%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM606+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 0.53s 0.69s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : NUM606+3 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 01:33:40 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.53/0.69 % SZS status Theorem
% 0.53/0.69 % SZS output start Proof
% 0.53/0.69 tff(aElementOf0_type, type, (
% 0.53/0.69 aElementOf0: ( $i * $i ) > $o)).
% 0.53/0.69 tff(xS_type, type, (
% 0.53/0.69 xS: $i)).
% 0.53/0.69 tff(tptp_fun_W0_44_type, type, (
% 0.53/0.69 tptp_fun_W0_44: $i)).
% 0.53/0.69 tff(szNzAzT0_type, type, (
% 0.53/0.69 szNzAzT0: $i)).
% 0.53/0.69 tff(xQ_type, type, (
% 0.53/0.69 xQ: $i)).
% 0.53/0.69 tff(aSubsetOf0_type, type, (
% 0.53/0.69 aSubsetOf0: ( $i * $i ) > $o)).
% 0.53/0.69 tff(aSet0_type, type, (
% 0.53/0.69 aSet0: $i > $o)).
% 0.53/0.69 tff(isCountable0_type, type, (
% 0.53/0.69 isCountable0: $i > $o)).
% 0.53/0.69 tff(xO_type, type, (
% 0.53/0.69 xO: $i)).
% 0.53/0.69 tff(xK_type, type, (
% 0.53/0.69 xK: $i)).
% 0.53/0.69 tff(sbrdtbr0_type, type, (
% 0.53/0.69 sbrdtbr0: $i > $i)).
% 0.53/0.69 tff(slbdtsldtrb0_type, type, (
% 0.53/0.69 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.53/0.69 tff(1,plain,
% 0.53/0.69 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(2,plain,
% 0.53/0.69 ((~![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, szNzAzT0))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(3,axiom,(~(![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, szNzAzT0)) | aSubsetOf0(xQ, szNzAzT0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.53/0.69 tff(4,plain,
% 0.53/0.69 (~![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(or_elim,[status(thm)],[3])).
% 0.53/0.69 tff(5,plain,
% 0.53/0.69 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.53/0.69 tff(6,plain,
% 0.53/0.69 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.53/0.69 tff(7,plain,
% 0.53/0.69 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.53/0.69 tff(8,plain,
% 0.53/0.69 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.53/0.69 tff(9,plain,(
% 0.53/0.69 ~((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, szNzAzT0))),
% 0.53/0.69 inference(skolemize,[status(sab)],[8])).
% 0.53/0.69 tff(10,plain,
% 0.53/0.69 (~aElementOf0(W0!44, szNzAzT0)),
% 0.53/0.69 inference(or_elim,[status(thm)],[9])).
% 0.53/0.69 tff(11,plain,
% 0.53/0.69 (^[W0: $i] : refl(((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)) <=> ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(12,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[11])).
% 0.53/0.69 tff(13,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(14,plain,
% 0.53/0.69 (^[W0: $i] : rewrite((aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0)) <=> ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(15,plain,
% 0.53/0.69 (![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0)) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[14])).
% 0.53/0.69 tff(16,axiom,(((aSet0(xS) & ![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))) & aSubsetOf0(xS, szNzAzT0)) & isCountable0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3435')).
% 0.53/0.69 tff(17,plain,
% 0.53/0.69 ((aSet0(xS) & ![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))) & aSubsetOf0(xS, szNzAzT0)),
% 0.53/0.69 inference(and_elim,[status(thm)],[16])).
% 0.53/0.69 tff(18,plain,
% 0.53/0.69 (aSet0(xS) & ![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(and_elim,[status(thm)],[17])).
% 0.53/0.69 tff(19,plain,
% 0.53/0.69 (![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(and_elim,[status(thm)],[18])).
% 0.53/0.69 tff(20,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.53/0.69 tff(21,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.53/0.69 tff(22,plain,(
% 0.53/0.69 ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(skolemize,[status(sab)],[21])).
% 0.53/0.69 tff(23,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.53/0.69 tff(24,plain,
% 0.53/0.69 (((~![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))) | ((~aElementOf0(W0!44, xS)) | aElementOf0(W0!44, szNzAzT0))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))) | (~aElementOf0(W0!44, xS)) | aElementOf0(W0!44, szNzAzT0))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(25,plain,
% 0.53/0.69 ((~![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))) | ((~aElementOf0(W0!44, xS)) | aElementOf0(W0!44, szNzAzT0))),
% 0.53/0.69 inference(quant_inst,[status(thm)],[])).
% 0.53/0.69 tff(26,plain,
% 0.53/0.69 ((~![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))) | (~aElementOf0(W0!44, xS)) | aElementOf0(W0!44, szNzAzT0)),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.53/0.69 tff(27,plain,
% 0.53/0.69 (~aElementOf0(W0!44, xS)),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.53/0.69 tff(28,plain,
% 0.53/0.69 (aElementOf0(W0!44, xQ)),
% 0.53/0.69 inference(or_elim,[status(thm)],[9])).
% 0.53/0.69 tff(29,plain,
% 0.53/0.69 (^[W0: $i] : refl(((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(30,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[29])).
% 0.53/0.69 tff(31,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(32,plain,
% 0.53/0.69 (^[W0: $i] : rewrite((aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(33,plain,
% 0.53/0.69 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[32])).
% 0.53/0.69 tff(34,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')).
% 0.53/0.69 tff(35,plain,
% 0.53/0.69 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)) & (sbrdtbr0(xQ) = xK)),
% 0.53/0.69 inference(and_elim,[status(thm)],[34])).
% 0.53/0.69 tff(36,plain,
% 0.53/0.69 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)),
% 0.53/0.69 inference(and_elim,[status(thm)],[35])).
% 0.53/0.69 tff(37,plain,
% 0.53/0.69 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.53/0.69 inference(and_elim,[status(thm)],[36])).
% 0.53/0.69 tff(38,plain,
% 0.53/0.69 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.53/0.69 inference(and_elim,[status(thm)],[37])).
% 0.53/0.69 tff(39,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.53/0.69 tff(40,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.53/0.69 tff(41,plain,(
% 0.53/0.69 ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.53/0.69 inference(skolemize,[status(sab)],[40])).
% 0.53/0.69 tff(42,plain,
% 0.53/0.69 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[41, 30])).
% 0.53/0.69 tff(43,plain,
% 0.53/0.69 (((~![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))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(44,plain,
% 0.53/0.69 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | ((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, xO))),
% 0.53/0.69 inference(quant_inst,[status(thm)],[])).
% 0.53/0.69 tff(45,plain,
% 0.53/0.69 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | (~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, xO)),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.53/0.69 tff(46,plain,
% 0.53/0.69 (aElementOf0(W0!44, xO)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[45, 42, 28])).
% 0.53/0.70 tff(47,plain,
% 0.53/0.70 (^[W0: $i] : refl(((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(48,plain,
% 0.53/0.70 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.53/0.70 inference(quant_intro,[status(thm)],[47])).
% 0.53/0.70 tff(49,plain,
% 0.53/0.70 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(50,plain,
% 0.53/0.70 (^[W0: $i] : rewrite((aElementOf0(W0, xO) => aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(51,plain,
% 0.53/0.70 (![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.53/0.70 inference(quant_intro,[status(thm)],[50])).
% 0.53/0.70 tff(52,axiom,(![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) & aSubsetOf0(xO, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4998')).
% 0.53/0.70 tff(53,plain,
% 0.53/0.70 (![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS))),
% 0.53/0.70 inference(and_elim,[status(thm)],[52])).
% 0.53/0.70 tff(54,plain,
% 0.53/0.70 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[53, 51])).
% 0.53/0.70 tff(55,plain,
% 0.53/0.70 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.53/0.70 tff(56,plain,(
% 0.53/0.70 ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.53/0.70 inference(skolemize,[status(sab)],[55])).
% 0.53/0.70 tff(57,plain,
% 0.53/0.70 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[56, 48])).
% 0.53/0.70 tff(58,plain,
% 0.53/0.70 (((~![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))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(59,plain,
% 0.53/0.70 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) | ((~aElementOf0(W0!44, xO)) | aElementOf0(W0!44, xS))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(60,plain,
% 0.53/0.70 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))) | (~aElementOf0(W0!44, xO)) | aElementOf0(W0!44, xS)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.53/0.70 tff(61,plain,
% 0.53/0.70 ($false),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[60, 57, 46, 27])).
% 0.53/0.70 % SZS output end Proof
% 0.53/0.71 % E exiting
%------------------------------------------------------------------------------