%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM609+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:35 AM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM609+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 01:33:55 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(aElementOf0_type, type, (
% 0.20/0.47 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.47 tff(xP_type, type, (
% 0.20/0.47 xP: $i)).
% 0.20/0.47 tff(tptp_fun_W0_45_type, type, (
% 0.20/0.47 tptp_fun_W0_45: $i)).
% 0.20/0.47 tff(szmzizndt0_type, type, (
% 0.20/0.47 szmzizndt0: $i > $i)).
% 0.20/0.47 tff(xQ_type, type, (
% 0.20/0.47 xQ: $i)).
% 0.20/0.47 tff(aElement0_type, type, (
% 0.20/0.47 aElement0: $i > $o)).
% 0.20/0.47 tff(aSubsetOf0_type, type, (
% 0.20/0.47 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.47 tff(sdtlseqdt0_type, type, (
% 0.20/0.47 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.20/0.47 tff(aSet0_type, type, (
% 0.20/0.47 aSet0: $i > $o)).
% 0.20/0.47 tff(sdtmndt0_type, type, (
% 0.20/0.47 sdtmndt0: ( $i * $i ) > $i)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))) <=> (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 ((~![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ))) <=> (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(3,axiom,(~(![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ)) | aSubsetOf0(xP, xQ))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (~![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ))),
% 0.20/0.47 inference(or_elim,[status(thm)],[3])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.47 tff(9,plain,(
% 0.20/0.47 ~((~aElementOf0(W0!45, xP)) | aElementOf0(W0!45, xQ))),
% 0.20/0.47 inference(skolemize,[status(sab)],[8])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (~aElementOf0(W0!45, xQ)),
% 0.20/0.47 inference(or_elim,[status(thm)],[9])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))) | aElementOf0(W0!45, xQ)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 ((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (aElementOf0(W0!45, xP)),
% 0.20/0.47 inference(or_elim,[status(thm)],[9])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 ((((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))) <=> aElementOf0(W0!45, xP)) | (~((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ)))) | (~aElementOf0(W0!45, xP))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))) <=> aElementOf0(W0!45, xP)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[14, 13, 12])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (^[W0: $i] : refl((~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 (^[W0: $i] : trans(trans(monotonicity(rewrite((aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))))), ((aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> (aElementOf0(W0, xP) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))))))), rewrite((aElementOf0(W0, xP) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))), ((aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP))))), rewrite((~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))), ((aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (^[W0: $i] : rewrite((aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ))))) <=> (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.48 tff(23,axiom,(((aSet0(xP) & ![W0: $i] : (aElementOf0(W0, xQ) => sdtlseqdt0(szmzizndt0(xQ), W0))) & ![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ)))))) & (xP = sdtmndt0(xQ, szmzizndt0(xQ)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__5164')).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 ((aSet0(xP) & ![W0: $i] : (aElementOf0(W0, xQ) => sdtlseqdt0(szmzizndt0(xQ), W0))) & ![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ)))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[23])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ)))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[24])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.20/0.48 tff(28,plain,(
% 0.20/0.48 ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[27])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[28, 19])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 ((~![W0: $i] : (~(((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))) <=> aElementOf0(W0, xP)))) | (~(((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))) <=> aElementOf0(W0!45, xP)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[31, 30, 15])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------