%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN323-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:45 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN323-1 : TPTP v9.0.0. Released v1.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 12:31:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(g_type, type, (
% 0.12/0.37 g: ( $i * $i ) > $o)).
% 0.12/0.37 tff(a_type, type, (
% 0.12/0.37 a: $i)).
% 0.12/0.37 tff(f_type, type, (
% 0.12/0.37 f: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,assumption,(~f(a, a)), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[X: $i] : refl((f(X, a) | g(X, a)) <=> (f(X, a) | g(X, a)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | g(X, a)) <=> ![X: $i] : (f(X, a) | g(X, a))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | g(X, a)) <=> ![X: $i] : (f(X, a) | g(X, a))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(![X: $i] : (f(X, a) | g(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | g(X, a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,(
% 0.12/0.37 ![X: $i] : (f(X, a) | g(X, a))),
% 0.12/0.37 inference(skolemize,[status(sab)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | g(X, a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (((~![X: $i] : (f(X, a) | g(X, a))) | (f(a, a) | g(a, a))) <=> ((~![X: $i] : (f(X, a) | g(X, a))) | f(a, a) | g(a, a))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ((~![X: $i] : (f(X, a) | g(X, a))) | (f(a, a) | g(a, a))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![X: $i] : (f(X, a) | g(X, a))) | f(a, a) | g(a, a)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (g(a, a)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[X: $i] : refl((f(X, a) | (~g(X, a))) <=> (f(X, a) | (~g(X, a))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | (~g(X, a))) <=> ![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | (~g(X, a))) <=> ![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,axiom,(![X: $i] : (f(X, a) | (~g(X, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,(
% 0.12/0.37 ![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (((~![X: $i] : (f(X, a) | (~g(X, a)))) | (f(a, a) | (~g(a, a)))) <=> ((~![X: $i] : (f(X, a) | (~g(X, a)))) | f(a, a) | (~g(a, a)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![X: $i] : (f(X, a) | (~g(X, a)))) | (f(a, a) | (~g(a, a)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![X: $i] : (f(X, a) | (~g(X, a)))) | f(a, a) | (~g(a, a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[22, 19, 1, 12])).
% 0.12/0.37 tff(24,plain,(f(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (^[X: $i] : refl(((~f(a, X)) | g(X, a)) <=> ((~f(a, X)) | g(X, a)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![X: $i] : ((~f(a, X)) | g(X, a)) <=> ![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![X: $i] : ((~f(a, X)) | g(X, a)) <=> ![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(28,axiom,(![X: $i] : ((~f(a, X)) | g(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.37 tff(30,plain,(
% 0.12/0.37 ![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.12/0.37 inference(skolemize,[status(sab)],[29])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (((~![X: $i] : ((~f(a, X)) | g(X, a))) | ((~f(a, a)) | g(a, a))) <=> ((~![X: $i] : ((~f(a, X)) | g(X, a))) | (~f(a, a)) | g(a, a))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((~![X: $i] : ((~f(a, X)) | g(X, a))) | ((~f(a, a)) | g(a, a))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![X: $i] : ((~f(a, X)) | g(X, a))) | (~f(a, a)) | g(a, a)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~f(a, a)) | g(a, a)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (g(a, a)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 24])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (^[X: $i] : refl(((~f(a, X)) | (~g(X, a))) <=> ((~f(a, X)) | (~g(X, a))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![X: $i] : ((~f(a, X)) | (~g(X, a))) <=> ![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![X: $i] : ((~f(a, X)) | (~g(X, a))) <=> ![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(40,axiom,(![X: $i] : ((~f(a, X)) | (~g(X, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.38 tff(42,plain,(
% 0.12/0.38 ![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | ((~f(a, a)) | (~g(a, a)))) <=> ((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | (~f(a, a)) | (~g(a, a)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | ((~f(a, a)) | (~g(a, a)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | (~f(a, a)) | (~g(a, a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[46, 43, 24, 36])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------