%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN325-1 : TPTP v9.0.0. Released v1.2.0.
% 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 05:38:46 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN325-1 : TPTP v9.0.0. Released v1.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:29:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(g_type, type, (
% 0.20/0.37 g: $i > $o)).
% 0.20/0.37 tff(y_type, type, (
% 0.20/0.37 y: $i > $i)).
% 0.20/0.37 tff(elem_0_type, type, (
% 0.20/0.37 elem_0: $i)).
% 0.20/0.37 tff(f_type, type, (
% 0.20/0.37 f: ( $i * $i ) > $o)).
% 0.20/0.37 tff(1,assumption,(g(y(elem!0))), introduced(assumption)).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (^[X: $i] : refl((~g(y(X))) <=> (~g(y(X))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![X: $i] : (~g(y(X))) <=> ![X: $i] : (~g(y(X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![X: $i] : (~g(y(X))) <=> ![X: $i] : (~g(y(X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,axiom,(![X: $i] : (~g(y(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (![X: $i] : (~g(y(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.37 tff(7,plain,(
% 0.20/0.37 ![X: $i] : (~g(y(X)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[6])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![X: $i] : (~g(y(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 ((~![X: $i] : (~g(y(X)))) | (~g(y(elem!0)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.37 tff(11,plain,(~g(y(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (^[X: $i] : refl((g(X) | (~f(y(X), y(X)))) <=> (g(X) | (~f(y(X), y(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (![X: $i] : (g(X) | (~f(y(X), y(X)))) <=> ![X: $i] : (g(X) | (~f(y(X), y(X))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (![X: $i] : (g(X) | (~f(y(X), y(X)))) <=> ![X: $i] : (g(X) | (~f(y(X), y(X))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (^[X: $i] : rewrite(((~f(y(X), y(X))) | g(X)) <=> (g(X) | (~f(y(X), y(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![X: $i] : ((~f(y(X), y(X))) | g(X)) <=> ![X: $i] : (g(X) | (~f(y(X), y(X))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.37 tff(17,axiom,(![X: $i] : ((~f(y(X), y(X))) | g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![X: $i] : (g(X) | (~f(y(X), y(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (![X: $i] : (g(X) | (~f(y(X), y(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.37 tff(20,plain,(
% 0.20/0.37 ![X: $i] : (g(X) | (~f(y(X), y(X))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[19])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![X: $i] : (g(X) | (~f(y(X), y(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (((~![X: $i] : (g(X) | (~f(y(X), y(X))))) | (g(y(elem!0)) | (~f(y(y(elem!0)), y(y(elem!0)))))) <=> ((~![X: $i] : (g(X) | (~f(y(X), y(X))))) | g(y(elem!0)) | (~f(y(y(elem!0)), y(y(elem!0)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((~![X: $i] : (g(X) | (~f(y(X), y(X))))) | (g(y(elem!0)) | (~f(y(y(elem!0)), y(y(elem!0)))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 ((~![X: $i] : (g(X) | (~f(y(X), y(X))))) | g(y(elem!0)) | (~f(y(y(elem!0)), y(y(elem!0))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (~f(y(y(elem!0)), y(y(elem!0)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (^[X: $i] : refl((g(X) | f(X, X)) <=> (g(X) | f(X, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![X: $i] : (g(X) | f(X, X)) <=> ![X: $i] : (g(X) | f(X, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X: $i] : (g(X) | f(X, X)) <=> ![X: $i] : (g(X) | f(X, X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (^[X: $i] : rewrite((f(X, X) | g(X)) <=> (g(X) | f(X, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![X: $i] : (f(X, X) | g(X)) <=> ![X: $i] : (g(X) | f(X, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.38 tff(31,axiom,(![X: $i] : (f(X, X) | g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![X: $i] : (g(X) | f(X, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X: $i] : (g(X) | f(X, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.38 tff(34,plain,(
% 0.20/0.38 ![X: $i] : (g(X) | f(X, X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![X: $i] : (g(X) | f(X, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (((~![X: $i] : (g(X) | f(X, X))) | (g(y(y(elem!0))) | f(y(y(elem!0)), y(y(elem!0))))) <=> ((~![X: $i] : (g(X) | f(X, X))) | g(y(y(elem!0))) | f(y(y(elem!0)), y(y(elem!0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 ((~![X: $i] : (g(X) | f(X, X))) | (g(y(y(elem!0))) | f(y(y(elem!0)), y(y(elem!0))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~![X: $i] : (g(X) | f(X, X))) | g(y(y(elem!0))) | f(y(y(elem!0)), y(y(elem!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (g(y(y(elem!0)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~![X: $i] : (~g(y(X)))) | (~g(y(y(elem!0))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[40, 8, 39])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------