%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN326-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.21s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN326-1 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.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 12:32:17 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.21/0.37 % SZS status Unsatisfiable
% 0.21/0.37 % SZS output start Proof
% 0.21/0.37 tff(f_type, type, (
% 0.21/0.37 f: ( $i * $i ) > $o)).
% 0.21/0.37 tff(z_type, type, (
% 0.21/0.37 z: $i > $i)).
% 0.21/0.37 tff(y_type, type, (
% 0.21/0.37 y: $i > $i)).
% 0.21/0.37 tff(elem_0_type, type, (
% 0.21/0.37 elem_0: $i)).
% 0.21/0.37 tff(h_type, type, (
% 0.21/0.37 h: $i > $o)).
% 0.21/0.37 tff(g_type, type, (
% 0.21/0.37 g: $i > $o)).
% 0.21/0.37 tff(1,plain,
% 0.21/0.37 (^[X: $i] : refl((~f(z(X), z(X))) <=> (~f(z(X), z(X))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(2,plain,
% 0.21/0.37 (![X: $i] : (~f(z(X), z(X))) <=> ![X: $i] : (~f(z(X), z(X)))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.37 tff(3,plain,
% 0.21/0.37 (![X: $i] : (~f(z(X), z(X))) <=> ![X: $i] : (~f(z(X), z(X)))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(4,axiom,(![X: $i] : (~f(z(X), z(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.21/0.37 tff(5,plain,
% 0.21/0.37 (![X: $i] : (~f(z(X), z(X)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.37 tff(6,plain,(
% 0.21/0.37 ![X: $i] : (~f(z(X), z(X)))),
% 0.21/0.37 inference(skolemize,[status(sab)],[5])).
% 0.21/0.37 tff(7,plain,
% 0.21/0.37 (![X: $i] : (~f(z(X), z(X)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.37 tff(8,plain,
% 0.21/0.37 ((~![X: $i] : (~f(z(X), z(X)))) | (~f(z(elem!0), z(elem!0)))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(9,plain,
% 0.21/0.37 (~f(z(elem!0), z(elem!0))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.37 tff(10,plain,
% 0.21/0.37 (^[X: $i] : refl((g(y(X)) | f(X, X)) <=> (g(y(X)) | f(X, X)))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(11,plain,
% 0.21/0.37 (![X: $i] : (g(y(X)) | f(X, X)) <=> ![X: $i] : (g(y(X)) | f(X, X))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.37 tff(12,plain,
% 0.21/0.37 (![X: $i] : (g(y(X)) | f(X, X)) <=> ![X: $i] : (g(y(X)) | f(X, X))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(13,axiom,(![X: $i] : (g(y(X)) | f(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.21/0.37 tff(14,plain,
% 0.21/0.37 (![X: $i] : (g(y(X)) | f(X, X))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.37 tff(15,plain,(
% 0.21/0.37 ![X: $i] : (g(y(X)) | f(X, X))),
% 0.21/0.37 inference(skolemize,[status(sab)],[14])).
% 0.21/0.37 tff(16,plain,
% 0.21/0.37 (![X: $i] : (g(y(X)) | f(X, X))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.37 tff(17,plain,
% 0.21/0.37 (((~![X: $i] : (g(y(X)) | f(X, X))) | (g(y(z(elem!0))) | f(z(elem!0), z(elem!0)))) <=> ((~![X: $i] : (g(y(X)) | f(X, X))) | g(y(z(elem!0))) | f(z(elem!0), z(elem!0)))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(18,plain,
% 0.21/0.37 ((~![X: $i] : (g(y(X)) | f(X, X))) | (g(y(z(elem!0))) | f(z(elem!0), z(elem!0)))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(19,plain,
% 0.21/0.37 ((~![X: $i] : (g(y(X)) | f(X, X))) | g(y(z(elem!0))) | f(z(elem!0), z(elem!0))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.37 tff(20,plain,
% 0.21/0.37 (g(y(z(elem!0)))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.21/0.37 tff(21,plain,
% 0.21/0.37 (^[X: $i] : refl((h(z(X)) | (~g(X))) <=> (h(z(X)) | (~g(X))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(22,plain,
% 0.21/0.37 (![X: $i] : (h(z(X)) | (~g(X))) <=> ![X: $i] : (h(z(X)) | (~g(X)))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.37 tff(23,plain,
% 0.21/0.37 (![X: $i] : (h(z(X)) | (~g(X))) <=> ![X: $i] : (h(z(X)) | (~g(X)))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(24,plain,
% 0.21/0.37 (^[X: $i] : rewrite(((~g(X)) | h(z(X))) <=> (h(z(X)) | (~g(X))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(25,plain,
% 0.21/0.37 (![X: $i] : ((~g(X)) | h(z(X))) <=> ![X: $i] : (h(z(X)) | (~g(X)))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.37 tff(26,axiom,(![X: $i] : ((~g(X)) | h(z(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.21/0.37 tff(27,plain,
% 0.21/0.37 (![X: $i] : (h(z(X)) | (~g(X)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.37 tff(28,plain,
% 0.21/0.37 (![X: $i] : (h(z(X)) | (~g(X)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.37 tff(29,plain,(
% 0.21/0.37 ![X: $i] : (h(z(X)) | (~g(X)))),
% 0.21/0.37 inference(skolemize,[status(sab)],[28])).
% 0.21/0.37 tff(30,plain,
% 0.21/0.37 (![X: $i] : (h(z(X)) | (~g(X)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.37 tff(31,plain,
% 0.21/0.37 (((~![X: $i] : (h(z(X)) | (~g(X)))) | (h(z(y(z(elem!0)))) | (~g(y(z(elem!0)))))) <=> ((~![X: $i] : (h(z(X)) | (~g(X)))) | h(z(y(z(elem!0)))) | (~g(y(z(elem!0)))))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 ((~![X: $i] : (h(z(X)) | (~g(X)))) | (h(z(y(z(elem!0)))) | (~g(y(z(elem!0)))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 ((~![X: $i] : (h(z(X)) | (~g(X)))) | h(z(y(z(elem!0)))) | (~g(y(z(elem!0))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (h(z(y(z(elem!0))))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 (^[X: $i] : refl(((~h(X)) | f(X, X)) <=> ((~h(X)) | f(X, X)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 (![X: $i] : ((~h(X)) | f(X, X)) <=> ![X: $i] : ((~h(X)) | f(X, X))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (![X: $i] : ((~h(X)) | f(X, X)) <=> ![X: $i] : ((~h(X)) | f(X, X))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(38,axiom,(![X: $i] : ((~h(X)) | f(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.21/0.38 tff(39,plain,
% 0.21/0.38 (![X: $i] : ((~h(X)) | f(X, X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.38 tff(40,plain,(
% 0.21/0.38 ![X: $i] : ((~h(X)) | f(X, X))),
% 0.21/0.38 inference(skolemize,[status(sab)],[39])).
% 0.21/0.38 tff(41,plain,
% 0.21/0.38 (![X: $i] : ((~h(X)) | f(X, X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.38 tff(42,plain,
% 0.21/0.38 (((~![X: $i] : ((~h(X)) | f(X, X))) | ((~h(z(y(z(elem!0))))) | f(z(y(z(elem!0))), z(y(z(elem!0)))))) <=> ((~![X: $i] : ((~h(X)) | f(X, X))) | (~h(z(y(z(elem!0))))) | f(z(y(z(elem!0))), z(y(z(elem!0)))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(43,plain,
% 0.21/0.38 ((~![X: $i] : ((~h(X)) | f(X, X))) | ((~h(z(y(z(elem!0))))) | f(z(y(z(elem!0))), z(y(z(elem!0)))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(44,plain,
% 0.21/0.38 ((~![X: $i] : ((~h(X)) | f(X, X))) | (~h(z(y(z(elem!0))))) | f(z(y(z(elem!0))), z(y(z(elem!0))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.38 tff(45,plain,
% 0.21/0.38 (f(z(y(z(elem!0))), z(y(z(elem!0))))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[44, 41, 34])).
% 0.21/0.38 tff(46,plain,
% 0.21/0.38 ((~![X: $i] : (~f(z(X), z(X)))) | (~f(z(y(z(elem!0))), z(y(z(elem!0)))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[46, 7, 45])).
% 0.21/0.38 % SZS output end Proof
% 0.21/0.38 % E exiting
%------------------------------------------------------------------------------