%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM551+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:21:22 AM UTC 2025
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM551+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:26:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(aElement0_type, type, (
% 0.18/0.39 aElement0: $i > $o)).
% 0.18/0.39 tff(tptp_fun_W0_14_type, type, (
% 0.18/0.39 tptp_fun_W0_14: $i)).
% 0.18/0.39 tff(aElementOf0_type, type, (
% 0.18/0.39 aElementOf0: ( $i * $i ) > $o)).
% 0.18/0.39 tff(xQ_type, type, (
% 0.18/0.39 xQ: $i)).
% 0.18/0.39 tff(slcrc0_type, type, (
% 0.18/0.39 slcrc0: $i)).
% 0.18/0.39 tff(xS_type, type, (
% 0.18/0.39 xS: $i)).
% 0.18/0.39 tff(aSet0_type, type, (
% 0.18/0.39 aSet0: $i > $o)).
% 0.18/0.39 tff(aSubsetOf0_type, type, (
% 0.18/0.39 aSubsetOf0: ( $i * $i ) > $o)).
% 0.18/0.39 tff(xk_type, type, (
% 0.18/0.39 xk: $i)).
% 0.18/0.39 tff(sbrdtbr0_type, type, (
% 0.18/0.39 sbrdtbr0: $i > $i)).
% 0.18/0.39 tff(slbdtsldtrb0_type, type, (
% 0.18/0.39 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.18/0.39 tff(xT_type, type, (
% 0.18/0.39 xT: $i)).
% 0.18/0.39 tff(sz00_type, type, (
% 0.18/0.39 sz00: $i)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 (^[W0: $i] : refl(((~aElement0(W0)) | (~aElementOf0(W0, xQ))) <=> ((~aElement0(W0)) | (~aElementOf0(W0, xQ))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ))) <=> ![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (^[W0: $i] : trans(monotonicity(rewrite((aElement0(W0) & aElementOf0(W0, xQ)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ))))), ((~(aElement0(W0) & aElementOf0(W0, xQ))) <=> (~(~((~aElement0(W0)) | (~aElementOf0(W0, xQ))))))), rewrite((~(~((~aElement0(W0)) | (~aElementOf0(W0, xQ))))) <=> ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))), ((~(aElement0(W0) & aElementOf0(W0, xQ))) <=> ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![W0: $i] : (~(aElement0(W0) & aElementOf0(W0, xQ))) <=> ![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 ((~?[W0: $i] : (aElement0(W0) & aElementOf0(W0, xQ))) <=> (~?[W0: $i] : (aElement0(W0) & aElementOf0(W0, xQ)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(6,axiom,(~?[W0: $i] : (aElement0(W0) & aElementOf0(W0, xQ))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (~?[W0: $i] : (aElement0(W0) & aElementOf0(W0, xQ))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (~?[W0: $i] : (aElement0(W0) & aElementOf0(W0, xQ))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (~?[W0: $i] : (aElement0(W0) & aElementOf0(W0, xQ))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (~?[W0: $i] : (aElement0(W0) & aElementOf0(W0, xQ))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 (^[W0: $i] : refl($oeq((~(aElement0(W0) & aElementOf0(W0, xQ))), (~(aElement0(W0) & aElementOf0(W0, xQ)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(12,plain,(
% 0.18/0.39 ![W0: $i] : (~(aElement0(W0) & aElementOf0(W0, xQ)))),
% 0.18/0.39 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (?[W0: $i] : aElementOf0(W0, xQ) <=> ?[W0: $i] : aElementOf0(W0, xQ)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(16,axiom,(~((~?[W0: $i] : aElementOf0(W0, xQ)) | (xQ = slcrc0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2313')).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (?[W0: $i] : aElementOf0(W0, xQ)),
% 0.18/0.39 inference(or_elim,[status(thm)],[16])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (?[W0: $i] : aElementOf0(W0, xQ)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.18/0.39 tff(19,plain,(
% 0.18/0.39 aElementOf0(W0!14, xQ)),
% 0.18/0.39 inference(skolemize,[status(sab)],[18])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (((~![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))) | ((~aElement0(W0!14)) | (~aElementOf0(W0!14, xQ)))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))) | (~aElement0(W0!14)) | (~aElementOf0(W0!14, xQ)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 ((~![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))) | ((~aElement0(W0!14)) | (~aElementOf0(W0!14, xQ)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 ((~![W0: $i] : ((~aElement0(W0)) | (~aElementOf0(W0, xQ)))) | (~aElement0(W0!14)) | (~aElementOf0(W0!14, xQ))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (~aElement0(W0!14)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[22, 19, 14])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (^[W0: $i] : refl(((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (^[W0: $i] : rewrite((aElementOf0(W0, xQ) => aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.39 tff(29,axiom,((((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)) & aElementOf0(xQ, slbdtsldtrb0(xS, xk))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2270')).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)),
% 0.18/0.39 inference(and_elim,[status(thm)],[29])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)),
% 0.18/0.39 inference(and_elim,[status(thm)],[30])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))),
% 0.18/0.39 inference(and_elim,[status(thm)],[31])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))),
% 0.18/0.39 inference(and_elim,[status(thm)],[32])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.18/0.39 tff(36,plain,(
% 0.18/0.39 ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.18/0.39 inference(skolemize,[status(sab)],[35])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 25])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))) | ((~aElementOf0(W0!14, xQ)) | aElementOf0(W0!14, xS))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))) | (~aElementOf0(W0!14, xQ)) | aElementOf0(W0!14, xS))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))) | ((~aElementOf0(W0!14, xQ)) | aElementOf0(W0!14, xS))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))) | (~aElementOf0(W0!14, xQ)) | aElementOf0(W0!14, xS)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (aElementOf0(W0!14, xS)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[40, 37, 19])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (aSet0(xS) <=> aSet0(xS)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(43,axiom,((aSet0(xS) & aSet0(xT)) & (~(xk = sz00))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2202_02')).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (aSet0(xS) & aSet0(xT)),
% 0.18/0.39 inference(and_elim,[status(thm)],[43])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (aSet0(xS)),
% 0.18/0.39 inference(and_elim,[status(thm)],[44])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (aSet0(xS)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[50, 48])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.39 tff(55,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.18/0.39 tff(58,plain,(
% 0.18/0.39 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[57])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[62, 59, 46])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(W0!14) | (~aElementOf0(W0!14, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(W0!14) | (~aElementOf0(W0!14, xS)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(W0!14) | (~aElementOf0(W0!14, xS)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(W0!14) | (~aElementOf0(W0!14, xS))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[66, 63, 41, 23])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------