%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET044-5 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:24:58 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET044-5 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:06:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(element_type, type, (
% 0.12/0.38 element: ( $i * $i ) > $o)).
% 0.12/0.38 tff(a_type, type, (
% 0.12/0.38 a: $i)).
% 0.12/0.38 tff(f_type, type, (
% 0.12/0.38 f: $i > $i)).
% 0.12/0.38 tff(1,assumption,(element(f(a), f(a))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : refl(((~element(Y, X)) | (~element(Y, f(X)))) <=> ((~element(Y, X)) | (~element(Y, f(X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X)))) <=> ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X)))) <=> ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : rewrite(((~element(Y, f(X))) | (~element(Y, X))) <=> ((~element(Y, X)) | (~element(Y, f(X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~element(Y, f(X))) | (~element(Y, X))) <=> ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.38 tff(7,axiom,(![Y: $i, X: $i] : ((~element(Y, f(X))) | (~element(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,(
% 0.12/0.38 ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))) | ((~element(f(a), a)) | (~element(f(a), f(a))))) <=> ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))) | (~element(f(a), a)) | (~element(f(a), f(a))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))) | ((~element(f(a), a)) | (~element(f(a), f(a))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(Y, f(X))))) | (~element(f(a), a)) | (~element(f(a), f(a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~element(f(a), a)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 11, 1])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (^[X: $i] : refl(((~element(X, X)) | element(X, a)) <=> ((~element(X, X)) | element(X, a)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X: $i] : ((~element(X, X)) | element(X, a)) <=> ![X: $i] : ((~element(X, X)) | element(X, a))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![X: $i] : ((~element(X, X)) | element(X, a)) <=> ![X: $i] : ((~element(X, X)) | element(X, a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(19,axiom,(![X: $i] : ((~element(X, X)) | element(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![X: $i] : ((~element(X, X)) | element(X, a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,(
% 0.12/0.38 ![X: $i] : ((~element(X, X)) | element(X, a))),
% 0.12/0.38 inference(skolemize,[status(sab)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![X: $i] : ((~element(X, X)) | element(X, a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (((~![X: $i] : ((~element(X, X)) | element(X, a))) | ((~element(f(a), f(a))) | element(f(a), a))) <=> ((~![X: $i] : ((~element(X, X)) | element(X, a))) | (~element(f(a), f(a))) | element(f(a), a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![X: $i] : ((~element(X, X)) | element(X, a))) | ((~element(f(a), f(a))) | element(f(a), a))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![X: $i] : ((~element(X, X)) | element(X, a))) | (~element(f(a), f(a))) | element(f(a), a)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[25, 22, 1, 15])).
% 0.12/0.39 tff(27,plain,(~element(f(a), f(a))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (^[Y: $i, X: $i] : refl((element(Y, X) | element(Y, f(X))) <=> (element(Y, X) | element(Y, f(X))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X))) <=> ![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X))) <=> ![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,axiom,(![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,(
% 0.12/0.39 ![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (((~![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))) | (element(f(a), a) | element(f(a), f(a)))) <=> ((~![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))) | element(f(a), a) | element(f(a), f(a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))) | (element(f(a), a) | element(f(a), f(a)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : (element(Y, X) | element(Y, f(X)))) | element(f(a), a) | element(f(a), f(a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (element(f(a), a) | element(f(a), f(a))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (element(f(a), a)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 27])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (^[X: $i] : refl(((~element(X, a)) | element(X, X)) <=> ((~element(X, a)) | element(X, X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![X: $i] : ((~element(X, a)) | element(X, X)) <=> ![X: $i] : ((~element(X, a)) | element(X, X))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![X: $i] : ((~element(X, a)) | element(X, X)) <=> ![X: $i] : ((~element(X, a)) | element(X, X))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(43,axiom,(![X: $i] : ((~element(X, a)) | element(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![X: $i] : ((~element(X, a)) | element(X, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.39 tff(45,plain,(
% 0.12/0.39 ![X: $i] : ((~element(X, a)) | element(X, X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[44])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![X: $i] : ((~element(X, a)) | element(X, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (((~![X: $i] : ((~element(X, a)) | element(X, X))) | ((~element(f(a), a)) | element(f(a), f(a)))) <=> ((~![X: $i] : ((~element(X, a)) | element(X, X))) | (~element(f(a), a)) | element(f(a), f(a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 ((~![X: $i] : ((~element(X, a)) | element(X, X))) | ((~element(f(a), a)) | element(f(a), f(a)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ((~![X: $i] : ((~element(X, a)) | element(X, X))) | (~element(f(a), a)) | element(f(a), f(a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[49, 46, 27, 39])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------