%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM136+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:01:07 AM UTC 2025
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COM136+1 : TPTP v9.0.0. Released v6.4.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 12:25:02 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 tff(visFreeVar_type, type, (
% 0.21/0.53 visFreeVar: ( $i * $i ) > $o)).
% 0.21/0.53 tff(veabs_type, type, (
% 0.21/0.53 veabs: $i)).
% 0.21/0.53 tff(tptp_fun_Vx_55_type, type, (
% 0.21/0.53 tptp_fun_Vx_55: $i)).
% 0.21/0.53 tff(tptp_fun_Ve2_45_type, type, (
% 0.21/0.53 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(vabs_type, type, (
% 0.21/0.53 vabs: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_VS1_51_type, type, (
% 0.21/0.53 tptp_fun_VS1_51: $i)).
% 0.21/0.53 tff(tptp_fun_Vy_52_type, type, (
% 0.21/0.53 tptp_fun_Vy_52: $i)).
% 0.21/0.53 tff(tptp_fun_VT_50_type, type, (
% 0.21/0.53 tptp_fun_VT_50: $i)).
% 0.21/0.53 tff(vbind_type, type, (
% 0.21/0.53 vbind: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_VC_53_type, type, (
% 0.21/0.53 tptp_fun_VC_53: $i)).
% 0.21/0.53 tff(tptp_fun_VS_54_type, type, (
% 0.21/0.53 tptp_fun_VS_54: $i)).
% 0.21/0.53 tff(tptp_fun_VT1_44_type, type, (
% 0.21/0.53 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_Vx_46_type, type, (
% 0.21/0.53 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(vtcheck_type, type, (
% 0.21/0.53 vtcheck: ( $i * $i * $i ) > $o)).
% 0.21/0.53 tff(tptp_fun_VT2_43_type, type, (
% 0.21/0.53 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(varrow_type, type, (
% 0.21/0.53 varrow: ( $i * $i ) > $i)).
% 0.21/0.53 tff(vsomeType_type, type, (
% 0.21/0.53 vsomeType: $i > $i)).
% 0.21/0.53 tff(vlookup_type, type, (
% 0.21/0.53 vlookup: ( $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_Vx_42_type, type, (
% 0.21/0.53 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(vvar_type, type, (
% 0.21/0.53 vvar: $i > $i)).
% 0.21/0.53 tff(tptp_fun_VS_47_type, type, (
% 0.21/0.53 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_Ve2_48_type, type, (
% 0.21/0.53 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_Ve1_49_type, type, (
% 0.21/0.53 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(vapp_type, type, (
% 0.21/0.53 vapp: ( $i * $i ) > $i)).
% 0.21/0.53 tff(1,plain,
% 0.21/0.53 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : refl((~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(2,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.53 tff(3,plain,
% 0.21/0.53 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : trans(monotonicity(rewrite(((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1)) <=> (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> (~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), rewrite((~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> (((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))), rewrite((((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), rewrite((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(4,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.53 tff(5,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(6,plain,
% 0.21/0.53 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : rewrite((((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(7,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.53 tff(8,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'')).
% 0.21/0.53 tff(9,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.53 tff(10,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.53 tff(11,plain,(
% 0.21/0.53 ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 0.21/0.53 inference(skolemize,[status(sab)],[10])).
% 0.21/0.53 tff(12,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.53 tff(13,plain,
% 0.21/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.53 tff(14,plain,
% 0.21/0.53 ((~![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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(15,plain,
% 0.21/0.53 (~((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.53 tff(16,plain,
% 0.21/0.53 (((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))) | ((~(vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(17,plain,
% 0.21/0.53 ((~(vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.37/0.54 tff(18,plain,
% 0.37/0.54 ((vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)) <=> (vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.37/0.54 inference(commutativity,[status(thm)],[])).
% 0.37/0.54 tff(19,plain,
% 0.37/0.54 ((~(vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) <=> (~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[18])).
% 0.37/0.54 tff(20,assumption,(vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)), introduced(assumption)).
% 0.37/0.54 tff(21,plain,
% 0.37/0.54 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(22,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[21])).
% 0.37/0.54 tff(23,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(24,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'')).
% 0.37/0.54 tff(25,plain,
% 0.37/0.54 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.37/0.54 tff(26,plain,(
% 0.37/0.54 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.37/0.54 inference(skolemize,[status(sab)],[25])).
% 0.37/0.54 tff(27,plain,
% 0.37/0.54 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.37/0.54 tff(28,plain,
% 0.37/0.54 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(29,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[28, 27, 20])).
% 0.37/0.54 tff(30,plain,(~(vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.54 tff(31,plain,
% 0.37/0.54 (~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.37/0.54 tff(32,plain,
% 0.37/0.54 (((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50)))) | (vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(33,plain,
% 0.37/0.54 ((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.37/0.54 tff(34,assumption,(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))), introduced(assumption)).
% 0.37/0.54 tff(35,plain,
% 0.37/0.54 (^[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))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(36,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[35])).
% 0.37/0.54 tff(37,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(38,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'')).
% 0.37/0.54 tff(39,plain,
% 0.37/0.54 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.37/0.54 tff(40,plain,(
% 0.37/0.54 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.37/0.54 inference(skolemize,[status(sab)],[39])).
% 0.37/0.54 tff(41,plain,
% 0.37/0.54 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.37/0.54 tff(42,plain,
% 0.37/0.54 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(43,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[42, 41, 34])).
% 0.37/0.54 tff(44,plain,(~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.54 tff(45,plain,
% 0.37/0.54 (((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(46,plain,
% 0.37/0.54 ((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.37/0.54 tff(47,plain,
% 0.37/0.54 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) | vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) | vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(48,plain,
% 0.37/0.54 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) => vtcheck(VC, vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) | vtcheck(VC, vabs(Vy, VS1, veabs), VT)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(49,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : (((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)) => vtcheck(VC, vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Strong-abs'')).
% 0.37/0.54 tff(50,plain,
% 0.37/0.54 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) | vtcheck(VC, vabs(Vy, VS1, veabs), VT))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.37/0.54 tff(51,plain,
% 0.37/0.54 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) | vtcheck(VC, vabs(Vy, VS1, veabs), VT))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.37/0.54 tff(52,plain,
% 0.37/0.54 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) | vtcheck(VC, vabs(Vy, VS1, veabs), VT))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.37/0.54 tff(53,plain,
% 0.37/0.54 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~visFreeVar(Vx, vabs(Vy, VS1, veabs))) & vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) | vtcheck(VC, vabs(Vy, VS1, veabs), VT))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[52, 47])).
% 0.37/0.54 tff(54,plain,(
% 0.37/0.54 ~((~((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) & 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))),
% 0.37/0.54 inference(skolemize,[status(sab)],[53])).
% 0.37/0.54 tff(55,plain,
% 0.37/0.54 ((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) & vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.37/0.54 inference(or_elim,[status(thm)],[54])).
% 0.37/0.54 tff(56,plain,
% 0.37/0.54 (vtcheck(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.37/0.54 inference(and_elim,[status(thm)],[55])).
% 0.37/0.54 tff(57,plain,
% 0.37/0.54 (^[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)))))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(58,plain,
% 0.37/0.54 (![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))))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[57])).
% 0.37/0.54 tff(59,plain,
% 0.37/0.54 (^[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))))))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(60,plain,
% 0.37/0.54 (![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))))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[59])).
% 0.37/0.54 tff(61,plain,
% 0.37/0.54 (^[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)))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(62,plain,
% 0.37/0.54 (![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))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[61])).
% 0.37/0.54 tff(63,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(64,plain,
% 0.37/0.54 (^[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)))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(65,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[64])).
% 0.37/0.54 tff(66,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'')).
% 0.37/0.54 tff(67,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.37/0.54 tff(68,plain,
% 0.37/0.54 (![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)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.37/0.54 tff(69,plain,(
% 0.37/0.54 ![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)))),
% 0.37/0.54 inference(skolemize,[status(sab)],[68])).
% 0.37/0.54 tff(70,plain,
% 0.37/0.54 (![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))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.37/0.54 tff(71,plain,
% 0.37/0.54 (![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))))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.37/0.54 tff(72,plain,
% 0.37/0.54 (![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))))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[71, 58])).
% 0.37/0.54 tff(73,plain,
% 0.37/0.54 (((~![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(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(vbind(Vx!55, VS!54, 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(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(74,plain,
% 0.37/0.55 ((~![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(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(75,plain,
% 0.37/0.55 ((~![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(vbind(Vx!55, VS!54, VC!53), vabs(Vy!52, VS1!51, veabs), VT!50)) | (~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.37/0.55 tff(76,plain,
% 0.37/0.55 ((~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve1_49(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VT!50))) | (~vtcheck(vbind(Vx!55, VS!54, VC!53), tptp_fun_Ve2_48(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VS_47(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[75, 72, 56])).
% 0.37/0.55 tff(77,plain,
% 0.37/0.55 ((~((~(vabs(Vy!52, VS1!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)) = vsomeType(VT!50))))) | (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[76, 46])).
% 0.37/0.55 tff(78,plain,
% 0.37/0.55 (~((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[77, 33])).
% 0.39/0.56 tff(79,plain,
% 0.39/0.56 (((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(80,plain,
% 0.39/0.56 (vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.39/0.56 tff(81,plain,
% 0.39/0.56 (vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs)),
% 0.39/0.56 inference(symmetry,[status(thm)],[80])).
% 0.39/0.56 tff(82,plain,
% 0.39/0.56 ((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~(vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(83,plain,
% 0.39/0.56 ((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = vabs(Vy!52, VS1!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))))) | (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.39/0.56 tff(84,plain,
% 0.39/0.56 (~((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[83, 17])).
% 0.39/0.56 tff(85,plain,
% 0.39/0.56 (((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))) | (tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs)),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(86,plain,
% 0.39/0.56 (tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.39/0.56 tff(87,plain,
% 0.39/0.56 (visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> visFreeVar(Vx!55, veabs)),
% 0.39/0.56 inference(monotonicity,[status(thm)],[86])).
% 0.39/0.56 tff(88,plain,
% 0.39/0.56 ((~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> (~visFreeVar(Vx!55, veabs))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[87])).
% 0.39/0.56 tff(89,plain,
% 0.39/0.56 (veabs = tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.39/0.56 inference(symmetry,[status(thm)],[86])).
% 0.39/0.56 tff(90,assumption,(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55), introduced(assumption)).
% 0.39/0.56 tff(91,plain,
% 0.39/0.56 (((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(92,plain,
% 0.39/0.56 (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[91, 84])).
% 0.39/0.56 tff(93,plain,
% 0.39/0.56 (Vy!52 = tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.39/0.56 inference(symmetry,[status(thm)],[92])).
% 0.39/0.56 tff(94,plain,
% 0.39/0.56 (Vy!52 = Vx!55),
% 0.39/0.56 inference(transitivity,[status(thm)],[93, 90])).
% 0.39/0.56 tff(95,plain,
% 0.39/0.56 (vbind(Vy!52, VS!54, VC!53) = vbind(Vx!55, VS!54, VC!53)),
% 0.39/0.56 inference(monotonicity,[status(thm)],[94])).
% 0.39/0.56 tff(96,plain,
% 0.39/0.56 (((~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = veabs))) | (tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51)),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(97,plain,
% 0.39/0.56 (tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = VS1!51),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[96, 84])).
% 0.39/0.56 tff(98,plain,
% 0.39/0.56 (VS1!51 = tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))),
% 0.39/0.56 inference(symmetry,[status(thm)],[97])).
% 0.39/0.56 tff(99,plain,
% 0.39/0.56 (vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)) = vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[93, 98, 95])).
% 0.39/0.56 tff(100,plain,
% 0.39/0.56 (vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[99, 89])).
% 0.39/0.56 tff(101,plain,
% 0.39/0.56 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(symmetry,[status(thm)],[100])).
% 0.39/0.56 tff(102,plain,
% 0.39/0.56 (((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(103,plain,
% 0.39/0.56 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[102, 78])).
% 0.39/0.56 tff(104,plain,
% 0.39/0.56 (vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[103, 101])).
% 0.39/0.56 tff(105,plain,
% 0.39/0.56 (vbind(Vy!52, VS1!51, VC!53) = vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)),
% 0.39/0.56 inference(monotonicity,[status(thm)],[93, 98])).
% 0.39/0.56 tff(106,plain,
% 0.39/0.56 (vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[105, 89])).
% 0.39/0.56 tff(107,plain,
% 0.39/0.56 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(symmetry,[status(thm)],[106])).
% 0.39/0.56 tff(108,plain,
% 0.39/0.56 ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> (~vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[107])).
% 0.39/0.56 tff(109,plain,
% 0.39/0.56 (((~(vabs(Vy!52, VS1!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~(VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(110,plain,
% 0.39/0.56 (VT!50 = varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[109, 78])).
% 0.39/0.56 tff(111,plain,
% 0.39/0.56 (varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) = VT!50),
% 0.39/0.56 inference(symmetry,[status(thm)],[110])).
% 0.39/0.56 tff(112,plain,
% 0.39/0.56 (vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.39/0.56 inference(monotonicity,[status(thm)],[81, 111])).
% 0.39/0.56 tff(113,plain,
% 0.39/0.56 (vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50) <=> vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.56 inference(symmetry,[status(thm)],[112])).
% 0.39/0.56 tff(114,plain,
% 0.39/0.56 ((~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)) <=> (~vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[113])).
% 0.39/0.56 tff(115,plain,
% 0.39/0.56 (~vtcheck(VC!53, vabs(Vy!52, VS1!51, veabs), VT!50)),
% 0.39/0.56 inference(or_elim,[status(thm)],[54])).
% 0.39/0.56 tff(116,plain,
% 0.39/0.56 (~vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.39/0.57 tff(117,plain,
% 0.39/0.57 (^[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))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(118,plain,
% 0.39/0.57 (![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)))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[117])).
% 0.39/0.57 tff(119,plain,
% 0.39/0.57 (![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)))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(120,plain,
% 0.39/0.57 (^[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))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(121,plain,
% 0.39/0.57 (![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)))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[120])).
% 0.39/0.57 tff(122,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'')).
% 0.39/0.57 tff(123,plain,
% 0.39/0.57 (![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)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.39/0.57 tff(124,plain,
% 0.39/0.57 (![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)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.39/0.57 tff(125,plain,(
% 0.39/0.57 ![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)))),
% 0.39/0.57 inference(skolemize,[status(sab)],[124])).
% 0.39/0.57 tff(126,plain,
% 0.39/0.57 (![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)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.39/0.57 tff(127,plain,
% 0.39/0.57 (((~![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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(128,plain,
% 0.39/0.57 ((~![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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(129,plain,
% 0.39/0.57 ((~![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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.39/0.57 tff(130,plain,
% 0.39/0.57 ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(VC!53, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))), varrow(tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.39/0.57 tff(131,plain,
% 0.39/0.57 (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[130, 116])).
% 0.39/0.57 tff(132,plain,
% 0.39/0.57 (~vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[131, 108])).
% 0.39/0.57 tff(133,plain,
% 0.39/0.57 (^[Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : refl((vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(134,plain,
% 0.39/0.57 (![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[133])).
% 0.39/0.57 tff(135,plain,
% 0.39/0.57 (![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(136,plain,
% 0.39/0.57 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(elim_unused_vars,[status(thm)],[])).
% 0.39/0.57 tff(137,plain,
% 0.39/0.57 (![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(Vx, VTx, VC), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.39/0.57 tff(138,plain,
% 0.39/0.57 (![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(Vx, VTx, VC), Ve, VT)) <=> ![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(transitivity,[status(thm)],[137, 136])).
% 0.39/0.57 tff(139,plain,
% 0.39/0.57 (^[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(Vx, VTx, VC), Ve, VT)) <=> ((~((Vx = Vy) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vx, VTx, VC), Ve, VT)))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(140,plain,
% 0.39/0.57 (![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(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(Vx, VTx, VC), Ve, VT))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[139])).
% 0.39/0.57 tff(141,plain,
% 0.39/0.57 (![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(Vx, VTx, VC), Ve, VT)) <=> ![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(transitivity,[status(thm)],[140, 138])).
% 0.39/0.57 tff(142,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(Vx, VTx, VC), Ve, VT))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''T-Context-Duplicate'')).
% 0.39/0.57 tff(143,plain,
% 0.39/0.57 (![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.39/0.57 tff(144,plain,
% 0.39/0.57 (![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[143, 135])).
% 0.39/0.57 tff(145,plain,(
% 0.39/0.57 ![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(skolemize,[status(sab)],[144])).
% 0.39/0.57 tff(146,plain,
% 0.39/0.57 (![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[145, 134])).
% 0.39/0.57 tff(147,plain,
% 0.39/0.57 (((~![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(148,plain,
% 0.39/0.57 ((~![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(149,plain,
% 0.39/0.57 ((~![Vy: $i, VTy: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTx, VC), Ve, VT) | (~vtcheck(vbind(Vy, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | vtcheck(vbind(Vy!52, VS1!51, VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (~vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.39/0.57 tff(150,plain,
% 0.39/0.57 (~vtcheck(vbind(Vy!52, VS1!51, vbind(Vy!52, VS!54, VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[149, 146, 132])).
% 0.39/0.57 tff(151,plain,
% 0.39/0.57 ($false),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[150, 104])).
% 0.39/0.57 tff(152,plain,(~(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.57 tff(153,plain,
% 0.39/0.57 (^[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)))))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(154,plain,
% 0.39/0.57 (![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))))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[153])).
% 0.39/0.57 tff(155,plain,
% 0.39/0.57 (^[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))))))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(156,plain,
% 0.39/0.57 (![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))))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[155])).
% 0.39/0.57 tff(157,plain,
% 0.39/0.57 (![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))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(158,plain,
% 0.39/0.57 (![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))))),
% 0.39/0.57 inference(elim_unused_vars,[status(thm)],[])).
% 0.39/0.57 tff(159,plain,
% 0.39/0.57 (![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))))),
% 0.39/0.57 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.39/0.57 tff(160,plain,
% 0.39/0.57 (![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))))),
% 0.39/0.57 inference(transitivity,[status(thm)],[159, 158])).
% 0.39/0.57 tff(161,plain,
% 0.39/0.57 (^[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)))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(162,plain,
% 0.39/0.57 (![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)))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[161])).
% 0.39/0.57 tff(163,plain,
% 0.39/0.57 (![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))))),
% 0.39/0.57 inference(transitivity,[status(thm)],[162, 160])).
% 0.39/0.57 tff(164,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')).
% 0.39/0.57 tff(165,plain,
% 0.39/0.57 (![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))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.39/0.57 tff(166,plain,
% 0.39/0.57 (![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))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[165, 157])).
% 0.39/0.57 tff(167,plain,(
% 0.39/0.57 ![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))))),
% 0.39/0.57 inference(skolemize,[status(sab)],[166])).
% 0.39/0.57 tff(168,plain,
% 0.39/0.57 (![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))))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[167, 156])).
% 0.39/0.58 tff(169,plain,
% 0.39/0.58 (![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))))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[168, 154])).
% 0.39/0.58 tff(170,plain,
% 0.39/0.58 ((~![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))))))))) | (~((~((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(171,plain,
% 0.39/0.58 (~((~((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.39/0.58 tff(172,plain,
% 0.39/0.58 (((~((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (~((~visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) | (~((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))))))) | ((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.58 inference(tautology,[status(thm)],[])).
% 0.39/0.58 tff(173,plain,
% 0.39/0.58 ((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.39/0.58 tff(174,plain,
% 0.39/0.58 (visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[81])).
% 0.39/0.58 tff(175,plain,
% 0.39/0.58 (visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs)) <=> visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[174])).
% 0.39/0.58 tff(176,plain,
% 0.39/0.58 ((~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))) <=> (~visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[175])).
% 0.39/0.58 tff(177,plain,
% 0.39/0.58 (~visFreeVar(Vx!55, vabs(Vy!52, VS1!51, veabs))),
% 0.39/0.58 inference(and_elim,[status(thm)],[55])).
% 0.39/0.58 tff(178,plain,
% 0.39/0.58 (~visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.39/0.58 tff(179,plain,
% 0.39/0.58 ((~((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, vabs(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.58 inference(tautology,[status(thm)],[])).
% 0.39/0.58 tff(180,plain,
% 0.39/0.58 ((tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[179, 178, 173])).
% 0.39/0.58 tff(181,plain,
% 0.39/0.58 (~visFreeVar(Vx!55, tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[180, 152])).
% 0.39/0.58 tff(182,plain,
% 0.39/0.58 (~visFreeVar(Vx!55, veabs)),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[181, 88])).
% 0.39/0.58 tff(183,plain,
% 0.39/0.58 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[89])).
% 0.39/0.58 tff(184,plain,
% 0.39/0.58 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.58 inference(symmetry,[status(thm)],[183])).
% 0.39/0.58 tff(185,plain,
% 0.39/0.58 (^[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))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(186,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[185])).
% 0.39/0.58 tff(187,plain,
% 0.39/0.58 (^[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)))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(188,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[187])).
% 0.39/0.58 tff(189,plain,
% 0.39/0.58 (![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))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(190,plain,
% 0.39/0.58 (^[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)))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(191,plain,
% 0.39/0.58 (![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))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[190])).
% 0.39/0.58 tff(192,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'')).
% 0.39/0.58 tff(193,plain,
% 0.39/0.58 (![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))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.39/0.58 tff(194,plain,
% 0.39/0.58 (![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))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.39/0.58 tff(195,plain,(
% 0.39/0.58 ![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))),
% 0.39/0.58 inference(skolemize,[status(sab)],[194])).
% 0.39/0.58 tff(196,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.39/0.58 tff(197,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[196, 186])).
% 0.39/0.58 tff(198,plain,
% 0.39/0.58 (((~![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(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55))) <=> ((~![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(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(199,plain,
% 0.39/0.59 ((vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) <=> ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(200,plain,
% 0.39/0.59 (((~![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(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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)))) | ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[199])).
% 0.39/0.59 tff(201,plain,
% 0.39/0.59 (((~![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(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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)))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55))),
% 0.39/0.59 inference(transitivity,[status(thm)],[200, 198])).
% 0.39/0.59 tff(202,plain,
% 0.39/0.59 ((~![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(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(203,plain,
% 0.39/0.59 ((~![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(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), vbind(Vx!55, VS!54, VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55)),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.39/0.59 tff(204,plain,
% 0.39/0.59 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)) = Vx!55)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[203, 197, 103])).
% 0.39/0.59 tff(205,plain,
% 0.39/0.59 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[204, 152])).
% 0.39/0.59 tff(206,plain,
% 0.39/0.59 (vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[205, 184])).
% 0.39/0.59 tff(207,assumption,(vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))), introduced(assumption)).
% 0.39/0.59 tff(208,plain,
% 0.39/0.59 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[89])).
% 0.39/0.59 tff(209,plain,
% 0.39/0.59 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[208])).
% 0.39/0.59 tff(210,plain,
% 0.39/0.59 ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), tptp_fun_Ve2_45(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) <=> (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[209])).
% 0.39/0.59 tff(211,plain,
% 0.39/0.59 (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[131, 210])).
% 0.39/0.59 tff(212,assumption,(~visFreeVar(Vx!55, veabs)), introduced(assumption)).
% 0.39/0.59 tff(213,plain,
% 0.39/0.59 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))) <=> (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(214,plain,
% 0.39/0.59 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[213])).
% 0.39/0.59 tff(215,plain,
% 0.39/0.59 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (~(visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))))), ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) <=> (~(~(visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))))))), rewrite((~(~(visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))))) <=> (visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))), ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) <=> (visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))))), (((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT)) <=> ((visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT)))), rewrite(((visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT)) <=> (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))), (((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT)) <=> (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(216,plain,
% 0.39/0.59 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[215])).
% 0.39/0.59 tff(217,plain,
% 0.39/0.59 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(218,plain,
% 0.39/0.59 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT)) => vtcheck(VC, veabs, VT)) <=> ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT)))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(219,plain,
% 0.39/0.59 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT)) => vtcheck(VC, veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[218])).
% 0.39/0.59 tff(220,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT)) => vtcheck(VC, veabs, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Strong-abs-IH'')).
% 0.39/0.60 tff(221,plain,
% 0.39/0.60 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.39/0.60 tff(222,plain,
% 0.39/0.60 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.39/0.60 tff(223,plain,(
% 0.39/0.60 ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((~visFreeVar(Vx, veabs)) & vtcheck(vbind(Vx, VS, VC), veabs, VT))) | vtcheck(VC, veabs, VT))),
% 0.39/0.60 inference(skolemize,[status(sab)],[222])).
% 0.39/0.60 tff(224,plain,
% 0.39/0.60 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.39/0.60 tff(225,plain,
% 0.39/0.60 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[224, 214])).
% 0.39/0.60 tff(226,plain,
% 0.39/0.60 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | (visFreeVar(Vx!55, veabs) | (~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | visFreeVar(Vx!55, veabs) | (~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(227,plain,
% 0.39/0.60 ((vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(228,plain,
% 0.39/0.60 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | (visFreeVar(Vx!55, veabs) | (~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[227])).
% 0.39/0.60 tff(229,plain,
% 0.39/0.60 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | visFreeVar(Vx!55, veabs) | (~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs))))),
% 0.39/0.60 inference(transitivity,[status(thm)],[228, 226])).
% 0.39/0.60 tff(230,plain,
% 0.39/0.60 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, 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(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(231,plain,
% 0.39/0.60 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(VC, veabs, VT) | visFreeVar(Vx, veabs) | (~vtcheck(vbind(Vx, VS, VC), veabs, VT)))) | visFreeVar(Vx!55, veabs) | (~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.39/0.60 tff(232,plain,
% 0.39/0.60 ((~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[231, 225, 212])).
% 0.39/0.60 tff(233,plain,
% 0.39/0.60 ($false),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[232, 211, 207])).
% 0.39/0.60 tff(234,plain,((~vtcheck(vbind(Vx!55, VS!54, vbind(tptp_fun_Vx_46(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), tptp_fun_VT1_44(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)), VC!53)), veabs, tptp_fun_VT2_43(vbind(Vx!55, VS!54, VC!53), VT!50, vabs(Vy!52, VS1!51, veabs)))) | visFreeVar(Vx!55, veabs)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.60 tff(235,plain,
% 0.39/0.60 ($false),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[234, 206, 182])).
% 0.39/0.60 % SZS output end Proof
% 0.39/0.61 % E exiting
%------------------------------------------------------------------------------