).
% 0.19/0.51 tff(291,axiom,(![VT: $i, VVar0: $i, VExp0: $i, Vx: $i, Vv: $i, Ve: $i] : (((VVar0 = Vv) & (VExp0 = vabs(Vx, VT, Ve))) => ((((~(Vx = Vv)) & visFreeVar(Vv, Ve)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => ((~(Vx = Vv)) & visFreeVar(Vv, Ve)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','isFreeVar1')).
% 0.19/0.51 tff(292,plain,
% 0.19/0.51 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.19/0.51 tff(293,plain,
% 0.19/0.51 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[292, 284])).
% 0.19/0.51 tff(294,plain,(
% 0.19/0.51 ![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (((~((~(Vx = Vv)) & visFreeVar(Vv, Ve))) | visFreeVar(Vv, vabs(Vx, VT, Ve))) & ((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | ((~(Vx = Vv)) & visFreeVar(Vv, Ve))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[293])).
% 0.19/0.51 tff(295,plain,
% 0.19/0.51 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[294, 283])).
% 0.19/0.51 tff(296,plain,
% 0.19/0.51 (![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[295, 281])).
% 0.19/0.51 tff(297,plain,
% 0.19/0.51 (((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))))))))) <=> ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(298,plain,
% 0.19/0.52 ((~((~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)) | visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))))))) <=> (~((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(299,plain,
% 0.19/0.52 (((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)) | visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))))))))) <=> ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[298])).
% 0.19/0.52 tff(300,plain,
% 0.19/0.52 (((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)) | visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))))))))) <=> ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[299, 297])).
% 0.19/0.52 tff(301,plain,
% 0.19/0.52 ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)) | visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(302,plain,
% 0.19/0.52 ((~![VT: $i, Vx: $i, Vv: $i, Ve: $i] : (~((~((Vx = Vv) | (~visFreeVar(Vv, Ve)) | visFreeVar(Vv, vabs(Vx, VT, Ve)))) | (~((~visFreeVar(Vv, vabs(Vx, VT, Ve))) | (~((Vx = Vv) | (~visFreeVar(Vv, Ve))))))))) | (~((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.19/0.52 tff(303,plain,
% 0.19/0.52 (~((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[302, 296])).
% 0.19/0.52 tff(304,plain,
% 0.19/0.52 (((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) | (~((Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))))))) | (visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(305,plain,
% 0.19/0.52 (visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.19/0.52 tff(306,plain,
% 0.19/0.52 ((Vy!52 = Vx!55) <=> (Vx!55 = Vy!52)),
% 0.19/0.52 inference(commutativity,[status(thm)],[])).
% 0.19/0.52 tff(307,plain,
% 0.19/0.52 ((Vx!55 = Vy!52) <=> (Vy!52 = Vx!55)),
% 0.19/0.52 inference(symmetry,[status(thm)],[306])).
% 0.19/0.52 tff(308,plain,
% 0.19/0.52 ((~(Vx!55 = Vy!52)) <=> (~(Vy!52 = Vx!55))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[307])).
% 0.19/0.52 tff(309,plain,
% 0.19/0.52 (~(Vy!52 = Vx!55)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[257, 308])).
% 0.19/0.52 tff(310,plain,
% 0.19/0.52 (~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))),
% 0.19/0.52 inference(and_elim,[status(thm)],[112])).
% 0.19/0.52 tff(311,plain,
% 0.19/0.52 ((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(312,plain,
% 0.19/0.52 ((~(visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs)))) | (Vy!52 = Vx!55) | (~visFreeVar(Vx!55, veabs))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[311, 310])).
% 0.19/0.52 tff(313,plain,
% 0.19/0.52 (~visFreeVar(Vx!55, veabs)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[312, 309, 305])).
% 0.19/0.52 tff(314,plain,
% 0.19/0.52 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(315,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[314])).
% 0.19/0.52 tff(316,plain,
% 0.19/0.52 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) <=> (~(visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))), ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) <=> (~(~(visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))))), rewrite((~(~(visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))) <=> (visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))), ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) <=> (visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))))), (((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ((visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))), rewrite(((visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))), (((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(317,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & 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) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[316])).
% 0.19/0.52 tff(318,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(319,plain,
% 0.19/0.52 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(320,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[319])).
% 0.19/0.52 tff(321,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak-FreeVar-abs-IH'')).
% 0.19/0.52 tff(322,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.19/0.52 tff(323,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.19/0.52 tff(324,plain,(
% 0.19/0.52 ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 0.19/0.52 inference(skolemize,[status(sab)],[323])).
% 0.19/0.52 tff(325,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[324, 317])).
% 0.19/0.52 tff(326,plain,
% 0.19/0.52 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[325, 315])).
% 0.19/0.52 tff(327,plain,
% 0.19/0.52 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | (visFreeVar(Vx!55, 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))) | (~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) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | visFreeVar(Vx!55, 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))) | (~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)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(328,plain,
% 0.19/0.52 ((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))) | visFreeVar(Vx!55, 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))))) <=> (visFreeVar(Vx!55, 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))) | (~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)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(329,plain,
% 0.19/0.52 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~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))) | visFreeVar(Vx!55, 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)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | (visFreeVar(Vx!55, 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))) | (~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))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[328])).
% 0.19/0.52 tff(330,plain,
% 0.19/0.52 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~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))) | visFreeVar(Vx!55, 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)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | visFreeVar(Vx!55, 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))) | (~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)))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[329, 327])).
% 0.19/0.52 tff(331,plain,
% 0.19/0.52 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~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))) | visFreeVar(Vx!55, 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)))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(332,plain,
% 0.19/0.52 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(VC, veabs, VT)))) | visFreeVar(Vx!55, veabs) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.19/0.52 tff(333,plain,
% 0.19/0.52 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[332, 326, 313])).
% 0.19/0.52 tff(334,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[333, 279, 45])).
% 0.19/0.52 tff(335,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))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(336,plain,
% 0.19/0.52 (^[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)))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(337,plain,
% 0.19/0.52 (![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))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[336])).
% 0.19/0.52 tff(338,plain,
% 0.19/0.52 (^[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))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(339,plain,
% 0.19/0.53 (![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))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[338])).
% 0.19/0.53 tff(340,plain,
% 0.19/0.53 (^[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)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(341,plain,
% 0.19/0.53 (![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))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[340])).
% 0.19/0.53 tff(342,plain,
% 0.19/0.53 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(343,plain,
% 0.19/0.53 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(344,plain,
% 0.19/0.53 (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[343])).
% 0.19/0.53 tff(345,axiom,(![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 0.19/0.53 tff(346,plain,
% 0.19/0.53 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.19/0.53 tff(347,plain,
% 0.19/0.53 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[346, 342])).
% 0.19/0.53 tff(348,plain,(
% 0.19/0.53 ![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)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[347])).
% 0.19/0.53 tff(349,plain,
% 0.19/0.53 (![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))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[348, 341])).
% 0.19/0.53 tff(350,plain,
% 0.19/0.53 (![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))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[349, 339])).
% 0.19/0.53 tff(351,plain,
% 0.19/0.53 (![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))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[350, 337])).
% 0.19/0.53 tff(352,plain,
% 0.19/0.53 (((~![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)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(353,plain,
% 0.19/0.53 ((~![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)))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(354,plain,
% 0.19/0.53 ((~![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))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.19/0.54 tff(355,plain,
% 0.19/0.54 ((~((~(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))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[354, 351, 113])).
% 0.19/0.54 tff(356,plain,
% 0.19/0.54 (~((~(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))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[355, 335, 13])).
% 0.19/0.54 tff(357,plain,
% 0.19/0.54 (((~(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))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(358,plain,
% 0.19/0.54 (vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[357, 356])).
% 0.19/0.54 tff(359,plain,
% 0.19/0.54 (vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)),
% 0.19/0.54 inference(symmetry,[status(thm)],[358])).
% 0.19/0.54 tff(360,plain,
% 0.19/0.54 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(361,plain,
% 0.19/0.54 (![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)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[360])).
% 0.19/0.54 tff(362,plain,
% 0.19/0.54 (![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)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(363,axiom,(![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-var-abs'')).
% 0.19/0.54 tff(364,plain,
% 0.19/0.54 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.19/0.54 tff(365,plain,(
% 0.19/0.54 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.19/0.54 inference(skolemize,[status(sab)],[364])).
% 0.19/0.54 tff(366,plain,
% 0.19/0.54 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[365, 361])).
% 0.19/0.54 tff(367,plain,
% 0.19/0.54 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(tptp_fun_Vx_42(VC!53, VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(368,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[367, 366, 359])).
% 0.19/0.54 % SZS output end Proof
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------