%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM533+2 : 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 05:21:18 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM533+2 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:25:11 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(aElementOf0_type, type, (
% 0.11/0.37 aElementOf0: ( $i * $i ) > $o)).
% 0.11/0.37 tff(xB_type, type, (
% 0.11/0.37 xB: $i)).
% 0.11/0.37 tff(tptp_fun_W0_2_type, type, (
% 0.11/0.37 tptp_fun_W0_2: $i)).
% 0.11/0.37 tff(xA_type, type, (
% 0.11/0.37 xA: $i)).
% 0.11/0.37 tff(aSubsetOf0_type, type, (
% 0.11/0.37 aSubsetOf0: ( $i * $i ) > $o)).
% 0.11/0.37 tff(xC_type, type, (
% 0.11/0.37 xC: $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[W0: $i] : refl(((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) <=> ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) <=> ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) <=> ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((~((((![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xB)) & aSubsetOf0(xA, xB)) & ![W0: $i] : (aElementOf0(W0, xB) => aElementOf0(W0, xC))) & aSubsetOf0(xB, xC)) => (![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xC)) | aSubsetOf0(xA, xC)))) <=> (~(aSubsetOf0(xA, xC) | ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC)) | (~(![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) & aSubsetOf0(xA, xB) & ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) & aSubsetOf0(xB, xC)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,axiom,(~((((![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xB)) & aSubsetOf0(xA, xB)) & ![W0: $i] : (aElementOf0(W0, xB) => aElementOf0(W0, xC))) & aSubsetOf0(xB, xC)) => (![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xC)) | aSubsetOf0(xA, xC)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (~(aSubsetOf0(xA, xC) | ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC)) | (~(![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) & aSubsetOf0(xA, xB) & ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) & aSubsetOf0(xB, xC))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) & aSubsetOf0(xA, xB) & ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) & aSubsetOf0(xB, xC)),
% 0.11/0.37 inference(or_elim,[status(thm)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.11/0.37 inference(and_elim,[status(thm)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.11/0.37 tff(10,plain,(
% 0.11/0.37 ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.11/0.37 inference(skolemize,[status(sab)],[9])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))) <=> (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(or_elim,[status(thm)],[6])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.11/0.37 tff(17,plain,(
% 0.11/0.37 ~((~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xC))),
% 0.11/0.37 inference(skolemize,[status(sab)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (aElementOf0(W0!2, xA)),
% 0.11/0.37 inference(or_elim,[status(thm)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | ((~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | (~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | ((~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | (~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (aElementOf0(W0!2, xB)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (^[W0: $i] : refl(((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) <=> ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) <=> ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) <=> ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(and_elim,[status(thm)],[7])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.37 tff(28,plain,(
% 0.11/0.37 ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(skolemize,[status(sab)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (~aElementOf0(W0!2, xC)),
% 0.11/0.37 inference(or_elim,[status(thm)],[17])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | ((~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | (~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | ((~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | (~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[33, 30, 29, 22])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------