%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM610+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 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM610+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % 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 01:34:25 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(aElementOf0_type, type, (
% 0.20/0.48 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(xQ_type, type, (
% 0.20/0.48 xQ: $i)).
% 0.20/0.48 tff(tptp_fun_W0_45_type, type, (
% 0.20/0.48 tptp_fun_W0_45: $i)).
% 0.20/0.48 tff(xP_type, type, (
% 0.20/0.48 xP: $i)).
% 0.20/0.48 tff(xO_type, type, (
% 0.20/0.48 xO: $i)).
% 0.20/0.48 tff(aSubsetOf0_type, type, (
% 0.20/0.48 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(aSet0_type, type, (
% 0.20/0.48 aSet0: $i > $o)).
% 0.20/0.48 tff(xK_type, type, (
% 0.20/0.48 xK: $i)).
% 0.20/0.48 tff(sbrdtbr0_type, type, (
% 0.20/0.48 sbrdtbr0: $i > $i)).
% 0.20/0.48 tff(slbdtsldtrb0_type, type, (
% 0.20/0.48 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xO))) <=> (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xO)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 ((~![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xO))) <=> (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xO)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,axiom,(~(![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xO)) | aSubsetOf0(xP, xO))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (~![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xO))),
% 0.20/0.48 inference(or_elim,[status(thm)],[3])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xO))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xO))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xO))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xO))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.48 tff(9,plain,(
% 0.20/0.48 ~((~aElementOf0(W0!45, xP)) | aElementOf0(W0!45, xO))),
% 0.20/0.48 inference(skolemize,[status(sab)],[8])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (aElementOf0(W0!45, xP)),
% 0.20/0.48 inference(or_elim,[status(thm)],[9])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (^[W0: $i] : refl(((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)) <=> ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (^[W0: $i] : rewrite((aElementOf0(W0, xP) => aElementOf0(W0, xQ)) <=> ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.48 tff(16,axiom,(![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ)) & aSubsetOf0(xP, xQ)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__5195')).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ))),
% 0.20/0.48 inference(and_elim,[status(thm)],[16])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.48 tff(20,plain,(
% 0.20/0.48 ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.48 inference(skolemize,[status(sab)],[19])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))) | ((~aElementOf0(W0!45, xP)) | aElementOf0(W0!45, xQ))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))) | (~aElementOf0(W0!45, xP)) | aElementOf0(W0!45, xQ))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))) | ((~aElementOf0(W0!45, xP)) | aElementOf0(W0!45, xQ))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))) | (~aElementOf0(W0!45, xP)) | aElementOf0(W0!45, xQ)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (aElementOf0(W0!45, xQ)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[24, 21, 10])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (~aElementOf0(W0!45, xO)),
% 0.20/0.49 inference(or_elim,[status(thm)],[9])).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 (^[W0: $i] : refl(((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (^[W0: $i] : rewrite((aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.49 tff(32,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')).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)) & (sbrdtbr0(xQ) = xK)),
% 0.20/0.49 inference(and_elim,[status(thm)],[32])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)),
% 0.20/0.49 inference(and_elim,[status(thm)],[33])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.20/0.49 inference(and_elim,[status(thm)],[34])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.20/0.49 inference(and_elim,[status(thm)],[35])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[37, 29])).
% 0.20/0.49 tff(39,plain,(
% 0.20/0.49 ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.20/0.49 inference(skolemize,[status(sab)],[38])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[39, 28])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | ((~aElementOf0(W0!45, xQ)) | aElementOf0(W0!45, xO))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | (~aElementOf0(W0!45, xQ)) | aElementOf0(W0!45, xO))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | ((~aElementOf0(W0!45, xQ)) | aElementOf0(W0!45, xO))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))) | (~aElementOf0(W0!45, xQ)) | aElementOf0(W0!45, xO)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[43, 40, 26, 25])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------