%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG115+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:24:14 AM UTC 2025
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG115+4 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 03:26:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(tptp_fun_W1_36_type, type, (
% 0.21/0.47 tptp_fun_W1_36: $i)).
% 0.21/0.47 tff(sdtasdt0_type, type, (
% 0.21/0.47 sdtasdt0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(xb_type, type, (
% 0.21/0.47 xb: $i)).
% 0.21/0.47 tff(aElement0_type, type, (
% 0.21/0.47 aElement0: $i > $o)).
% 0.21/0.47 tff(aElementOf0_type, type, (
% 0.21/0.47 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.47 tff(slsdtgt0_type, type, (
% 0.21/0.47 slsdtgt0: $i > $i)).
% 0.21/0.47 tff(xu_type, type, (
% 0.21/0.47 xu: $i)).
% 0.21/0.47 tff(sdtpldt0_type, type, (
% 0.21/0.47 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_W0_37_type, type, (
% 0.21/0.47 tptp_fun_W0_37: $i)).
% 0.21/0.47 tff(xa_type, type, (
% 0.21/0.47 xa: $i)).
% 0.21/0.47 tff(xI_type, type, (
% 0.21/0.47 xI: $i)).
% 0.21/0.47 tff(sz00_type, type, (
% 0.21/0.47 sz00: $i)).
% 0.21/0.47 tff(iLess0_type, type, (
% 0.21/0.47 iLess0: ( $i * $i ) > $o)).
% 0.21/0.47 tff(sbrdtbr0_type, type, (
% 0.21/0.47 sbrdtbr0: $i > $i)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : rewrite(((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) <=> (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.47 tff(4,axiom,(((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))) & ![W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => (~iLess0(sbrdtbr0(W0), sbrdtbr0(xu))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2273')).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 ((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))),
% 0.21/0.47 inference(and_elim,[status(thm)],[4])).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)),
% 0.21/0.47 inference(and_elim,[status(thm)],[5])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu))),
% 0.21/0.47 inference(and_elim,[status(thm)],[6])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.47 tff(10,plain,(
% 0.21/0.47 aElementOf0(W0!37, slsdtgt0(xa)) & aElementOf0(W1!36, slsdtgt0(xb)) & (sdtpldt0(W0!37, W1!36) = xu)),
% 0.21/0.47 inference(skolemize,[status(sab)],[9])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (aElementOf0(W1!36, slsdtgt0(xb))),
% 0.21/0.47 inference(and_elim,[status(thm)],[10])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 ((aElementOf0(W1!36, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36))))) | (~aElementOf0(W1!36, slsdtgt0(xb)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (aElementOf0(W1!36, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (aElementOf0(W0!37, slsdtgt0(xa))),
% 0.21/0.47 inference(and_elim,[status(thm)],[10])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 ((aElementOf0(W0!37, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37))))) | (~aElementOf0(W0!37, slsdtgt0(xa)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (aElementOf0(W0!37, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (sdtpldt0(W0!37, W1!36) = xu),
% 0.21/0.47 inference(and_elim,[status(thm)],[10])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (xu = sdtpldt0(W0!37, W1!36)),
% 0.21/0.47 inference(symmetry,[status(thm)],[17])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : refl(((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))) <=> ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))) <=> ![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : rewrite(((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))) <=> ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))) <=> ![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))) <=> ![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[22, 20])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite((aElement0(W2) & (sdtasdt0(xa, W2) = W0)) <=> (~((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0))))), ((~(aElement0(W2) & (sdtasdt0(xa, W2) = W0))) <=> (~(~((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0))))))), rewrite((~(~((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0))))) <=> ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))), ((~(aElement0(W2) & (sdtasdt0(xa, W2) = W0))) <=> ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))), (![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0))) <=> ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0))))), (((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))) <=> ((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))), rewrite(((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))) <=> (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0))))))), (((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))) <=> (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))))), trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite((aElement0(W2) & (sdtasdt0(xb, W2) = W1)) <=> (~((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))), ((~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))) <=> (~(~((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))), rewrite((~(~((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))) <=> ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))), ((~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))) <=> ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))), (![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))) <=> ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))), (((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) <=> ((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))), rewrite(((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))) <=> (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))))), (((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) <=> (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))), ((((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))) | ((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) | (~(xu = sdtpldt0(W0, W1)))) <=> ((~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))) | (~(xu = sdtpldt0(W0, W1)))))), rewrite(((~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))) | (~(xu = sdtpldt0(W0, W1)))) <=> ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))), ((((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))) | ((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) | (~(xu = sdtpldt0(W0, W1)))) <=> ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))) | ((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) | (~(xu = sdtpldt0(W0, W1)))) <=> ![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 ((~?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1)))) <=> (~?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 ((~?[W0: $i, W1: $i] : (((?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0)) | aElementOf0(W0, slsdtgt0(xa))) & (?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)) | aElementOf0(W1, slsdtgt0(xb)))) & (xu = sdtpldt0(W0, W1)))) <=> (~?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(28,axiom,(~?[W0: $i, W1: $i] : (((?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0)) | aElementOf0(W0, slsdtgt0(xa))) & (?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)) | aElementOf0(W1, slsdtgt0(xb)))) & (xu = sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (~?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (~?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (~?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (~?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : nnf_neg(nnf_neg(refl($oeq((~aElementOf0(W0, slsdtgt0(xa))), (~aElementOf0(W0, slsdtgt0(xa))))), nnf_neg(proof_bind(^[W2: $i] : refl($oeq((~(aElement0(W2) & (sdtasdt0(xa, W2) = W0))), (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))))), $oeq((~?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))), ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0))))), $oeq((~(aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0)))), ((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))))), nnf_neg(refl($oeq((~aElementOf0(W1, slsdtgt0(xb))), (~aElementOf0(W1, slsdtgt0(xb))))), nnf_neg(proof_bind(^[W2: $i] : refl($oeq((~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))), (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))))), $oeq((~?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))), ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))))), $oeq((~(aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))), ((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))))), refl($oeq((~(xu = sdtpldt0(W0, W1))), (~(xu = sdtpldt0(W0, W1))))), $oeq((~((aElementOf0(W0, slsdtgt0(xa)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W0))) & (aElementOf0(W1, slsdtgt0(xb)) | ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & (xu = sdtpldt0(W0, W1)))), (((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))) | ((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) | (~(xu = sdtpldt0(W0, W1))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(34,plain,(
% 0.21/0.47 ![W0: $i, W1: $i] : (((~aElementOf0(W0, slsdtgt0(xa))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W0)))) | ((~aElementOf0(W1, slsdtgt0(xb))) & ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) | (~(xu = sdtpldt0(W0, W1))))),
% 0.21/0.47 inference(nnf-neg,[status(sab)],[32, 33])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[34, 25])).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[35, 23])).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 (((~![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))) | ((~(xu = sdtpldt0(W0!37, W1!36))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36)))))))) <=> ((~![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))) | (~(xu = sdtpldt0(W0!37, W1!36))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 ((~![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))) | ((~(xu = sdtpldt0(W0!37, W1!36))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 ((~![W0: $i, W1: $i] : ((~(xu = sdtpldt0(W0, W1))) | (~(aElementOf0(W0, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0)))))) | (~(aElementOf0(W1, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1)))))))) | (~(xu = sdtpldt0(W0!37, W1!36))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | (~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[39, 36, 18, 16, 13])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------