%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN075-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:10 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
% 0.11/0.12 % Problem : SYN075-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 12:29:20 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(b_type, type, (
% 0.12/0.38 b: $i)).
% 0.12/0.38 tff(h_type, type, (
% 0.12/0.38 h: ( $i * $i ) > $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,(~(f(b) = b)), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[X: $i] : refl(((~big_f(g(X), f(X))) | (f(X) = X)) <=> ((~big_f(g(X), f(X))) | (f(X) = X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X)) <=> ![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X)) <=> ![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X)) <=> ![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X)))) <=> ![Y: $i, X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X)))) <=> ![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(transitivity,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~big_f(Y, f(X))) | (~(Y = g(X)))) <=> ((~(Y = g(X))) | (~big_f(Y, f(X))))), ((((~big_f(Y, f(X))) | (~(Y = g(X)))) | (f(X) = X)) <=> (((~(Y = g(X))) | (~big_f(Y, f(X)))) | (f(X) = X)))), rewrite((((~(Y = g(X))) | (~big_f(Y, f(X)))) | (f(X) = X)) <=> ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))), ((((~big_f(Y, f(X))) | (~(Y = g(X)))) | (f(X) = X)) <=> ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~big_f(Y, f(X))) | (~(Y = g(X)))) | (f(X) = X)) <=> ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~big_f(Y, f(X))) | (~(Y = g(X)))) | (f(X) = X)) <=> ![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(transitivity,[status(thm)],[9, 7])).
% 0.12/0.38 tff(11,axiom,(![Y: $i, X: $i] : (((~big_f(Y, f(X))) | (~(Y = g(X)))) | (f(X) = X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.12/0.38 tff(14,plain,(
% 0.12/0.38 ![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 3])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (((~![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))) | ((~big_f(g(b), f(b))) | (f(b) = b))) <=> ((~![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))) | (~big_f(g(b), f(b))) | (f(b) = b))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))) | ((~big_f(g(b), f(b))) | (f(b) = b))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![X: $i] : ((~big_f(g(X), f(X))) | (f(X) = X))) | (~big_f(g(b), f(b))) | (f(b) = b)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~big_f(g(b), f(b))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 15, 1])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[X: $i] : refl(((f(X) = X) | big_f(g(X), f(X))) <=> ((f(X) = X) | big_f(g(X), f(X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(g(X), f(X))) <=> ![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(g(X), f(X))) <=> ![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[X: $i] : rewrite((big_f(g(X), f(X)) | (f(X) = X)) <=> ((f(X) = X) | big_f(g(X), f(X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![X: $i] : (big_f(g(X), f(X)) | (f(X) = X)) <=> ![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (big_f(g(X), f(X)) | (f(X) = X)) <=> ![X: $i] : (big_f(g(X), f(X)) | (f(X) = X))),
% 0.12/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))) <=> ![Y: $i, X: $i] : (big_f(g(X), f(X)) | (f(X) = X))),
% 0.12/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))) <=> ![X: $i] : (big_f(g(X), f(X)) | (f(X) = X))),
% 0.12/0.38 inference(transitivity,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))) <=> ![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[27, 24])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : rewrite((((~(Y = g(X))) | big_f(Y, f(X))) | (f(X) = X)) <=> ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~(Y = g(X))) | big_f(Y, f(X))) | (f(X) = X)) <=> ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (((~(Y = g(X))) | big_f(Y, f(X))) | (f(X) = X)) <=> ![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.12/0.38 tff(32,axiom,(![Y: $i, X: $i] : (((~(Y = g(X))) | big_f(Y, f(X))) | (f(X) = X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 22])).
% 0.12/0.38 tff(35,plain,(
% 0.12/0.38 ![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 21])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (((~![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))) | ((f(b) = b) | big_f(g(b), f(b)))) <=> ((~![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))) | (f(b) = b) | big_f(g(b), f(b)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))) | ((f(b) = b) | big_f(g(b), f(b)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~![X: $i] : ((f(X) = X) | big_f(g(X), f(X)))) | (f(b) = b) | big_f(g(b), f(b))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 36, 1, 19])).
% 0.12/0.38 tff(41,plain,(f(b) = b), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (b = f(b)),
% 0.12/0.38 inference(symmetry,[status(thm)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (big_f(h(b, a), b) <=> big_f(h(b, a), f(b))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[42])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (big_f(h(b, a), f(b)) <=> big_f(h(b, a), b)),
% 0.12/0.39 inference(symmetry,[status(thm)],[43])).
% 0.12/0.39 tff(45,assumption,(h(b, a) = a), introduced(assumption)).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (big_f(h(b, a), f(b)) <=> big_f(a, b)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[45, 41])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (big_f(a, b) <=> big_f(h(b, a), f(b))),
% 0.12/0.39 inference(symmetry,[status(thm)],[46])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (big_f(a, b) <=> big_f(a, b)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![Y: $i, X: $i] : big_f(a, b) <=> big_f(a, b)),
% 0.12/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> ![Y: $i, X: $i] : big_f(a, b)),
% 0.12/0.39 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> big_f(a, b)),
% 0.12/0.39 inference(transitivity,[status(thm)],[50, 49])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (^[Y: $i, X: $i] : rewrite((((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> (big_f(X, Y) | (~(Y = b)) | (~(X = a))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> big_f(a, b)),
% 0.12/0.39 inference(transitivity,[status(thm)],[53, 51])).
% 0.12/0.39 tff(55,axiom,(![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (big_f(a, b)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (big_f(a, b)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[56, 48])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (big_f(h(b, a), f(b))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (^[Z: $i, X: $i] : refl(((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z))) <=> ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z))) <=> ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z))) <=> ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (^[Z: $i, X: $i] : rewrite((((~(f(X) = X)) | (~(h(X, Z) = Z))) | (~big_f(h(X, Z), f(X)))) <=> ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (![Z: $i, X: $i] : (((~(f(X) = X)) | (~(h(X, Z) = Z))) | (~big_f(h(X, Z), f(X)))) <=> ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.12/0.39 tff(64,axiom,(![Z: $i, X: $i] : (((~(f(X) = X)) | (~(h(X, Z) = Z))) | (~big_f(h(X, Z), f(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10')).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.12/0.39 tff(67,plain,(
% 0.12/0.39 ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[66])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | ((~(f(b) = b)) | (~big_f(h(b, a), f(b))) | (~(h(b, a) = a)))) <=> ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | (~(f(b) = b)) | (~big_f(h(b, a), f(b))) | (~(h(b, a) = a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | ((~(f(b) = b)) | (~big_f(h(b, a), f(b))) | (~(h(b, a) = a)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | (~(f(b) = b)) | (~big_f(h(b, a), f(b))) | (~(h(b, a) = a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 68, 41, 45, 58])).
% 0.12/0.39 tff(73,plain,(~(h(b, a) = a)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (^[Z: $i, X: $i] : refl(((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X))) <=> ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X))) <=> ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X))) <=> ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (^[Z: $i, X: $i] : rewrite((((~(f(X) = X)) | big_f(h(X, Z), f(X))) | (h(X, Z) = Z)) <=> ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (![Z: $i, X: $i] : (((~(f(X) = X)) | big_f(h(X, Z), f(X))) | (h(X, Z) = Z)) <=> ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[77])).
% 0.12/0.39 tff(79,axiom,(![Z: $i, X: $i] : (((~(f(X) = X)) | big_f(h(X, Z), f(X))) | (h(X, Z) = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_9')).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.12/0.39 tff(82,plain,(
% 0.12/0.39 ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[81])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | ((h(b, a) = a) | big_f(h(b, a), f(b)) | (~(f(b) = b)))) <=> ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | (h(b, a) = a) | big_f(h(b, a), f(b)) | (~(f(b) = b)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (((h(b, a) = a) | (~(f(b) = b)) | big_f(h(b, a), f(b))) <=> ((h(b, a) = a) | big_f(h(b, a), f(b)) | (~(f(b) = b)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | ((h(b, a) = a) | (~(f(b) = b)) | big_f(h(b, a), f(b)))) <=> ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | ((h(b, a) = a) | big_f(h(b, a), f(b)) | (~(f(b) = b))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[85])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | ((h(b, a) = a) | (~(f(b) = b)) | big_f(h(b, a), f(b)))) <=> ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | (h(b, a) = a) | big_f(h(b, a), f(b)) | (~(f(b) = b)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[86, 84])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | ((h(b, a) = a) | (~(f(b) = b)) | big_f(h(b, a), f(b)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 ((~![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))) | (h(b, a) = a) | big_f(h(b, a), f(b)) | (~(f(b) = b))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 ((h(b, a) = a) | big_f(h(b, a), f(b))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[89, 83, 41])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (big_f(h(b, a), f(b))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[90, 73])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (big_f(h(b, a), b)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[91, 44])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (^[Y: $i, X: $i] : refl(((~big_f(X, Y)) | (X = a)) <=> ((~big_f(X, Y)) | (X = a)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[93])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(96,axiom,(![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.12/0.39 tff(98,plain,(
% 0.12/0.39 ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.39 inference(skolemize,[status(sab)],[97])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | ((~big_f(h(b, a), b)) | (h(b, a) = a))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | (~big_f(h(b, a), b)) | (h(b, a) = a))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | ((~big_f(h(b, a), b)) | (h(b, a) = a))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | (~big_f(h(b, a), b)) | (h(b, a) = a)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 (~big_f(h(b, a), b)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[102, 99, 73])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[103, 92])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------