%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN319-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:38:44 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN319-1 : TPTP v9.0.0. Released v1.2.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.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 12:30:48 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(g_type, type, (
% 0.11/0.36 g: $i > $o)).
% 0.11/0.36 tff(z2_type, type, (
% 0.11/0.36 z2: ( $i * $i ) > $i)).
% 0.11/0.36 tff(elem_0_type, type, (
% 0.11/0.36 elem_0: $i)).
% 0.11/0.36 tff(h_type, type, (
% 0.11/0.36 h: $i > $o)).
% 0.11/0.36 tff(f_type, type, (
% 0.11/0.36 f: $i > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((~h(z2(X, Y))) <=> (~h(z2(X, Y))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (~h(z2(X, Y))) <=> ![Y: $i, X: $i] : (~h(z2(X, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (~h(z2(X, Y))) <=> ![Y: $i, X: $i] : (~h(z2(X, Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,axiom,(![Y: $i, X: $i] : (~h(z2(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (~h(z2(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (~h(z2(X, Y)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[5])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (~h(z2(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (~h(z2(X, Y)))) | (~h(z2(elem!0, elem!0)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (~h(z2(elem!0, elem!0))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (^[X: $i] : refl((h(X) | (~g(X))) <=> (h(X) | (~g(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~g(X))) <=> ![X: $i] : (h(X) | (~g(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~g(X))) <=> ![X: $i] : (h(X) | (~g(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[X: $i] : rewrite(((~g(X)) | h(X)) <=> (h(X) | (~g(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![X: $i] : ((~g(X)) | h(X)) <=> ![X: $i] : (h(X) | (~g(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,axiom,(![X: $i] : ((~g(X)) | h(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~g(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~g(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.36 tff(18,plain,(
% 0.11/0.36 ![X: $i] : (h(X) | (~g(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[17])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~g(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (((~![X: $i] : (h(X) | (~g(X)))) | (h(z2(elem!0, elem!0)) | (~g(z2(elem!0, elem!0))))) <=> ((~![X: $i] : (h(X) | (~g(X)))) | h(z2(elem!0, elem!0)) | (~g(z2(elem!0, elem!0))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 ((~![X: $i] : (h(X) | (~g(X)))) | (h(z2(elem!0, elem!0)) | (~g(z2(elem!0, elem!0))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 ((~![X: $i] : (h(X) | (~g(X)))) | h(z2(elem!0, elem!0)) | (~g(z2(elem!0, elem!0)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (~g(z2(elem!0, elem!0))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (^[X: $i] : refl((h(X) | (~f(X))) <=> (h(X) | (~f(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~f(X))) <=> ![X: $i] : (h(X) | (~f(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~f(X))) <=> ![X: $i] : (h(X) | (~f(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (^[X: $i] : rewrite(((~f(X)) | h(X)) <=> (h(X) | (~f(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (![X: $i] : ((~f(X)) | h(X)) <=> ![X: $i] : (h(X) | (~f(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.36 tff(29,axiom,(![X: $i] : ((~f(X)) | h(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~f(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~f(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.11/0.36 tff(32,plain,(
% 0.11/0.36 ![X: $i] : (h(X) | (~f(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[31])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (![X: $i] : (h(X) | (~f(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (((~![X: $i] : (h(X) | (~f(X)))) | (h(z2(elem!0, elem!0)) | (~f(z2(elem!0, elem!0))))) <=> ((~![X: $i] : (h(X) | (~f(X)))) | h(z2(elem!0, elem!0)) | (~f(z2(elem!0, elem!0))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 ((~![X: $i] : (h(X) | (~f(X)))) | (h(z2(elem!0, elem!0)) | (~f(z2(elem!0, elem!0))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 ((~![X: $i] : (h(X) | (~f(X)))) | h(z2(elem!0, elem!0)) | (~f(z2(elem!0, elem!0)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (~f(z2(elem!0, elem!0))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[36, 33, 9])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((f(Y) | g(X)) <=> (f(Y) | g(X)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (f(Y) | g(X)) <=> ![Y: $i, X: $i] : (f(Y) | g(X))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (f(Y) | g(X)) <=> ![Y: $i, X: $i] : (f(Y) | g(X))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(41,axiom,(![Y: $i, X: $i] : (f(Y) | g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (f(Y) | g(X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.36 tff(43,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (f(Y) | g(X))),
% 0.11/0.36 inference(skolemize,[status(sab)],[42])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (f(Y) | g(X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (((~![Y: $i, X: $i] : (f(Y) | g(X))) | (f(z2(elem!0, elem!0)) | g(z2(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (f(Y) | g(X))) | f(z2(elem!0, elem!0)) | g(z2(elem!0, elem!0)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (f(Y) | g(X))) | (f(z2(elem!0, elem!0)) | g(z2(elem!0, elem!0)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (f(Y) | g(X))) | f(z2(elem!0, elem!0)) | g(z2(elem!0, elem!0))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[47, 44, 37, 23])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------