%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM135+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:01:07 AM UTC 2025
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM135+1 : TPTP v9.0.0. Released v6.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 12:24:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(tptp_fun_Vx_53_type, type, (
% 0.21/0.45 tptp_fun_Vx_53: $i)).
% 0.21/0.45 tff(tptp_fun_Vy_51_type, type, (
% 0.21/0.45 tptp_fun_Vy_51: $i)).
% 0.21/0.45 tff(visFreeVar_type, type, (
% 0.21/0.45 visFreeVar: ( $i * $i ) > $o)).
% 0.21/0.45 tff(vvar_type, type, (
% 0.21/0.45 vvar: $i > $i)).
% 0.21/0.45 tff(vsomeType_type, type, (
% 0.21/0.45 vsomeType: $i > $i)).
% 0.21/0.45 tff(tptp_fun_VT2_50_type, type, (
% 0.21/0.45 tptp_fun_VT2_50: $i)).
% 0.21/0.45 tff(vlookup_type, type, (
% 0.21/0.45 vlookup: ( $i * $i ) > $i)).
% 0.21/0.45 tff(vbind_type, type, (
% 0.21/0.45 vbind: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_VC_54_type, type, (
% 0.21/0.45 tptp_fun_VC_54: $i)).
% 0.21/0.45 tff(tptp_fun_VT_55_type, type, (
% 0.21/0.45 tptp_fun_VT_55: $i)).
% 0.21/0.45 tff(tptp_fun_Vx_42_type, type, (
% 0.21/0.45 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(vtcheck_type, type, (
% 0.21/0.45 vtcheck: ( $i * $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_Ve_52_type, type, (
% 0.21/0.45 tptp_fun_Ve_52: $i)).
% 0.21/0.45 tff(vsubst_type, type, (
% 0.21/0.45 vsubst: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(vgetSomeType_type, type, (
% 0.21/0.45 vgetSomeType: $i > $i)).
% 0.21/0.45 tff(tptp_fun_VS_47_type, type, (
% 0.21/0.45 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_Ve2_48_type, type, (
% 0.21/0.45 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(varrow_type, type, (
% 0.21/0.45 varrow: ( $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_Ve1_49_type, type, (
% 0.21/0.45 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(vapp_type, type, (
% 0.21/0.45 vapp: ( $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_VT2_43_type, type, (
% 0.21/0.45 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_Ve2_45_type, type, (
% 0.21/0.45 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_VT1_44_type, type, (
% 0.21/0.45 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_Vx_46_type, type, (
% 0.21/0.45 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(vabs_type, type, (
% 0.21/0.45 vabs: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 (![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve) <=> ![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve) <=> ![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (![VOptTyp0: $i, RESULT: $i, Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve) <=> ![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (![VOptTyp0: $i, RESULT: $i, Ve: $i] : ((RESULT = Ve) | (~(RESULT = vgetSomeType(VOptTyp0))) | (~(VOptTyp0 = vsomeType(Ve)))) <=> ![VOptTyp0: $i, RESULT: $i, Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (![VOptTyp0: $i, RESULT: $i, Ve: $i] : ((RESULT = Ve) | (~(RESULT = vgetSomeType(VOptTyp0))) | (~(VOptTyp0 = vsomeType(Ve)))) <=> ![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(transitivity,[status(thm)],[4, 3])).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (^[VOptTyp0: $i, RESULT: $i, Ve: $i] : trans(monotonicity(rewrite(((RESULT = vgetSomeType(VOptTyp0)) => (RESULT = Ve)) <=> ((~(RESULT = vgetSomeType(VOptTyp0))) | (RESULT = Ve))), (((VOptTyp0 = vsomeType(Ve)) => ((RESULT = vgetSomeType(VOptTyp0)) => (RESULT = Ve))) <=> ((VOptTyp0 = vsomeType(Ve)) => ((~(RESULT = vgetSomeType(VOptTyp0))) | (RESULT = Ve))))), rewrite(((VOptTyp0 = vsomeType(Ve)) => ((~(RESULT = vgetSomeType(VOptTyp0))) | (RESULT = Ve))) <=> ((RESULT = Ve) | (~(RESULT = vgetSomeType(VOptTyp0))) | (~(VOptTyp0 = vsomeType(Ve))))), (((VOptTyp0 = vsomeType(Ve)) => ((RESULT = vgetSomeType(VOptTyp0)) => (RESULT = Ve))) <=> ((RESULT = Ve) | (~(RESULT = vgetSomeType(VOptTyp0))) | (~(VOptTyp0 = vsomeType(Ve))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (![VOptTyp0: $i, RESULT: $i, Ve: $i] : ((VOptTyp0 = vsomeType(Ve)) => ((RESULT = vgetSomeType(VOptTyp0)) => (RESULT = Ve))) <=> ![VOptTyp0: $i, RESULT: $i, Ve: $i] : ((RESULT = Ve) | (~(RESULT = vgetSomeType(VOptTyp0))) | (~(VOptTyp0 = vsomeType(Ve))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (![VOptTyp0: $i, RESULT: $i, Ve: $i] : ((VOptTyp0 = vsomeType(Ve)) => ((RESULT = vgetSomeType(VOptTyp0)) => (RESULT = Ve))) <=> ![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(transitivity,[status(thm)],[7, 5])).
% 0.21/0.45 tff(9,axiom,(![VOptTyp0: $i, RESULT: $i, Ve: $i] : ((VOptTyp0 = vsomeType(Ve)) => ((RESULT = vgetSomeType(VOptTyp0)) => (RESULT = Ve)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','getSomeType0')).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.21/0.45 tff(12,plain,(
% 0.21/0.45 ![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(skolemize,[status(sab)],[11])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 ((~![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)) | (vgetSomeType(vsomeType(VT2!50)) = VT2!50)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (vgetSomeType(vsomeType(VT2!50)) = VT2!50),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (^[VC: $i, Vy: $i, VTy: $i] : refl((vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy)) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(transitivity,[status(thm)],[20, 19])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (^[VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : trans(monotonicity(trans(monotonicity(rewrite(((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))) <=> ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vsomeType(VTy)))), (((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy)))) <=> ((Vx = Vy) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vsomeType(VTy)))))), rewrite(((Vx = Vy) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vsomeType(VTy)))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)))), (((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy)))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> ![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : ((RESULT = vsomeType(VTy)) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy))))) <=> ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(transitivity,[status(thm)],[23, 21])).
% 0.21/0.45 tff(25,axiom,(![VC: $i, Vx: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, VTy: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((Vx = Vy) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vsomeType(VTy)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','lookup1')).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.21/0.45 tff(28,plain,(
% 0.21/0.45 ![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(skolemize,[status(sab)],[27])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 ((~![VC: $i, Vy: $i, VTy: $i] : (vlookup(Vy, vbind(Vy, VTy, VC)) = vsomeType(VTy))) | (vlookup(Vx!53, vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT!55))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (vlookup(Vx!53, vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT!55)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.45 tff(32,assumption,(~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50))))), introduced(assumption)).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50)))) | (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50)))) | (vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.21/0.45 tff(37,assumption,(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))), introduced(assumption)).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51)),
% 0.21/0.45 inference(symmetry,[status(thm)],[37])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50) <=> vtcheck(VC!54, vvar(Vy!51), VT2!50)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (vtcheck(VC!54, vvar(Vy!51), VT2!50) <=> vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50)),
% 0.21/0.45 inference(symmetry,[status(thm)],[39])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 ((~vtcheck(VC!54, vvar(Vy!51), VT2!50)) <=> (~vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[40])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 ((Vx!53 = tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) <=> (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53)),
% 0.21/0.45 inference(commutativity,[status(thm)],[])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 (^[VVar0: $i, VVar1: $i] : refl((~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))) <=> (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))) <=> ![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 (^[VVar0: $i, VVar1: $i] : rewrite((((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(46,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> ![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.45 tff(47,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) <=> ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (^[VVar0: $i, VVar1: $i] : rewrite((((vvar(VVar0) = vvar(VVar1)) => (VVar0 = VVar1)) & ((VVar0 = VVar1) => (vvar(VVar0) = vvar(VVar1)))) <=> (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((vvar(VVar0) = vvar(VVar1)) => (VVar0 = VVar1)) & ((VVar0 = VVar1) => (vvar(VVar0) = vvar(VVar1)))) <=> ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.45 tff(50,axiom,(![VVar0: $i, VVar1: $i] : (((vvar(VVar0) = vvar(VVar1)) => (VVar0 = VVar1)) & ((VVar0 = VVar1) => (vvar(VVar0) = vvar(VVar1))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''EQ-var'')).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.21/0.45 tff(53,plain,(
% 0.21/0.45 ![VVar0: $i, VVar1: $i] : (((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)) & ((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[52])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 ((~![VVar0: $i, VVar1: $i] : (~((~((~(VVar0 = VVar1)) | (vvar(VVar0) = vvar(VVar1)))) | (~((~(vvar(VVar0) = vvar(VVar1))) | (VVar0 = VVar1)))))) | (~((~((~(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)) | (vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51)))) | (~((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 (~((~((~(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)) | (vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51)))) | (~((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (((~((~(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)) | (vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51)))) | (~((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)))) | ((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 ((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 ((~((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51))) | (~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 ((~((~(vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[60, 38])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vy!51),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[61, 59])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (Vy!51 = tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))),
% 0.21/0.46 inference(symmetry,[status(thm)],[62])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 ((Vx!53 = Vy!51) <=> (Vx!53 = tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 ((Vx!53 = Vy!51) <=> (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53)),
% 0.21/0.46 inference(transitivity,[status(thm)],[64, 42])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 ((tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53) <=> (Vx!53 = Vy!51)),
% 0.21/0.46 inference(symmetry,[status(thm)],[65])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 ((~(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53)) <=> (~(Vx!53 = Vy!51))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[66])).
% 0.21/0.46 tff(68,assumption,(~(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53)), introduced(assumption)).
% 0.21/0.46 tff(69,plain,
% 0.21/0.46 (~(Vx!53 = Vy!51)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.46 tff(70,plain,
% 0.21/0.46 (^[Ve: $i, Vx: $i, Vy: $i] : refl(((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy))) <=> ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(71,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy))) <=> ![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.46 tff(72,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy))) <=> ![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (^[Ve: $i, Vx: $i, Vy: $i] : rewrite(((vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)) | (Vx = Vy)) <=> ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, Vy: $i] : ((vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)) | (Vx = Vy)) <=> ![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)) | (Vx = Vy)) <=> ![Ve: $i, Vx: $i, Vy: $i] : ((vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)) | (Vx = Vy))),
% 0.21/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))))) <=> ![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)) | (Vx = Vy))),
% 0.21/0.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))))) <=> ![Ve: $i, Vx: $i, Vy: $i] : ((vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)) | (Vx = Vy))),
% 0.21/0.46 inference(transitivity,[status(thm)],[76, 75])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))))) <=> ![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[77, 74])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (^[Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : trans(monotonicity(rewrite((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) <=> ((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))), trans(monotonicity(rewrite(((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy))) <=> ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vvar(Vy)))), (((~(Vx = Vy)) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy)))) <=> ((~(Vx = Vy)) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vvar(Vy)))))), rewrite(((~(Vx = Vy)) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = vvar(Vy)))) <=> ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))))), (((~(Vx = Vy)) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy)))) <=> ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1)))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((~(Vx = Vy)) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy))))) <=> (((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))) => ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))))))), rewrite((((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))) => ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))))) <=> ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((~(Vx = Vy)) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy))))) <=> ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((~(Vx = Vy)) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy))))) <=> ![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((RESULT = vvar(Vy)) | (Vx = Vy) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((~(Vx = Vy)) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy))))) <=> ![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.46 tff(82,axiom,(![Ve: $i, Vx: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Vy: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((~(Vx = Vy)) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = vvar(Vy)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','subst1')).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[83, 72])).
% 0.21/0.46 tff(85,plain,(
% 0.21/0.46 ![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[84])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[85, 71])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (((~![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))) | ((Vx!53 = Vy!51) | (vsubst(Vx!53, Ve!52, vvar(Vy!51)) = vvar(Vy!51)))) <=> ((~![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))) | (Vx!53 = Vy!51) | (vsubst(Vx!53, Ve!52, vvar(Vy!51)) = vvar(Vy!51)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 ((~![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))) | ((Vx!53 = Vy!51) | (vsubst(Vx!53, Ve!52, vvar(Vy!51)) = vvar(Vy!51)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 ((~![Ve: $i, Vx: $i, Vy: $i] : ((Vx = Vy) | (vsubst(Vx, Ve, vvar(Vy)) = vvar(Vy)))) | (Vx!53 = Vy!51) | (vsubst(Vx!53, Ve!52, vvar(Vy!51)) = vvar(Vy!51))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 ((Vx!53 = Vy!51) | (vsubst(Vx!53, Ve!52, vvar(Vy!51)) = vvar(Vy!51))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (vsubst(Vx!53, Ve!52, vvar(Vy!51)) = vvar(Vy!51)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[90, 69])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50) <=> vtcheck(VC!54, vvar(Vy!51), VT2!50)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 ((~vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50)) <=> (~vtcheck(VC!54, vvar(Vy!51), VT2!50))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2))) <=> (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 ((~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2))) <=> (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(96,axiom,(~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2)) => vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-subst-var'')).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.21/0.47 tff(100,plain,
% 0.21/0.47 (~![VT: $i, VC: $i, Vx: $i, Ve: $i, Vy: $i, VT2: $i] : ((~(vtcheck(VC, Ve, VT) & vtcheck(vbind(Vx, VT, VC), vvar(Vy), VT2))) | vtcheck(VC, vsubst(Vx, Ve, vvar(Vy)), VT2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[99, 94])).
% 0.21/0.47 tff(101,plain,(
% 0.21/0.47 ~((~(vtcheck(VC!54, Ve!52, VT!55) & vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50))) | vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50))),
% 0.21/0.47 inference(skolemize,[status(sab)],[100])).
% 0.21/0.47 tff(102,plain,
% 0.21/0.47 (~vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50)),
% 0.21/0.47 inference(or_elim,[status(thm)],[101])).
% 0.21/0.47 tff(103,plain,
% 0.21/0.47 (~vtcheck(VC!54, vvar(Vy!51), VT2!50)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[102, 93])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (~vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[103, 41])).
% 0.21/0.47 tff(105,assumption,(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50)), introduced(assumption)).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 (^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : refl(((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 (^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : rewrite(((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy)) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)) | (Vx = Vy))),
% 0.21/0.47 inference(transitivity,[status(thm)],[112, 111])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[113, 110])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (^[VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite(((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))) <=> ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))), (((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))) <=> ((~(Vx = Vy)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))))), rewrite(((~(Vx = Vy)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vlookup(Vx, VC)))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))), (((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))), ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : ((RESULT = vlookup(Vx, VC)) | (Vx = Vy) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC))))) <=> ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[116, 114])).
% 0.21/0.47 tff(118,axiom,(![VTy: $i, Vy: $i, VVar0: $i, VCtx0: $i, RESULT: $i, Vx: $i, VC: $i] : (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) => ((~(Vx = Vy)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vlookup(Vx, VC)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','lookup2')).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[119, 108])).
% 0.21/0.47 tff(121,plain,(
% 0.21/0.47 ![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[120])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[121, 107])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | ((tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53) | (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54)))) <=> ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53) | (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | ((tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53) | (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 ((~![VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((Vx = Vy) | (vlookup(Vx, vbind(Vy, VTy, VC)) = vlookup(Vx, VC)))) | (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53) | (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 ((tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53) | (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[126, 68])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54))),
% 0.21/0.47 inference(symmetry,[status(thm)],[127])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54) = vsomeType(VT2!50)),
% 0.21/0.47 inference(transitivity,[status(thm)],[128, 105])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (^[VC: $i, Vx: $i, VT: $i] : refl(((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)) <=> ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)) <=> ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)) <=> ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (^[VC: $i, Vx: $i, VT: $i] : rewrite(((vlookup(Vx, VC) = vsomeType(VT)) => vtcheck(VC, vvar(Vx), VT)) <=> ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, VT: $i] : ((vlookup(Vx, VC) = vsomeType(VT)) => vtcheck(VC, vvar(Vx), VT)) <=> ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.47 tff(135,axiom,(![VC: $i, Vx: $i, VT: $i] : ((vlookup(Vx, VC) = vsomeType(VT)) => vtcheck(VC, vvar(Vx), VT))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''T-var'')).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.47 tff(138,plain,(
% 0.21/0.47 ![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.47 inference(skolemize,[status(sab)],[137])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | ((~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54) = vsomeType(VT2!50))) | vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50))) <=> ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54) = vsomeType(VT2!50))) | vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | ((~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54) = vsomeType(VT2!50))) | vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 ((~![VC: $i, Vx: $i, VT: $i] : ((~(vlookup(Vx, VC) = vsomeType(VT))) | vtcheck(VC, vvar(Vx), VT))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VC!54) = vsomeType(VT2!50))) | vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (vtcheck(VC!54, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))), VT2!50)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[142, 139, 129])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[143, 104])).
% 0.21/0.47 tff(145,plain,((tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53) | (~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)) = Vx!53),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[145, 36, 34])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 (Vx!53 = tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))),
% 0.21/0.47 inference(symmetry,[status(thm)],[146])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (vlookup(Vx!53, vbind(Vx!53, VT!55, VC!54)) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vlookup(Vx!53, vbind(Vx!53, VT!55, VC!54))),
% 0.21/0.47 inference(symmetry,[status(thm)],[148])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 (vsomeType(VT2!50) = vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54))),
% 0.21/0.47 inference(symmetry,[status(thm)],[34])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (vsomeType(VT2!50) = vsomeType(VT!55)),
% 0.21/0.47 inference(transitivity,[status(thm)],[150, 149, 31])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (vgetSomeType(vsomeType(VT2!50)) = vgetSomeType(vsomeType(VT!55))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (vgetSomeType(vsomeType(VT!55)) = vgetSomeType(vsomeType(VT2!50))),
% 0.21/0.48 inference(symmetry,[status(thm)],[152])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 ((~![Ve: $i] : (vgetSomeType(vsomeType(Ve)) = Ve)) | (vgetSomeType(vsomeType(VT!55)) = VT!55)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (vgetSomeType(vsomeType(VT!55)) = VT!55),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[154, 13])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 (VT!55 = vgetSomeType(vsomeType(VT!55))),
% 0.21/0.48 inference(symmetry,[status(thm)],[155])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 (VT!55 = VT2!50),
% 0.21/0.48 inference(transitivity,[status(thm)],[156, 153, 15])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))) = vvar(Vy!51)),
% 0.21/0.48 inference(symmetry,[status(thm)],[36])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (vsubst(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), Ve!52, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))) = vsubst(Vx!53, Ve!52, vvar(Vy!51))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[146, 158])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (^[Vy: $i, Ve: $i] : refl((vsubst(Vy, Ve, vvar(Vy)) = Ve) <=> (vsubst(Vy, Ve, vvar(Vy)) = Ve))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 (![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve) <=> ![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 (![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve) <=> ![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 (![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve) <=> ![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))))) <=> ![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))))) <=> ![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(transitivity,[status(thm)],[164, 163])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 (^[Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : trans(monotonicity(rewrite((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) <=> ((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))), trans(monotonicity(rewrite(((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve)) <=> ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = Ve))), (((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve))) <=> ((Vx = Vy) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = Ve))))), rewrite(((Vx = Vy) => ((~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (RESULT = Ve))) <=> ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)))), (((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve))) <=> ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve)))) <=> (((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))) => ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)))))), rewrite((((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy))) => ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)))) <=> ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))))), (((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve)))) <=> ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve)))) <=> ![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : ((RESULT = Ve) | (~(RESULT = vsubst(VVar0, VExp0, VExp1))) | (~(Vx = Vy)) | (~((VVar0 = Vx) & (VExp0 = Ve) & (VExp1 = vvar(Vy)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[166])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve)))) <=> ![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(transitivity,[status(thm)],[167, 165])).
% 0.21/0.48 tff(169,axiom,(![Vx: $i, Vy: $i, VVar0: $i, VExp0: $i, VExp1: $i, RESULT: $i, Ve: $i] : ((((VVar0 = Vx) & (VExp0 = Ve)) & (VExp1 = vvar(Vy))) => ((Vx = Vy) => ((RESULT = vsubst(VVar0, VExp0, VExp1)) => (RESULT = Ve))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','subst0')).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 (![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[170, 162])).
% 0.21/0.48 tff(172,plain,(
% 0.21/0.48 ![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(skolemize,[status(sab)],[171])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[172, 161])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 ((~![Vy: $i, Ve: $i] : (vsubst(Vy, Ve, vvar(Vy)) = Ve)) | (vsubst(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), Ve!52, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))) = Ve!52)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 (vsubst(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), Ve!52, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))) = Ve!52),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 (Ve!52 = vsubst(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), Ve!52, vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(symmetry,[status(thm)],[175])).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 (Ve!52 = vsubst(Vx!53, Ve!52, vvar(Vy!51))),
% 0.21/0.48 inference(transitivity,[status(thm)],[176, 159])).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 (vtcheck(VC!54, Ve!52, VT!55) <=> vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[177, 157])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 (vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50) <=> vtcheck(VC!54, Ve!52, VT!55)),
% 0.21/0.48 inference(symmetry,[status(thm)],[178])).
% 0.21/0.48 tff(180,plain,
% 0.21/0.48 ((~vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50)) <=> (~vtcheck(VC!54, Ve!52, VT!55))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[179])).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 (~vtcheck(VC!54, Ve!52, VT!55)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[102, 180])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 (vtcheck(VC!54, Ve!52, VT!55) & vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)),
% 0.21/0.48 inference(or_elim,[status(thm)],[101])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 (vtcheck(VC!54, Ve!52, VT!55)),
% 0.21/0.48 inference(and_elim,[status(thm)],[182])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[183, 181])).
% 0.21/0.48 tff(185,plain,((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(186,assumption,(Vy!51 = Vx!53), introduced(assumption)).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 (Vx!53 = Vy!51),
% 0.21/0.48 inference(symmetry,[status(thm)],[186])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 (vvar(Vx!53) = vvar(Vy!51)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[187])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 ((vvar(Vx!53) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))) <=> (vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 ((~(vvar(Vx!53) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) <=> (~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[189])).
% 0.21/0.48 tff(191,assumption,(vvar(Vx!53) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))), introduced(assumption)).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(195,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.48 tff(197,plain,(
% 0.21/0.48 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[196])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(Vx!53) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[199, 198, 191])).
% 0.21/0.48 tff(201,plain,(~(vvar(Vx!53) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[201, 190])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VT2!50))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 ((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VT2!50))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 ((vvar(Vx!53) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))) <=> (vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 ((~(vvar(Vx!53) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) <=> (~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[205])).
% 0.21/0.48 tff(207,assumption,(vvar(Vx!53) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))), introduced(assumption)).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[208])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(211,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'')).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.21/0.48 tff(213,plain,(
% 0.21/0.48 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[212])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(Vx!53) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(216,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[215, 214, 207])).
% 0.21/0.48 tff(217,plain,(~(vvar(Vx!53) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(218,plain,
% 0.21/0.48 (~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[217, 206])).
% 0.21/0.48 tff(219,plain,
% 0.21/0.48 (((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 ((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 (vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)),
% 0.21/0.48 inference(and_elim,[status(thm)],[182])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (^[Ve: $i, VT: $i, VC: $i] : refl(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(223,plain,
% 0.21/0.48 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[222])).
% 0.21/0.48 tff(224,plain,
% 0.21/0.48 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(rewrite(((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) <=> (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT)))))), rewrite(((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) <=> (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))))), rewrite(((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) <=> (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))), rewrite(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[224])).
% 0.21/0.48 tff(226,plain,
% 0.21/0.48 (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[226])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[229])).
% 0.21/0.49 tff(231,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'')).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.21/0.49 tff(234,plain,(
% 0.21/0.49 ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[233])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[235, 225])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[236, 223])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 (((~![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!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VT2!50))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))))) <=> ((~![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!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VT2!50))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 ((~![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!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VT2!50))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 ((~![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!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | (~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VT2!50))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 ((~((~(vvar(Vy!51) = vvar(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(vlookup(tptp_fun_Vx_42(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)) = vsomeType(VT2!50))))) | (~((~(vvar(Vy!51) = vabs(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~(VT2!50 = varrow(tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT1_44(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), vbind(Vx!53, VT!55, VC!54)), tptp_fun_Ve2_45(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VT2_43(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)))))) | (~((~(vvar(Vy!51) = vapp(tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve1_49(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), varrow(tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), VT2!50))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), tptp_fun_Ve2_48(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51)), tptp_fun_VS_47(vbind(Vx!53, VT!55, VC!54), VT2!50, vvar(Vy!51))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[240, 237, 221])).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[241, 220, 204, 185])).
% 0.21/0.50 tff(243,plain,(~(Vy!51 = Vx!53)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 ((Vy!51 = Vx!53) <=> (Vx!53 = Vy!51)),
% 0.21/0.50 inference(commutativity,[status(thm)],[])).
% 0.21/0.50 tff(245,plain,
% 0.21/0.50 ((~(Vy!51 = Vx!53)) <=> (~(Vx!53 = Vy!51))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[244])).
% 0.21/0.50 tff(246,plain,
% 0.21/0.50 (~(Vx!53 = Vy!51)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[243, 245])).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (vsubst(Vx!53, Ve!52, vvar(Vy!51)) = vvar(Vy!51)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[90, 246])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 (vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50) <=> vtcheck(VC!54, vvar(Vy!51), VT2!50)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[247])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 ((~vtcheck(VC!54, vsubst(Vx!53, Ve!52, vvar(Vy!51)), VT2!50)) <=> (~vtcheck(VC!54, vvar(Vy!51), VT2!50))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[248])).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 (~vtcheck(VC!54, vvar(Vy!51), VT2!50)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[102, 249])).
% 0.21/0.50 tff(251,plain,
% 0.21/0.50 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : refl((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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[251])).
% 0.21/0.50 tff(253,plain,
% 0.21/0.50 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) <=> (~(visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))), ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) <=> (~(~(visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))))), rewrite((~(~(visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))) <=> (visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))), ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) <=> (visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))))), (((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> ((visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)))), rewrite(((visFreeVar(Vx, Ve) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))), (((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[253])).
% 0.21/0.50 tff(255,plain,
% 0.21/0.50 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(256,plain,
% 0.21/0.50 (^[Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : rewrite((((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) => vtcheck(VC, Ve, VT)) <=> ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) => vtcheck(VC, Ve, VT)) <=> ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[256])).
% 0.21/0.50 tff(258,axiom,(![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT)) => vtcheck(VC, Ve, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''T-Strong'')).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.21/0.50 tff(261,plain,(
% 0.21/0.50 ![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : ((~((~visFreeVar(Vx, Ve)) & vtcheck(vbind(Vx, VS, VC), Ve, VT))) | vtcheck(VC, Ve, VT))),
% 0.21/0.50 inference(skolemize,[status(sab)],[260])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[261, 254])).
% 0.21/0.50 tff(263,plain,
% 0.21/0.50 (![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[262, 252])).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | ((~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 ((visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50))) <=> ((~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(266,plain,
% 0.21/0.50 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | ((~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[265])).
% 0.21/0.50 tff(267,plain,
% 0.21/0.50 (((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)))) <=> ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50))),
% 0.21/0.50 inference(transitivity,[status(thm)],[266, 264])).
% 0.21/0.50 tff(268,plain,
% 0.21/0.50 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(269,plain,
% 0.21/0.50 ((~![Vx: $i, VS: $i, VC: $i, Ve: $i, VT: $i] : (visFreeVar(Vx, Ve) | vtcheck(VC, Ve, VT) | (~vtcheck(vbind(Vx, VS, VC), Ve, VT)))) | (~vtcheck(vbind(Vx!53, VT!55, VC!54), vvar(Vy!51), VT2!50)) | visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.21/0.50 tff(270,plain,
% 0.21/0.50 (visFreeVar(Vx!53, vvar(Vy!51)) | vtcheck(VC!54, vvar(Vy!51), VT2!50)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[269, 263, 221])).
% 0.21/0.50 tff(271,plain,
% 0.21/0.50 (visFreeVar(Vx!53, vvar(Vy!51))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[270, 250])).
% 0.21/0.50 tff(272,plain,
% 0.21/0.50 ((~((~visFreeVar(Vx!53, vvar(Vy!51))) | (Vy!51 = Vx!53))) | (~visFreeVar(Vx!53, vvar(Vy!51))) | (Vy!51 = Vx!53)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(273,plain,
% 0.21/0.50 (~((~visFreeVar(Vx!53, vvar(Vy!51))) | (Vy!51 = Vx!53))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[272, 271, 243])).
% 0.21/0.50 tff(274,plain,
% 0.21/0.50 (((~((~(Vy!51 = Vx!53)) | visFreeVar(Vx!53, vvar(Vy!51)))) | (~((~visFreeVar(Vx!53, vvar(Vy!51))) | (Vy!51 = Vx!53)))) | ((~visFreeVar(Vx!53, vvar(Vy!51))) | (Vy!51 = Vx!53))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(275,plain,
% 0.21/0.50 ((~((~(Vy!51 = Vx!53)) | visFreeVar(Vx!53, vvar(Vy!51)))) | (~((~visFreeVar(Vx!53, vvar(Vy!51))) | (Vy!51 = Vx!53)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.21/0.50 tff(276,plain,
% 0.21/0.50 (^[Vx: $i, Vv: $i] : refl((~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))) <=> (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(277,plain,
% 0.21/0.50 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))) <=> ![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[276])).
% 0.21/0.50 tff(278,plain,
% 0.21/0.50 (^[Vx: $i, Vv: $i] : rewrite((((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(279,plain,
% 0.21/0.50 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[278])).
% 0.21/0.50 tff(280,plain,
% 0.21/0.50 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(281,plain,
% 0.21/0.50 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.50 tff(282,plain,
% 0.21/0.50 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.50 tff(283,plain,
% 0.21/0.50 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[282, 281])).
% 0.21/0.50 tff(284,plain,
% 0.21/0.50 (^[VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : trans(monotonicity(rewrite((((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))) <=> (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))), rewrite((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(285,plain,
% 0.21/0.50 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[284])).
% 0.21/0.50 tff(286,plain,
% 0.21/0.50 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[285, 283])).
% 0.21/0.50 tff(287,axiom,(![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','isFreeVar0')).
% 0.21/0.50 tff(288,plain,
% 0.21/0.50 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.21/0.50 tff(289,plain,
% 0.21/0.50 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[288, 280])).
% 0.21/0.50 tff(290,plain,(
% 0.21/0.50 ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[289])).
% 0.21/0.50 tff(291,plain,
% 0.21/0.50 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[290, 279])).
% 0.21/0.50 tff(292,plain,
% 0.21/0.50 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[291, 277])).
% 0.21/0.50 tff(293,plain,
% 0.21/0.50 ((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | (~((~((~(Vy!51 = Vx!53)) | visFreeVar(Vx!53, vvar(Vy!51)))) | (~((~visFreeVar(Vx!53, vvar(Vy!51))) | (Vy!51 = Vx!53)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(294,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[293, 292, 275])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------