%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN331-1 : 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 05:38:47 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN331-1 : TPTP v9.0.0. Released v1.2.0.
% 0.10/0.11 % 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 12:31:03 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(f_type, type, (
% 0.11/0.38 f: ( $i * $i ) > $o)).
% 0.11/0.38 tff(z_type, type, (
% 0.11/0.38 z: ( $i * $i ) > $i)).
% 0.11/0.38 tff(elem_0_type, type, (
% 0.11/0.38 elem_0: $i)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : refl((~f(z(X, Y), Y)) <=> (~f(z(X, Y), Y)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![Y: $i, X: $i] : (~f(z(X, Y), Y)) <=> ![Y: $i, X: $i] : (~f(z(X, Y), Y))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![Y: $i, X: $i] : (~f(z(X, Y), Y)) <=> ![Y: $i, X: $i] : (~f(z(X, Y), Y))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,axiom,(![Y: $i, X: $i] : (~f(z(X, Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![Y: $i, X: $i] : (~f(z(X, Y), Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : (~f(z(X, Y), Y))),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![Y: $i, X: $i] : (~f(z(X, Y), Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : (~f(z(X, Y), Y))) | (~f(z(elem!0, elem!0), elem!0))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (~f(z(elem!0, elem!0), elem!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : refl(((~f(z(X, Y), z(X, Y))) | f(X, Y)) <=> ((~f(z(X, Y), z(X, Y))) | f(X, Y)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y)) <=> ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y)) <=> ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : rewrite((f(X, Y) | (~f(z(X, Y), z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | f(X, Y)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![Y: $i, X: $i] : (f(X, Y) | (~f(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.38 tff(15,axiom,(![Y: $i, X: $i] : (f(X, Y) | (~f(z(X, Y), z(X, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.38 tff(18,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.11/0.38 inference(skolemize,[status(sab)],[17])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | ((~f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))) | f(z(elem!0, elem!0), elem!0))) <=> ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | (~f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))) | f(z(elem!0, elem!0), elem!0))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | ((~f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))) | f(z(elem!0, elem!0), elem!0))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | (~f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))) | f(z(elem!0, elem!0), elem!0)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (~f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | ((~f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))) | f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | (~f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))) | f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | ((~f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))) | f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | f(X, Y))) | (~f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))) | f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 (~f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[26, 19, 23])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (^[Y: $i, X: $i] : refl((f(Y, X) | f(z(X, Y), z(X, Y))) <=> (f(Y, X) | f(z(X, Y), z(X, Y))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.39 tff(30,plain,
% 0.11/0.39 (![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(31,axiom,(![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 (![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.11/0.39 tff(33,plain,(
% 0.11/0.39 ![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[32])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))) | (f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)) | f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))))) <=> ((~![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))) | f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)) | f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))) | (f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)) | f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : (f(Y, X) | f(z(X, Y), z(X, Y)))) | f(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)) | f(z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)), z(z(z(elem!0, elem!0), elem!0), z(z(elem!0, elem!0), elem!0)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[37, 34, 23, 27])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------