%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN082-1 : TPTP v9.0.0. Released v1.0.0.
% 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 05:38:12 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN082-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:27:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(big_f_type, type, (
% 0.12/0.36 big_f: ( $i * $i ) > $o)).
% 0.12/0.36 tff(f_type, type, (
% 0.12/0.36 f: $i > $i)).
% 0.12/0.36 tff(a_type, type, (
% 0.12/0.36 a: $i)).
% 0.12/0.36 tff(g_type, type, (
% 0.12/0.36 g: $i > $i)).
% 0.12/0.36 tff(b_type, type, (
% 0.12/0.36 b: $i)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[X: $i] : refl(((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X))) <=> ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X))) <=> ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X))) <=> ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (^[X: $i] : trans(monotonicity(rewrite(((~big_f(g(X), X)) | (~big_f(a, X))) <=> ((~big_f(a, X)) | (~big_f(g(X), X)))), ((((~big_f(g(X), X)) | (~big_f(a, X))) | (~big_f(a, f(a)))) <=> (((~big_f(a, X)) | (~big_f(g(X), X))) | (~big_f(a, f(a)))))), rewrite((((~big_f(a, X)) | (~big_f(g(X), X))) | (~big_f(a, f(a)))) <=> ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))), ((((~big_f(g(X), X)) | (~big_f(a, X))) | (~big_f(a, f(a)))) <=> ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (![X: $i] : (((~big_f(g(X), X)) | (~big_f(a, X))) | (~big_f(a, f(a)))) <=> ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.36 tff(6,axiom,(![X: $i] : (((~big_f(g(X), X)) | (~big_f(a, X))) | (~big_f(a, f(a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.36 tff(9,plain,(
% 0.12/0.36 ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[8])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.36 tff(11,assumption,(~big_f(a, f(a))), introduced(assumption)).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 ((big_f(a, b) | big_f(a, f(a))) <=> (big_f(a, b) | big_f(a, f(a)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 ((big_f(a, f(a)) | big_f(a, b)) <=> (big_f(a, b) | big_f(a, f(a)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(14,axiom,(big_f(a, f(a)) | big_f(a, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (big_f(a, b) | big_f(a, f(a))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (big_f(a, b) | big_f(a, f(a))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (big_f(a, b)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (^[Y: $i] : refl((big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b))) <=> (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 (![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b))) <=> ![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b))) <=> ![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (^[Y: $i] : trans(monotonicity(rewrite((big_f(a, f(a)) | (~big_f(Y, b))) <=> (big_f(a, f(a)) | (~big_f(Y, b)))), (((big_f(a, f(a)) | (~big_f(Y, b))) | big_f(Y, f(a))) <=> ((big_f(a, f(a)) | (~big_f(Y, b))) | big_f(Y, f(a))))), rewrite(((big_f(a, f(a)) | (~big_f(Y, b))) | big_f(Y, f(a))) <=> (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))), (((big_f(a, f(a)) | (~big_f(Y, b))) | big_f(Y, f(a))) <=> (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![Y: $i] : ((big_f(a, f(a)) | (~big_f(Y, b))) | big_f(Y, f(a))) <=> ![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.37 tff(23,axiom,(![Y: $i] : ((big_f(a, f(a)) | (~big_f(Y, b))) | big_f(Y, f(a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.37 tff(26,plain,(
% 0.12/0.37 ![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[25])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | (big_f(a, f(a)) | (~big_f(a, b)))) <=> ((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | big_f(a, f(a)) | (~big_f(a, b)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((big_f(a, f(a)) | big_f(a, f(a)) | (~big_f(a, b))) <=> (big_f(a, f(a)) | (~big_f(a, b)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | (big_f(a, f(a)) | big_f(a, f(a)) | (~big_f(a, b)))) <=> ((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | (big_f(a, f(a)) | (~big_f(a, b))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | (big_f(a, f(a)) | big_f(a, f(a)) | (~big_f(a, b)))) <=> ((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | big_f(a, f(a)) | (~big_f(a, b)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[30, 28])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | (big_f(a, f(a)) | big_f(a, f(a)) | (~big_f(a, b)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((~![Y: $i] : (big_f(a, f(a)) | big_f(Y, f(a)) | (~big_f(Y, b)))) | big_f(a, f(a)) | (~big_f(a, b))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 27, 17, 11])).
% 0.12/0.37 tff(35,plain,(big_f(a, f(a))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | ((~big_f(a, f(a))) | (~big_f(g(f(a)), f(a))))) <=> ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | (~big_f(a, f(a))) | (~big_f(g(f(a)), f(a))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (((~big_f(a, f(a))) | (~big_f(a, f(a))) | (~big_f(g(f(a)), f(a)))) <=> ((~big_f(a, f(a))) | (~big_f(g(f(a)), f(a))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | ((~big_f(a, f(a))) | (~big_f(a, f(a))) | (~big_f(g(f(a)), f(a))))) <=> ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | ((~big_f(a, f(a))) | (~big_f(g(f(a)), f(a)))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | ((~big_f(a, f(a))) | (~big_f(a, f(a))) | (~big_f(g(f(a)), f(a))))) <=> ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | (~big_f(a, f(a))) | (~big_f(g(f(a)), f(a))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[38, 36])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | ((~big_f(a, f(a))) | (~big_f(a, f(a))) | (~big_f(g(f(a)), f(a))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | (~big_f(g(X), X)))) | (~big_f(a, f(a))) | (~big_f(g(f(a)), f(a)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (~big_f(g(f(a)), f(a))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 35, 10])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (^[X: $i] : refl(((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X)) <=> ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X)) <=> ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X)) <=> ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (^[X: $i] : trans(monotonicity(rewrite((big_f(g(X), X) | (~big_f(a, X))) <=> ((~big_f(a, X)) | big_f(g(X), X))), (((big_f(g(X), X) | (~big_f(a, X))) | (~big_f(a, f(a)))) <=> (((~big_f(a, X)) | big_f(g(X), X)) | (~big_f(a, f(a)))))), rewrite((((~big_f(a, X)) | big_f(g(X), X)) | (~big_f(a, f(a)))) <=> ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))), (((big_f(g(X), X) | (~big_f(a, X))) | (~big_f(a, f(a)))) <=> ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (![X: $i] : ((big_f(g(X), X) | (~big_f(a, X))) | (~big_f(a, f(a)))) <=> ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.37 tff(48,axiom,(![X: $i] : ((big_f(g(X), X) | (~big_f(a, X))) | (~big_f(a, f(a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.37 tff(51,plain,(
% 0.19/0.37 ![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))),
% 0.19/0.37 inference(skolemize,[status(sab)],[50])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | ((~big_f(a, f(a))) | big_f(g(f(a)), f(a)))) <=> ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | (~big_f(a, f(a))) | big_f(g(f(a)), f(a)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 (((~big_f(a, f(a))) | (~big_f(a, f(a))) | big_f(g(f(a)), f(a))) <=> ((~big_f(a, f(a))) | big_f(g(f(a)), f(a)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | ((~big_f(a, f(a))) | (~big_f(a, f(a))) | big_f(g(f(a)), f(a)))) <=> ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | ((~big_f(a, f(a))) | big_f(g(f(a)), f(a))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | ((~big_f(a, f(a))) | (~big_f(a, f(a))) | big_f(g(f(a)), f(a)))) <=> ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | (~big_f(a, f(a))) | big_f(g(f(a)), f(a)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[55, 53])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | ((~big_f(a, f(a))) | (~big_f(a, f(a))) | big_f(g(f(a)), f(a)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 ((~![X: $i] : ((~big_f(a, f(a))) | (~big_f(a, X)) | big_f(g(X), X))) | (~big_f(a, f(a))) | big_f(g(f(a)), f(a))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.37 tff(59,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[58, 35, 52, 42])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------