%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN074-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:38:09 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN074-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:27:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(big_f_type, type, (
% 0.12/0.38 big_f: ( $i * $i ) > $o)).
% 0.12/0.38 tff(h_type, type, (
% 0.12/0.38 h: ( $i * $i ) > $i)).
% 0.12/0.38 tff(b_type, type, (
% 0.12/0.38 b: $i)).
% 0.12/0.38 tff(a_type, type, (
% 0.12/0.38 a: $i)).
% 0.12/0.38 tff(f_type, type, (
% 0.12/0.38 f: $i > $i)).
% 0.12/0.38 tff(g_type, type, (
% 0.12/0.38 g: $i > $i)).
% 0.12/0.38 tff(1,assumption,(~big_f(f(a), h(a, b))), introduced(assumption)).
% 0.12/0.38 tff(2,assumption,(~(f(a) = a)), introduced(assumption)).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[X: $i] : refl(((f(X) = X) | big_f(f(X), g(X))) <=> ((f(X) = X) | big_f(f(X), g(X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(f(X), g(X))) <=> ![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(f(X), g(X))) <=> ![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), g(X))) <=> ![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X)))) <=> ![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X)))) <=> ![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : rewrite((((~(Y = g(X))) | big_f(f(X), Y)) | (f(X) = X)) <=> ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~(Y = g(X))) | big_f(f(X), Y)) | (f(X) = X)) <=> ![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~(Y = g(X))) | big_f(f(X), Y)) | (f(X) = X)) <=> ![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[10, 8])).
% 0.12/0.38 tff(12,axiom,(![Y: $i, X: $i] : (((~(Y = g(X))) | big_f(f(X), Y)) | (f(X) = X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.12/0.38 tff(15,plain,(
% 0.12/0.38 ![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (((~![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))) | ((f(a) = a) | big_f(f(a), g(a)))) <=> ((~![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))) | (f(a) = a) | big_f(f(a), g(a)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))) | ((f(a) = a) | big_f(f(a), g(a)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((~![X: $i] : ((f(X) = X) | big_f(f(X), g(X)))) | (f(a) = a) | big_f(f(a), g(a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((f(a) = a) | big_f(f(a), g(a))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (big_f(f(a), g(a))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 2])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : refl(((~big_f(X, Y)) | (X = a)) <=> ((~big_f(X, Y)) | (X = a)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,axiom,(![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,(
% 0.12/0.38 ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.38 inference(skolemize,[status(sab)],[26])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | ((~big_f(f(a), g(a))) | (f(a) = a))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | (~big_f(f(a), g(a))) | (f(a) = a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | ((~big_f(f(a), g(a))) | (f(a) = a))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | (~big_f(f(a), g(a))) | (f(a) = a)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 28, 2, 21])).
% 0.12/0.38 tff(33,plain,(f(a) = a), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[Z: $i, X: $i] : refl(((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z))) <=> ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z))) <=> ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z))) <=> ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (^[Z: $i, X: $i] : rewrite((((~(f(X) = X)) | big_f(f(X), h(X, Z))) | (h(X, Z) = Z)) <=> ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![Z: $i, X: $i] : (((~(f(X) = X)) | big_f(f(X), h(X, Z))) | (h(X, Z) = Z)) <=> ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.38 tff(39,axiom,(![Z: $i, X: $i] : (((~(f(X) = X)) | big_f(f(X), h(X, Z))) | (h(X, Z) = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_10')).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.38 tff(42,plain,(
% 0.12/0.38 ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | ((~(f(a) = a)) | (h(a, b) = b) | big_f(f(a), h(a, b)))) <=> ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | (~(f(a) = a)) | (h(a, b) = b) | big_f(f(a), h(a, b)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((h(a, b) = b) | (~(f(a) = a)) | big_f(f(a), h(a, b))) <=> ((~(f(a) = a)) | (h(a, b) = b) | big_f(f(a), h(a, b)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | ((h(a, b) = b) | (~(f(a) = a)) | big_f(f(a), h(a, b)))) <=> ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | ((~(f(a) = a)) | (h(a, b) = b) | big_f(f(a), h(a, b))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | ((h(a, b) = b) | (~(f(a) = a)) | big_f(f(a), h(a, b)))) <=> ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | (~(f(a) = a)) | (h(a, b) = b) | big_f(f(a), h(a, b)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[46, 44])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | ((h(a, b) = b) | (~(f(a) = a)) | big_f(f(a), h(a, b)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))) | (~(f(a) = a)) | (h(a, b) = b) | big_f(f(a), h(a, b))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((h(a, b) = b) | big_f(f(a), h(a, b))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[49, 43, 33])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (h(a, b) = b),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 1])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (big_f(f(a), h(a, b)) <=> big_f(a, b)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[33, 51])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (big_f(a, b) <=> big_f(f(a), h(a, b))),
% 0.12/0.38 inference(symmetry,[status(thm)],[52])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (big_f(a, b) <=> big_f(a, b)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![Y: $i, X: $i] : big_f(a, b) <=> big_f(a, b)),
% 0.12/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> ![Y: $i, X: $i] : big_f(a, b)),
% 0.12/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> big_f(a, b)),
% 0.12/0.38 inference(transitivity,[status(thm)],[56, 55])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : rewrite((((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> (big_f(X, Y) | (~(Y = b)) | (~(X = a))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> big_f(a, b)),
% 0.12/0.38 inference(transitivity,[status(thm)],[59, 57])).
% 0.12/0.38 tff(61,axiom,(![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (big_f(a, b)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (big_f(a, b)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[62, 54])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (big_f(f(a), h(a, b))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[1, 64])).
% 0.12/0.38 tff(66,plain,(big_f(f(a), h(a, b))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : refl(((~big_f(X, Y)) | (Y = b)) <=> ((~big_f(X, Y)) | (Y = b)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(70,axiom,(![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.38 tff(72,plain,(
% 0.12/0.38 ![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.12/0.38 inference(skolemize,[status(sab)],[71])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | ((~big_f(f(a), h(a, b))) | (h(a, b) = b))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | (~big_f(f(a), h(a, b))) | (h(a, b) = b))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | ((~big_f(f(a), h(a, b))) | (h(a, b) = b))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | (~big_f(f(a), h(a, b))) | (h(a, b) = b)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 (h(a, b) = b),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[76, 73, 66])).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 (^[Z: $i, X: $i] : refl(((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z))) <=> ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z))) <=> ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z))) <=> ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (^[Z: $i, X: $i] : rewrite((((~(f(X) = X)) | (~(h(X, Z) = Z))) | (~big_f(f(X), h(X, Z)))) <=> ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (![Z: $i, X: $i] : (((~(f(X) = X)) | (~(h(X, Z) = Z))) | (~big_f(f(X), h(X, Z)))) <=> ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.12/0.39 tff(83,axiom,(![Z: $i, X: $i] : (((~(f(X) = X)) | (~(h(X, Z) = Z))) | (~big_f(f(X), h(X, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_11')).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.12/0.39 tff(86,plain,(
% 0.12/0.39 ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[85])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))) | ((~(f(a) = a)) | (~big_f(f(a), h(a, b))) | (~(h(a, b) = b)))) <=> ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))) | (~(f(a) = a)) | (~big_f(f(a), h(a, b))) | (~(h(a, b) = b)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))) | ((~(f(a) = a)) | (~big_f(f(a), h(a, b))) | (~(h(a, b) = b)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))) | (~(f(a) = a)) | (~big_f(f(a), h(a, b))) | (~(h(a, b) = b))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[90, 87, 33, 77, 66])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------