%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM607+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 05:21:34 AM UTC 2025
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM607+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % 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 01:34:10 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(aElementOf0_type, type, (
% 0.19/0.46 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(xO_type, type, (
% 0.19/0.46 xO: $i)).
% 0.19/0.46 tff(tptp_fun_W0_44_type, type, (
% 0.19/0.46 tptp_fun_W0_44: $i)).
% 0.19/0.46 tff(xQ_type, type, (
% 0.19/0.46 xQ: $i)).
% 0.19/0.46 tff(xS_type, type, (
% 0.19/0.46 xS: $i)).
% 0.19/0.46 tff(aSubsetOf0_type, type, (
% 0.19/0.46 aSubsetOf0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(szDzozmdt0_type, type, (
% 0.19/0.46 szDzozmdt0: $i > $i)).
% 0.19/0.46 tff(xc_type, type, (
% 0.19/0.46 xc: $i)).
% 0.19/0.46 tff(aSet0_type, type, (
% 0.19/0.46 aSet0: $i > $o)).
% 0.19/0.46 tff(xK_type, type, (
% 0.19/0.46 xK: $i)).
% 0.19/0.46 tff(sbrdtbr0_type, type, (
% 0.19/0.46 sbrdtbr0: $i > $i)).
% 0.19/0.46 tff(slbdtsldtrb0_type, type, (
% 0.19/0.46 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 ((~![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(3,axiom,(~((((![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS)) | aSubsetOf0(xQ, xS)) | ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) | aSubsetOf0(xQ, xS)) | aElementOf0(xQ, szDzozmdt0(xc)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (~(((![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS)) | aSubsetOf0(xQ, xS)) | ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) | aSubsetOf0(xQ, xS))),
% 0.19/0.46 inference(or_elim,[status(thm)],[3])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (~((![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS)) | aSubsetOf0(xQ, xS)) | ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS)))),
% 0.19/0.46 inference(or_elim,[status(thm)],[4])).
% 0.19/0.46 tff(6,plain,
% 0.19/0.46 (~(![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS)) | aSubsetOf0(xQ, xS))),
% 0.19/0.46 inference(or_elim,[status(thm)],[5])).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (~![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))),
% 0.19/0.46 inference(or_elim,[status(thm)],[6])).
% 0.19/0.46 tff(8,plain,
% 0.19/0.46 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.46 tff(11,plain,
% 0.19/0.46 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xS))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.19/0.46 tff(12,plain,(
% 0.19/0.46 ~((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, xS))),
% 0.19/0.46 inference(skolemize,[status(sab)],[11])).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (aElementOf0(W0!44, xQ)),
% 0.19/0.46 inference(or_elim,[status(thm)],[12])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (^[W0: $i] : refl(((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (^[W0: $i] : rewrite((aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.46 tff(19,axiom,((((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)) & (sbrdtbr0(xQ) = xK)) & aElementOf0(xQ, slbdtsldtrb0(xO, xK))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__5078')).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)) & (sbrdtbr0(xQ) = xK)),
% 0.19/0.46 inference(and_elim,[status(thm)],[19])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)),
% 0.19/0.47 inference(and_elim,[status(thm)],[20])).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.19/0.47 inference(and_elim,[status(thm)],[21])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.19/0.47 inference(and_elim,[status(thm)],[22])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.19/0.47 tff(26,plain,(
% 0.19/0.47 ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.19/0.47 inference(skolemize,[status(sab)],[25])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[26, 15])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 (((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | ((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, xO))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | (~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, xO))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | ((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, xO))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | (~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, xO)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (aElementOf0(W0!44, xO)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[30, 27, 13])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (~aElementOf0(W0!44, xS)),
% 0.19/0.47 inference(or_elim,[status(thm)],[12])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 (^[W0: $i] : refl(((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (^[W0: $i] : rewrite((aElementOf0(W0, xO) => aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.47 tff(38,axiom,(![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) & aSubsetOf0(xO, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4998')).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS))),
% 0.19/0.47 inference(and_elim,[status(thm)],[38])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[39, 37])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.47 tff(42,plain,(
% 0.19/0.47 ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.19/0.47 inference(skolemize,[status(sab)],[41])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[42, 34])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) | ((~aElementOf0(W0!44, xO)) | aElementOf0(W0!44, xS))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) | (~aElementOf0(W0!44, xO)) | aElementOf0(W0!44, xS))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) | ((~aElementOf0(W0!44, xO)) | aElementOf0(W0!44, xS))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) | (~aElementOf0(W0!44, xO)) | aElementOf0(W0!44, xS)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[46, 43, 32, 31])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------