%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM131+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:01:06 AM UTC 2025
% Result : Theorem 0.23s 0.51s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : COM131+1 : TPTP v9.0.0. Released v6.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 12:23:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.51 % SZS status Theorem
% 0.23/0.51 % SZS output start Proof
% 0.23/0.51 tff(vtcheck_type, type, (
% 0.23/0.51 vtcheck: ( $i * $i * $i ) > $o)).
% 0.23/0.51 tff(tptp_fun_VT_56_type, type, (
% 0.23/0.51 tptp_fun_VT_56: $i)).
% 0.23/0.51 tff(tptp_fun_Ve_53_type, type, (
% 0.23/0.51 tptp_fun_Ve_53: $i)).
% 0.23/0.51 tff(vbind_type, type, (
% 0.23/0.51 vbind: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(tptp_fun_VC_55_type, type, (
% 0.23/0.51 tptp_fun_VC_55: $i)).
% 0.23/0.51 tff(tptp_fun_VS_51_type, type, (
% 0.23/0.51 tptp_fun_VS_51: $i)).
% 0.23/0.51 tff(tptp_fun_Vy_52_type, type, (
% 0.23/0.51 tptp_fun_Vy_52: $i)).
% 0.23/0.51 tff(tptp_fun_VT1_44_type, type, (
% 0.23/0.51 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(vabs_type, type, (
% 0.23/0.51 vabs: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(veabs_type, type, (
% 0.23/0.51 veabs: $i)).
% 0.23/0.51 tff(tptp_fun_VT2_50_type, type, (
% 0.23/0.51 tptp_fun_VT2_50: $i)).
% 0.23/0.51 tff(tptp_fun_Vx_54_type, type, (
% 0.23/0.51 tptp_fun_Vx_54: $i)).
% 0.23/0.51 tff(tptp_fun_Vx_46_type, type, (
% 0.23/0.51 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(tptp_fun_Ve2_45_type, type, (
% 0.23/0.51 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(tptp_fun_VT2_43_type, type, (
% 0.23/0.51 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(varrow_type, type, (
% 0.23/0.51 varrow: ( $i * $i ) > $i)).
% 0.23/0.51 tff(vsomeType_type, type, (
% 0.23/0.51 vsomeType: $i > $i)).
% 0.23/0.51 tff(vlookup_type, type, (
% 0.23/0.51 vlookup: ( $i * $i ) > $i)).
% 0.23/0.51 tff(tptp_fun_Vx_42_type, type, (
% 0.23/0.51 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(vvar_type, type, (
% 0.23/0.51 vvar: $i > $i)).
% 0.23/0.51 tff(tptp_fun_VS_47_type, type, (
% 0.23/0.51 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(tptp_fun_Ve2_48_type, type, (
% 0.23/0.51 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(tptp_fun_Ve1_49_type, type, (
% 0.23/0.51 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(vapp_type, type, (
% 0.23/0.51 vapp: ( $i * $i ) > $i)).
% 0.23/0.51 tff(visFreeVar_type, type, (
% 0.23/0.51 visFreeVar: ( $i * $i ) > $o)).
% 0.23/0.51 tff(vsubst_type, type, (
% 0.23/0.51 vsubst: ( $i * $i * $i ) > $i)).
% 0.23/0.51 tff(1,plain,
% 0.23/0.51 (^[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)))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(2,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.51 tff(3,plain,
% 0.23/0.51 (^[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))))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(4,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.51 tff(5,plain,
% 0.23/0.51 (![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))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(6,plain,
% 0.23/0.51 (^[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)))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(7,plain,
% 0.23/0.51 (![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))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[6])).
% 0.23/0.51 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'')).
% 0.23/0.51 tff(9,plain,
% 0.23/0.51 (![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))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.23/0.51 tff(10,plain,
% 0.23/0.51 (![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))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.23/0.51 tff(11,plain,(
% 0.23/0.51 ![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))))),
% 0.23/0.51 inference(skolemize,[status(sab)],[10])).
% 0.23/0.51 tff(12,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.23/0.51 tff(13,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.23/0.51 tff(14,plain,
% 0.23/0.51 (((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))))))) <=> ((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(15,plain,
% 0.23/0.51 ((~((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)))))) <=> (~((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(16,plain,
% 0.23/0.52 (((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs))))))) <=> ((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)))))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[15])).
% 0.23/0.52 tff(17,plain,
% 0.23/0.52 (((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs))))))) <=> ((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)))))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[16, 14])).
% 0.23/0.52 tff(18,plain,
% 0.23/0.52 ((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs))))))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(19,plain,
% 0.23/0.52 ((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.23/0.52 tff(20,plain,
% 0.23/0.52 (~((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.23/0.52 tff(21,plain,
% 0.23/0.52 (((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)) | (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))))) | ((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(22,plain,
% 0.23/0.53 ((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.23/0.53 tff(23,plain,
% 0.23/0.53 ((vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)) <=> (vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.53 inference(commutativity,[status(thm)],[])).
% 0.23/0.53 tff(24,plain,
% 0.23/0.53 ((~(vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) <=> (~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[23])).
% 0.23/0.53 tff(25,assumption,(vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)), introduced(assumption)).
% 0.23/0.53 tff(26,plain,
% 0.23/0.53 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(27,plain,
% 0.23/0.53 (![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)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.53 tff(28,plain,
% 0.23/0.53 (![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)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(29,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'')).
% 0.23/0.53 tff(30,plain,
% 0.23/0.53 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.23/0.53 tff(31,plain,(
% 0.23/0.53 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.23/0.53 inference(skolemize,[status(sab)],[30])).
% 0.23/0.53 tff(32,plain,
% 0.23/0.53 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.23/0.53 tff(33,plain,
% 0.23/0.53 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(34,plain,
% 0.23/0.53 ($false),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[33, 32, 25])).
% 0.23/0.53 tff(35,plain,(~(vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.53 tff(36,plain,
% 0.23/0.53 (~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[35, 24])).
% 0.23/0.53 tff(37,plain,
% 0.23/0.53 (((~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)) = vsomeType(VT2!50)))) | (vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(38,plain,
% 0.23/0.53 ((~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)) = vsomeType(VT2!50)))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.23/0.53 tff(39,assumption,(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))), introduced(assumption)).
% 0.23/0.53 tff(40,plain,
% 0.23/0.53 (^[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))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(41,plain,
% 0.23/0.53 (![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)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[40])).
% 0.23/0.53 tff(42,plain,
% 0.23/0.53 (![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)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(43,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'')).
% 0.23/0.53 tff(44,plain,
% 0.23/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.23/0.53 tff(45,plain,(
% 0.23/0.53 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.23/0.53 inference(skolemize,[status(sab)],[44])).
% 0.23/0.53 tff(46,plain,
% 0.23/0.53 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.23/0.53 tff(47,plain,
% 0.23/0.53 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(48,plain,
% 0.23/0.53 ($false),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[47, 46, 39])).
% 0.23/0.53 tff(49,plain,(~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.53 tff(50,plain,
% 0.23/0.53 (((~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VT2!50))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(51,plain,
% 0.23/0.53 ((~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VT2!50))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.23/0.53 tff(52,plain,
% 0.23/0.53 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))) <=> (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(53,plain,
% 0.23/0.53 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))) <=> (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(54,axiom,(~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : (((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) & vtcheck(VC, Ve, VT)) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-subst-abs-2'')).
% 0.23/0.53 tff(55,plain,
% 0.23/0.53 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.23/0.53 tff(56,plain,
% 0.23/0.53 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.23/0.53 tff(57,plain,
% 0.23/0.53 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.23/0.53 tff(58,plain,
% 0.23/0.53 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VS: $i, VT2: $i] : ((~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)) & vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vabs(Vy, VS, veabs), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vabs(Vy, VS, veabs)), VT2))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[57, 52])).
% 0.23/0.53 tff(59,plain,(
% 0.23/0.53 ~((~((~(Vx!54 = Vy!52)) & (~visFreeVar(Vy!52, Ve!53)) & vtcheck(VC!55, Ve!53, VT!56) & vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50))) | vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50))),
% 0.23/0.53 inference(skolemize,[status(sab)],[58])).
% 0.23/0.53 tff(60,plain,
% 0.23/0.53 ((~(Vx!54 = Vy!52)) & (~visFreeVar(Vy!52, Ve!53)) & vtcheck(VC!55, Ve!53, VT!56) & vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.23/0.53 inference(or_elim,[status(thm)],[59])).
% 0.23/0.53 tff(61,plain,
% 0.23/0.53 (vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)),
% 0.23/0.53 inference(and_elim,[status(thm)],[60])).
% 0.23/0.53 tff(62,plain,
% 0.23/0.53 (^[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)))))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(63,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[62])).
% 0.23/0.53 tff(64,plain,
% 0.23/0.53 (^[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))))))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(65,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[64])).
% 0.23/0.53 tff(66,plain,
% 0.23/0.53 (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(67,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[66])).
% 0.23/0.53 tff(68,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(69,plain,
% 0.23/0.53 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(70,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[69])).
% 0.23/0.53 tff(71,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'')).
% 0.23/0.53 tff(72,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.23/0.53 tff(73,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.23/0.53 tff(74,plain,(
% 0.23/0.53 ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.53 inference(skolemize,[status(sab)],[73])).
% 0.23/0.53 tff(75,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.23/0.53 tff(76,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.23/0.53 tff(77,plain,
% 0.23/0.53 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[76, 63])).
% 0.23/0.53 tff(78,plain,
% 0.23/0.53 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(vbind(Vx!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~((~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)) = vsomeType(VT2!50))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VT2!50))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!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!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~((~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)) = vsomeType(VT2!50))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VT2!50))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(79,plain,
% 0.23/0.54 ((~![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!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~((~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)) = vsomeType(VT2!50))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VT2!50))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))))),
% 0.23/0.54 inference(quant_inst,[status(thm)],[])).
% 0.23/0.54 tff(80,plain,
% 0.23/0.54 ((~![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!54, VT!56, VC!55), vabs(Vy!52, VS!51, veabs), VT2!50)) | (~((~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)) = vsomeType(VT2!50))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VT2!50))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.23/0.54 tff(81,plain,
% 0.23/0.54 ((~((~(vabs(Vy!52, VS!51, veabs) = vvar(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)) = vsomeType(VT2!50))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) | (~((~(vabs(Vy!52, VS!51, veabs) = vapp(tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve1_49(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), varrow(tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VT2!50))) | (~vtcheck(vbind(Vx!54, VT!56, VC!55), tptp_fun_Ve2_48(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VS_47(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[80, 77, 61])).
% 0.23/0.54 tff(82,plain,
% 0.23/0.54 (~((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[81, 51, 38])).
% 0.23/0.55 tff(83,plain,
% 0.23/0.55 (((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.55 inference(tautology,[status(thm)],[])).
% 0.23/0.55 tff(84,plain,
% 0.23/0.55 (vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.23/0.55 tff(85,plain,
% 0.23/0.55 (vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs)),
% 0.23/0.55 inference(symmetry,[status(thm)],[84])).
% 0.23/0.55 tff(86,plain,
% 0.23/0.55 ((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51))))),
% 0.23/0.55 inference(tautology,[status(thm)],[])).
% 0.23/0.55 tff(87,plain,
% 0.23/0.55 ((~((~(vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = vabs(Vy!52, VS!51, veabs))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))))) | (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51))))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.23/0.55 tff(88,plain,
% 0.23/0.55 (~((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[87, 22])).
% 0.23/0.55 tff(89,plain,
% 0.23/0.55 (((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51))) | (tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51)),
% 0.23/0.55 inference(tautology,[status(thm)],[])).
% 0.23/0.55 tff(90,plain,
% 0.23/0.55 (tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.23/0.55 tff(91,plain,
% 0.23/0.55 (VS!51 = tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))),
% 0.23/0.55 inference(symmetry,[status(thm)],[90])).
% 0.23/0.55 tff(92,plain,
% 0.23/0.55 (((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)),
% 0.23/0.55 inference(tautology,[status(thm)],[])).
% 0.23/0.55 tff(93,plain,
% 0.23/0.55 (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[92, 88])).
% 0.23/0.55 tff(94,plain,
% 0.23/0.55 (Vy!52 = tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))),
% 0.23/0.55 inference(symmetry,[status(thm)],[93])).
% 0.23/0.55 tff(95,plain,
% 0.23/0.55 (vbind(Vy!52, VS!51, VC!55) = vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)),
% 0.23/0.55 inference(monotonicity,[status(thm)],[94, 91])).
% 0.23/0.55 tff(96,plain,
% 0.23/0.55 (vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56) <=> vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)),
% 0.23/0.55 inference(monotonicity,[status(thm)],[95])).
% 0.23/0.55 tff(97,plain,
% 0.23/0.55 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56) <=> vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56)),
% 0.23/0.55 inference(symmetry,[status(thm)],[96])).
% 0.23/0.55 tff(98,plain,
% 0.23/0.55 ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) <=> (~vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[97])).
% 0.23/0.55 tff(99,plain,
% 0.23/0.55 (vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55) = vbind(Vy!52, VS!51, VC!55)),
% 0.23/0.55 inference(symmetry,[status(thm)],[95])).
% 0.23/0.55 tff(100,plain,
% 0.23/0.55 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) <=> vtcheck(vbind(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[99])).
% 0.23/0.55 tff(101,plain,
% 0.23/0.55 (vtcheck(vbind(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.55 inference(symmetry,[status(thm)],[100])).
% 0.23/0.55 tff(102,plain,
% 0.23/0.55 ((~vtcheck(vbind(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) <=> (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[101])).
% 0.23/0.55 tff(103,plain,
% 0.23/0.55 (((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.55 inference(tautology,[status(thm)],[])).
% 0.23/0.55 tff(104,plain,
% 0.23/0.55 (VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[103, 82])).
% 0.23/0.55 tff(105,plain,
% 0.23/0.55 (varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = VT2!50),
% 0.23/0.55 inference(symmetry,[status(thm)],[104])).
% 0.23/0.55 tff(106,plain,
% 0.23/0.55 (varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[91])).
% 0.23/0.55 tff(107,plain,
% 0.23/0.55 (varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) = VT2!50),
% 0.23/0.55 inference(transitivity,[status(thm)],[106, 105])).
% 0.23/0.55 tff(108,plain,
% 0.23/0.55 (~visFreeVar(Vy!52, Ve!53)),
% 0.23/0.55 inference(and_elim,[status(thm)],[60])).
% 0.23/0.55 tff(109,plain,
% 0.23/0.55 (~(Vx!54 = Vy!52)),
% 0.23/0.55 inference(and_elim,[status(thm)],[60])).
% 0.23/0.55 tff(110,plain,
% 0.23/0.55 (^[Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : refl((visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))) <=> (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(111,plain,
% 0.23/0.55 (![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))) <=> ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[110])).
% 0.23/0.55 tff(112,plain,
% 0.23/0.55 (![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))) <=> ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(113,plain,
% 0.23/0.55 (^[Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : rewrite(((vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | visFreeVar(Vy, Ve) | (Vx = Vy)) <=> (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(114,plain,
% 0.23/0.55 (![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | visFreeVar(Vy, Ve) | (Vx = Vy)) <=> ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[113])).
% 0.23/0.55 tff(115,plain,
% 0.23/0.55 (![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | visFreeVar(Vy, Ve) | (Vx = Vy)) <=> ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | visFreeVar(Vy, Ve) | (Vx = Vy))),
% 0.23/0.55 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.55 tff(116,plain,
% 0.23/0.55 (![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | visFreeVar(Vy, Ve) | (Vx = Vy))),
% 0.23/0.55 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.23/0.55 tff(117,plain,
% 0.23/0.55 (![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))))) <=> ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | visFreeVar(Vy, Ve) | (Vx = Vy))),
% 0.23/0.55 inference(transitivity,[status(thm)],[116, 115])).
% 0.23/0.55 tff(118,plain,
% 0.23/0.55 (![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))))) <=> ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[117, 114])).
% 0.23/0.55 tff(119,plain,
% 0.23/0.55 (^[VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : trans(monotonicity(rewrite((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) <=> ((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))), trans(monotonicity(rewrite(((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))) <=> ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))), ((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) <=> (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))))), rewrite((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) <=> ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))))), ((((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) <=> ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))))) <=> (((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))) => ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))))))), rewrite((((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1))) => ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))))) <=> ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))))) <=> ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(120,plain,
% 0.23/0.55 (![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((~(Vx = Vy)) & (~visFreeVar(Vy, Ve)))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vabs(Vy, VT, Ve1)))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[119])).
% 0.23/0.55 tff(121,plain,
% 0.23/0.55 (![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1)))))) <=> ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[120, 118])).
% 0.23/0.55 tff(122,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vabs(Vy, VT, Ve1))) => (((~(Vx = Vy)) & (~visFreeVar(Vy, Ve))) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','subst5')).
% 0.23/0.55 tff(123,plain,
% 0.23/0.55 (![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.23/0.55 tff(124,plain,
% 0.23/0.55 (![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[123, 112])).
% 0.23/0.55 tff(125,plain,(
% 0.23/0.55 ![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(skolemize,[status(sab)],[124])).
% 0.23/0.55 tff(126,plain,
% 0.23/0.55 (![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[125, 111])).
% 0.23/0.55 tff(127,plain,
% 0.23/0.55 (((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | ((Vx!54 = Vy!52) | visFreeVar(Vy!52, Ve!53) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))))) <=> ((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | (Vx!54 = Vy!52) | visFreeVar(Vy!52, Ve!53) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(128,plain,
% 0.23/0.56 ((visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)))) <=> ((Vx!54 = Vy!52) | visFreeVar(Vy!52, Ve!53) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(129,plain,
% 0.23/0.56 (((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | (visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))))) <=> ((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | ((Vx!54 = Vy!52) | visFreeVar(Vy!52, Ve!53) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[128])).
% 0.23/0.56 tff(130,plain,
% 0.23/0.56 (((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | (visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))))) <=> ((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | (Vx!54 = Vy!52) | visFreeVar(Vy!52, Ve!53) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[129, 127])).
% 0.23/0.56 tff(131,plain,
% 0.23/0.56 ((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | (visFreeVar(Vy!52, Ve!53) | (Vx!54 = Vy!52) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))))),
% 0.23/0.56 inference(quant_inst,[status(thm)],[])).
% 0.23/0.56 tff(132,plain,
% 0.23/0.56 ((~![Vy: $i, VT: $i, Vx: $i, Ve: $i, Ve1: $i] : (visFreeVar(Vy, Ve) | (Vx = Vy) | (vsubst(Vx, Ve, vabs(Vy, VT, Ve1)) = vabs(Vy, VT, vsubst(Vx, Ve, Ve1))))) | (Vx!54 = Vy!52) | visFreeVar(Vy!52, Ve!53) | (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.23/0.56 tff(133,plain,
% 0.23/0.56 (vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)) = vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[132, 126, 109, 108])).
% 0.23/0.56 tff(134,plain,
% 0.23/0.56 (vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)) = vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs))),
% 0.23/0.56 inference(symmetry,[status(thm)],[133])).
% 0.23/0.56 tff(135,plain,
% 0.23/0.56 (vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) <=> vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)),
% 0.23/0.56 inference(monotonicity,[status(thm)],[134, 107])).
% 0.23/0.56 tff(136,plain,
% 0.23/0.56 (vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50) <=> vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.56 inference(symmetry,[status(thm)],[135])).
% 0.23/0.56 tff(137,plain,
% 0.23/0.56 ((~vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)) <=> (~vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[136])).
% 0.23/0.56 tff(138,plain,
% 0.23/0.56 (~vtcheck(VC!55, vsubst(Vx!54, Ve!53, vabs(Vy!52, VS!51, veabs)), VT2!50)),
% 0.23/0.56 inference(or_elim,[status(thm)],[59])).
% 0.23/0.56 tff(139,plain,
% 0.23/0.56 (~vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.23/0.56 tff(140,plain,
% 0.23/0.56 (^[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))))),
% 0.23/0.56 inference(bind,[status(th)],[])).
% 0.23/0.56 tff(141,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(quant_intro,[status(thm)],[140])).
% 0.23/0.56 tff(142,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(143,plain,
% 0.23/0.56 (^[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))))),
% 0.23/0.56 inference(bind,[status(th)],[])).
% 0.23/0.56 tff(144,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(quant_intro,[status(thm)],[143])).
% 0.23/0.56 tff(145,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'')).
% 0.23/0.56 tff(146,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.23/0.56 tff(147,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.23/0.56 tff(148,plain,(
% 0.23/0.56 ![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)))),
% 0.23/0.56 inference(skolemize,[status(sab)],[147])).
% 0.23/0.56 tff(149,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.23/0.56 tff(150,plain,
% 0.23/0.56 (((~![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(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!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(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(151,plain,
% 0.23/0.56 ((~![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(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.56 inference(quant_inst,[status(thm)],[])).
% 0.23/0.56 tff(152,plain,
% 0.23/0.56 ((~![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(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.23/0.56 tff(153,plain,
% 0.23/0.56 ((~vtcheck(vbind(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | vtcheck(VC!55, vabs(Vy!52, VS!51, vsubst(Vx!54, Ve!53, veabs)), varrow(VS!51, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.23/0.56 tff(154,plain,
% 0.23/0.56 (~vtcheck(vbind(Vy!52, VS!51, VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[153, 139])).
% 0.23/0.56 tff(155,plain,
% 0.23/0.56 (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[154, 102])).
% 0.23/0.56 tff(156,plain,
% 0.23/0.56 (((~(tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)) | (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vy!52)) | (~(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = VS!51))) | (tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs)),
% 0.23/0.56 inference(tautology,[status(thm)],[])).
% 0.23/0.56 tff(157,plain,
% 0.23/0.56 (tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = veabs),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[156, 88])).
% 0.23/0.56 tff(158,plain,
% 0.23/0.56 (veabs = tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))),
% 0.23/0.56 inference(symmetry,[status(thm)],[157])).
% 0.23/0.56 tff(159,plain,
% 0.23/0.56 (vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) <=> vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[158])).
% 0.23/0.56 tff(160,plain,
% 0.23/0.56 (vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) <=> vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.56 inference(symmetry,[status(thm)],[159])).
% 0.23/0.56 tff(161,plain,
% 0.23/0.56 ((Vy!52 = Vx!54) <=> (Vx!54 = Vy!52)),
% 0.23/0.56 inference(commutativity,[status(thm)],[])).
% 0.23/0.56 tff(162,plain,
% 0.23/0.56 ((tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) <=> (Vy!52 = Vx!54)),
% 0.23/0.56 inference(monotonicity,[status(thm)],[93])).
% 0.23/0.56 tff(163,plain,
% 0.23/0.56 ((tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) <=> (Vx!54 = Vy!52)),
% 0.23/0.56 inference(transitivity,[status(thm)],[162, 161])).
% 0.23/0.56 tff(164,plain,
% 0.23/0.56 ((Vx!54 = Vy!52) <=> (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54)),
% 0.23/0.56 inference(symmetry,[status(thm)],[163])).
% 0.23/0.56 tff(165,plain,
% 0.23/0.56 ((~(Vx!54 = Vy!52)) <=> (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[164])).
% 0.23/0.56 tff(166,plain,
% 0.23/0.56 (~(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54)),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[109, 165])).
% 0.23/0.56 tff(167,plain,
% 0.23/0.56 (((~(vabs(Vy!52, VS!51, veabs) = vabs(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.56 inference(tautology,[status(thm)],[])).
% 0.23/0.56 tff(168,plain,
% 0.23/0.56 (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[167, 82])).
% 0.23/0.56 tff(169,plain,
% 0.23/0.56 (^[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))))),
% 0.23/0.56 inference(bind,[status(th)],[])).
% 0.23/0.56 tff(170,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(quant_intro,[status(thm)],[169])).
% 0.23/0.56 tff(171,plain,
% 0.23/0.56 (^[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)))))),
% 0.23/0.56 inference(bind,[status(th)],[])).
% 0.23/0.56 tff(172,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(quant_intro,[status(thm)],[171])).
% 0.23/0.56 tff(173,plain,
% 0.23/0.56 (![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))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(174,plain,
% 0.23/0.56 (^[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)))),
% 0.23/0.56 inference(bind,[status(th)],[])).
% 0.23/0.56 tff(175,plain,
% 0.23/0.56 (![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))),
% 0.23/0.56 inference(quant_intro,[status(thm)],[174])).
% 0.23/0.56 tff(176,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'')).
% 0.23/0.56 tff(177,plain,
% 0.23/0.56 (![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))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.23/0.56 tff(178,plain,
% 0.23/0.56 (![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))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.23/0.56 tff(179,plain,(
% 0.23/0.56 ![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))),
% 0.23/0.56 inference(skolemize,[status(sab)],[178])).
% 0.23/0.56 tff(180,plain,
% 0.23/0.56 (![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)))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.23/0.57 tff(181,plain,
% 0.23/0.57 (![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)))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.23/0.57 tff(182,plain,
% 0.23/0.57 (((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.57 inference(rewrite,[status(thm)],[])).
% 0.23/0.57 tff(183,plain,
% 0.23/0.57 ((vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) <=> ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.57 inference(rewrite,[status(thm)],[])).
% 0.23/0.57 tff(184,plain,
% 0.23/0.57 (((~![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!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.57 inference(monotonicity,[status(thm)],[183])).
% 0.23/0.57 tff(185,plain,
% 0.23/0.57 (((~![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!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.57 inference(transitivity,[status(thm)],[184, 182])).
% 0.23/0.57 tff(186,plain,
% 0.23/0.57 ((~![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!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.57 inference(quant_inst,[status(thm)],[])).
% 0.23/0.57 tff(187,plain,
% 0.23/0.57 ((~![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!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), vbind(Vx!54, VT!56, VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))) | (tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.23/0.57 tff(188,plain,
% 0.23/0.57 ((tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)) = Vx!54) | vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[187, 181, 168])).
% 0.23/0.57 tff(189,plain,
% 0.23/0.57 (vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), tptp_fun_Ve2_45(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[188, 166])).
% 0.23/0.57 tff(190,plain,
% 0.23/0.57 (vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[189, 160])).
% 0.23/0.57 tff(191,plain,
% 0.23/0.57 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : refl((vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))) <=> (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))))),
% 0.23/0.57 inference(bind,[status(th)],[])).
% 0.23/0.57 tff(192,plain,
% 0.23/0.57 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))),
% 0.23/0.57 inference(quant_intro,[status(thm)],[191])).
% 0.23/0.57 tff(193,plain,
% 0.23/0.57 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : trans(monotonicity(trans(monotonicity(rewrite((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2)) <=> (~((~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))))), ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) <=> (~(~((~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))))))), rewrite((~(~((~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))))) <=> ((~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))), ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) <=> ((~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))))), (((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)) <=> (((~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)))), rewrite((((~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)) <=> (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))), (((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)) <=> (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))))),
% 0.23/0.57 inference(bind,[status(th)],[])).
% 0.23/0.57 tff(194,plain,
% 0.23/0.57 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))),
% 0.23/0.57 inference(quant_intro,[status(thm)],[193])).
% 0.23/0.57 tff(195,plain,
% 0.23/0.57 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2))),
% 0.23/0.57 inference(rewrite,[status(thm)],[])).
% 0.23/0.57 tff(196,plain,
% 0.23/0.57 (^[VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : rewrite(((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2)) => vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)) <=> ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)))),
% 0.23/0.57 inference(bind,[status(th)],[])).
% 0.23/0.57 tff(197,plain,
% 0.23/0.57 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2)) => vtcheck(VC, vsubst(Vx, Ve, veabs), VT2)) <=> ![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2))),
% 0.23/0.57 inference(quant_intro,[status(thm)],[196])).
% 0.23/0.57 tff(198,axiom,(![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2)) => vtcheck(VC, vsubst(Vx, Ve, veabs), VT2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-subst-IH-abs'')).
% 0.23/0.57 tff(199,plain,
% 0.23/0.57 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.23/0.57 tff(200,plain,
% 0.23/0.57 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.23/0.57 tff(201,plain,(
% 0.23/0.57 ![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), veabs, VT2))) | vtcheck(VC, vsubst(Vx, Ve, veabs), VT2))),
% 0.23/0.57 inference(skolemize,[status(sab)],[200])).
% 0.23/0.57 tff(202,plain,
% 0.23/0.58 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.23/0.58 tff(203,plain,
% 0.23/0.58 (![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[202, 192])).
% 0.23/0.58 tff(204,plain,
% 0.23/0.58 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.58 inference(rewrite,[status(thm)],[])).
% 0.23/0.58 tff(205,plain,
% 0.23/0.58 ((vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))) <=> ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.58 inference(rewrite,[status(thm)],[])).
% 0.23/0.58 tff(206,plain,
% 0.23/0.58 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))))),
% 0.23/0.58 inference(monotonicity,[status(thm)],[205])).
% 0.23/0.58 tff(207,plain,
% 0.23/0.58 (((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))) <=> ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.58 inference(transitivity,[status(thm)],[206, 204])).
% 0.23/0.58 tff(208,plain,
% 0.23/0.58 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | (vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))))),
% 0.23/0.58 inference(quant_inst,[status(thm)],[])).
% 0.23/0.58 tff(209,plain,
% 0.23/0.58 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, VT2: $i] : (vtcheck(VC, vsubst(Vx, Ve, veabs), VT2) | (~vtcheck(VC, Ve, VT)) | (~vtcheck(vbind(Vx, VT, VC), veabs, VT2)))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))) | (~vtcheck(vbind(Vx!54, VT!56, vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55)), veabs, tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs))))),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.23/0.58 tff(210,plain,
% 0.23/0.58 ((~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)) | vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), vsubst(Vx!54, Ve!53, veabs), tptp_fun_VT2_43(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)))),
% 0.23/0.58 inference(unit_resolution,[status(thm)],[209, 203, 190])).
% 0.23/0.58 tff(211,plain,
% 0.23/0.58 (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), tptp_fun_VT1_44(vbind(Vx!54, VT!56, VC!55), VT2!50, vabs(Vy!52, VS!51, veabs)), VC!55), Ve!53, VT!56)),
% 0.23/0.58 inference(unit_resolution,[status(thm)],[210, 155])).
% 0.23/0.58 tff(212,plain,
% 0.23/0.58 (~vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56)),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[211, 98])).
% 0.23/0.58 tff(213,plain,
% 0.23/0.58 (vtcheck(VC!55, Ve!53, VT!56)),
% 0.23/0.58 inference(and_elim,[status(thm)],[60])).
% 0.23/0.58 tff(214,plain,
% 0.23/0.58 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))) <=> (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))))),
% 0.23/0.58 inference(bind,[status(th)],[])).
% 0.23/0.58 tff(215,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.58 inference(quant_intro,[status(thm)],[214])).
% 0.23/0.58 tff(216,plain,
% 0.23/0.58 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT)) <=> (~(visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))))), ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) <=> (~(~(visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))))))), rewrite((~(~(visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))))) <=> (visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))), ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) <=> (visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))))), (((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ((visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)))), rewrite(((visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))), (((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))))),
% 0.23/0.58 inference(bind,[status(th)],[])).
% 0.23/0.58 tff(217,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.58 inference(quant_intro,[status(thm)],[216])).
% 0.23/0.58 tff(218,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.23/0.58 inference(rewrite,[status(thm)],[])).
% 0.23/0.58 tff(219,plain,
% 0.23/0.58 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : rewrite((((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT)) => vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.23/0.58 inference(bind,[status(th)],[])).
% 0.23/0.58 tff(220,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT)) => vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.23/0.58 inference(quant_intro,[status(thm)],[219])).
% 0.23/0.58 tff(221,axiom,(![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT)) => vtcheck(vbind(Vx, VS, VC), Ve, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Weak-FreeVar'')).
% 0.23/0.58 tff(222,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.23/0.58 tff(223,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.23/0.58 tff(224,plain,(
% 0.23/0.58 ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(VC, Ve, VT))) | vtcheck(vbind(Vx, VS, VC), Ve, VT))),
% 0.23/0.58 inference(skolemize,[status(sab)],[223])).
% 0.23/0.58 tff(225,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.23/0.58 tff(226,plain,
% 0.23/0.58 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))),
% 0.23/0.58 inference(modus_ponens,[status(thm)],[225, 215])).
% 0.23/0.58 tff(227,plain,
% 0.23/0.58 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | (visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56))),
% 0.23/0.58 inference(rewrite,[status(thm)],[])).
% 0.23/0.58 tff(228,plain,
% 0.23/0.58 ((vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56) | visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56))) <=> (visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56))),
% 0.23/0.58 inference(rewrite,[status(thm)],[])).
% 0.23/0.58 tff(229,plain,
% 0.23/0.58 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56) | visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | (visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56)))),
% 0.23/0.59 inference(monotonicity,[status(thm)],[228])).
% 0.23/0.59 tff(230,plain,
% 0.23/0.59 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56) | visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56))),
% 0.23/0.59 inference(transitivity,[status(thm)],[229, 227])).
% 0.23/0.59 tff(231,plain,
% 0.23/0.59 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | (vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56) | visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)))),
% 0.23/0.59 inference(quant_inst,[status(thm)],[])).
% 0.23/0.59 tff(232,plain,
% 0.23/0.59 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) | visFreeVar(Vx, Ve) | (~vtcheck(VC, Ve, VT)))) | visFreeVar(Vy!52, Ve!53) | (~vtcheck(VC!55, Ve!53, VT!56)) | vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56)),
% 0.23/0.59 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.23/0.59 tff(233,plain,
% 0.23/0.59 (vtcheck(vbind(Vy!52, VS!51, VC!55), Ve!53, VT!56)),
% 0.23/0.59 inference(unit_resolution,[status(thm)],[232, 226, 108, 213])).
% 0.23/0.59 tff(234,plain,
% 0.23/0.59 ($false),
% 0.23/0.59 inference(unit_resolution,[status(thm)],[233, 212])).
% 0.23/0.59 % SZS output end Proof
% 0.23/0.59 % E exiting
%------------------------------------------------------------------------------