TSTP Solution File: SYN074-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN074-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Thu Sep 29 23:53:33 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN074-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.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 : Mon Sep 5 01:45:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.42 % SZS status Unsatisfiable
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 tff(big_f_type, type, (
% 0.18/0.42 big_f: ( $i * $i ) > $o)).
% 0.18/0.42 tff(h_type, type, (
% 0.18/0.42 h: ( $i * $i ) > $i)).
% 0.18/0.42 tff(b_type, type, (
% 0.18/0.42 b: $i)).
% 0.18/0.42 tff(a_type, type, (
% 0.18/0.42 a: $i)).
% 0.18/0.42 tff(f_type, type, (
% 0.18/0.42 f: $i > $i)).
% 0.18/0.42 tff(g_type, type, (
% 0.18/0.42 g: $i > $i)).
% 0.18/0.42 tff(1,assumption,(~(f(a) = a)), introduced(assumption)).
% 0.18/0.42 tff(2,plain,
% 0.18/0.42 (^[Y: $i, X: $i] : refl(((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X)))) <=> ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(3,plain,
% 0.18/0.42 (![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), Y) | (~(Y = g(X))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.42 tff(4,plain,
% 0.18/0.42 (![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), Y) | (~(Y = g(X))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(5,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(6,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.18/0.42 tff(7,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')).
% 0.18/0.42 tff(8,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.42 tff(9,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.42 tff(10,plain,(
% 0.18/0.42 ![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[9])).
% 0.18/0.42 tff(11,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.18/0.42 tff(12,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | ((f(a) = a) | big_f(f(a), g(a)))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | (f(a) = a) | big_f(f(a), g(a)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(13,plain,
% 0.18/0.42 (((f(a) = a) | big_f(f(a), g(a)) | $false) <=> ((f(a) = a) | big_f(f(a), g(a)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(14,plain,
% 0.18/0.42 ((~$true) <=> $false),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(15,plain,
% 0.18/0.42 ((g(a) = g(a)) <=> $true),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(16,plain,
% 0.18/0.42 ((~(g(a) = g(a))) <=> (~$true)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.42 tff(17,plain,
% 0.18/0.42 ((~(g(a) = g(a))) <=> $false),
% 0.18/0.42 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.42 tff(18,plain,
% 0.18/0.42 (((f(a) = a) | big_f(f(a), g(a)) | (~(g(a) = g(a)))) <=> ((f(a) = a) | big_f(f(a), g(a)) | $false)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[17])).
% 0.18/0.42 tff(19,plain,
% 0.18/0.42 (((f(a) = a) | big_f(f(a), g(a)) | (~(g(a) = g(a)))) <=> ((f(a) = a) | big_f(f(a), g(a)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[18, 13])).
% 0.18/0.42 tff(20,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | ((f(a) = a) | big_f(f(a), g(a)) | (~(g(a) = g(a))))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | ((f(a) = a) | big_f(f(a), g(a))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[19])).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | ((f(a) = a) | big_f(f(a), g(a)) | (~(g(a) = g(a))))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | (f(a) = a) | big_f(f(a), g(a)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[20, 12])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | ((f(a) = a) | big_f(f(a), g(a)) | (~(g(a) = g(a))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((f(X) = X) | big_f(f(X), Y) | (~(Y = g(X))))) | (f(a) = a) | big_f(f(a), g(a))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.42 tff(24,plain,
% 0.18/0.42 ((f(a) = a) | big_f(f(a), g(a))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[23, 11])).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (big_f(f(a), g(a))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 (^[Y: $i, X: $i] : refl(((~big_f(X, Y)) | (X = a)) <=> ((~big_f(X, Y)) | (X = a)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.42 tff(28,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(29,axiom,(![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.18/0.42 tff(30,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.42 tff(31,plain,(
% 0.18/0.42 ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.18/0.42 inference(skolemize,[status(sab)],[30])).
% 0.18/0.42 tff(32,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.18/0.42 tff(33,plain,
% 0.18/0.42 (((~![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))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(34,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | ((~big_f(f(a), g(a))) | (f(a) = a))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(35,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | (~big_f(f(a), g(a))) | (f(a) = a)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.42 tff(36,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[35, 32, 1, 25])).
% 0.18/0.42 tff(37,plain,(f(a) = a), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(38,plain,
% 0.18/0.42 (a = f(a)),
% 0.18/0.42 inference(symmetry,[status(thm)],[37])).
% 0.18/0.42 tff(39,plain,
% 0.18/0.42 (big_f(a, h(a, b)) <=> big_f(f(a), h(a, b))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[38])).
% 0.18/0.42 tff(40,plain,
% 0.18/0.42 (big_f(f(a), h(a, b)) <=> big_f(a, h(a, b))),
% 0.18/0.42 inference(symmetry,[status(thm)],[39])).
% 0.18/0.42 tff(41,assumption,(~big_f(f(a), h(a, b))), introduced(assumption)).
% 0.18/0.42 tff(42,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(43,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.42 tff(44,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(45,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(46,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.42 tff(47,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')).
% 0.18/0.42 tff(48,plain,
% 0.18/0.42 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.42 tff(49,plain,
% 0.18/0.42 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.18/0.42 tff(50,plain,(
% 0.18/0.42 ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[49])).
% 0.18/0.42 tff(51,plain,
% 0.18/0.42 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(f(X), h(X, Z)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.18/0.42 tff(52,plain,
% 0.18/0.42 (((~![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(53,plain,
% 0.18/0.43 (((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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(54,plain,
% 0.18/0.43 (((~![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))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.18/0.43 tff(55,plain,
% 0.18/0.43 (((~![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)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.18/0.43 tff(56,plain,
% 0.18/0.43 ((~![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)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(57,plain,
% 0.18/0.43 ((~![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))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.43 tff(58,plain,
% 0.18/0.43 ((h(a, b) = b) | big_f(f(a), h(a, b))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[57, 51, 37])).
% 0.18/0.43 tff(59,plain,
% 0.18/0.43 (h(a, b) = b),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[58, 41])).
% 0.18/0.43 tff(60,plain,
% 0.18/0.43 (big_f(f(a), h(a, b)) <=> big_f(a, b)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[37, 59])).
% 0.18/0.43 tff(61,plain,
% 0.18/0.43 (big_f(a, b) <=> big_f(f(a), h(a, b))),
% 0.18/0.43 inference(symmetry,[status(thm)],[60])).
% 0.18/0.43 tff(62,plain,
% 0.18/0.43 (^[Y: $i, X: $i] : refl((big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> (big_f(X, Y) | (~(Y = b)) | (~(X = a))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(63,plain,
% 0.18/0.43 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.43 tff(64,plain,
% 0.18/0.43 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(65,plain,
% 0.18/0.43 (^[Y: $i, X: $i] : rewrite((((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> (big_f(X, Y) | (~(Y = b)) | (~(X = a))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(66,plain,
% 0.18/0.43 (![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.43 tff(67,axiom,(![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.18/0.43 tff(68,plain,
% 0.18/0.43 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.43 tff(69,plain,
% 0.18/0.43 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.43 tff(70,plain,(
% 0.18/0.43 ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[69])).
% 0.18/0.43 tff(71,plain,
% 0.18/0.43 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.18/0.43 tff(72,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | big_f(a, b)) <=> ((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | big_f(a, b))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(73,plain,
% 0.18/0.43 ((big_f(a, b) | $false | $false) <=> big_f(a, b)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(74,plain,
% 0.18/0.43 ((a = a) <=> $true),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(75,plain,
% 0.18/0.43 ((~(a = a)) <=> (~$true)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.43 tff(76,plain,
% 0.18/0.43 ((~(a = a)) <=> $false),
% 0.18/0.43 inference(transitivity,[status(thm)],[75, 14])).
% 0.18/0.43 tff(77,plain,
% 0.18/0.43 ((b = b) <=> $true),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(78,plain,
% 0.18/0.43 ((~(b = b)) <=> (~$true)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[77])).
% 0.18/0.43 tff(79,plain,
% 0.18/0.43 ((~(b = b)) <=> $false),
% 0.18/0.43 inference(transitivity,[status(thm)],[78, 14])).
% 0.18/0.43 tff(80,plain,
% 0.18/0.43 ((big_f(a, b) | (~(b = b)) | (~(a = a))) <=> (big_f(a, b) | $false | $false)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[79, 76])).
% 0.18/0.43 tff(81,plain,
% 0.18/0.43 ((big_f(a, b) | (~(b = b)) | (~(a = a))) <=> big_f(a, b)),
% 0.18/0.43 inference(transitivity,[status(thm)],[80, 73])).
% 0.18/0.43 tff(82,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | (big_f(a, b) | (~(b = b)) | (~(a = a)))) <=> ((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | big_f(a, b))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[81])).
% 0.18/0.43 tff(83,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | (big_f(a, b) | (~(b = b)) | (~(a = a)))) <=> ((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | big_f(a, b))),
% 0.18/0.43 inference(transitivity,[status(thm)],[82, 72])).
% 0.18/0.43 tff(84,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | (big_f(a, b) | (~(b = b)) | (~(a = a)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(85,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | big_f(a, b)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.18/0.43 tff(86,plain,
% 0.18/0.43 (big_f(a, b)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[85, 71])).
% 0.18/0.43 tff(87,plain,
% 0.18/0.43 (big_f(f(a), h(a, b))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[86, 61])).
% 0.18/0.43 tff(88,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[41, 87])).
% 0.18/0.43 tff(89,plain,(big_f(f(a), h(a, b))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(90,plain,
% 0.18/0.43 (big_f(a, h(a, b))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[89, 40])).
% 0.18/0.43 tff(91,plain,
% 0.18/0.43 (^[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))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(92,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.43 tff(93,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(94,plain,
% 0.18/0.43 (^[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))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(95,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[94])).
% 0.18/0.43 tff(96,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')).
% 0.18/0.43 tff(97,plain,
% 0.18/0.43 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.18/0.43 tff(98,plain,
% 0.18/0.43 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.18/0.43 tff(99,plain,(
% 0.18/0.43 ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[98])).
% 0.18/0.43 tff(100,plain,
% 0.18/0.43 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.18/0.43 tff(101,plain,
% 0.18/0.43 (((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))) | ((~(f(a) = a)) | (~(h(a, b) = b)) | (~big_f(f(a), h(a, b))))) <=> ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))) | (~(f(a) = a)) | (~(h(a, b) = b)) | (~big_f(f(a), h(a, b))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(102,plain,
% 0.18/0.43 (((~(f(a) = a)) | (~big_f(f(a), h(a, b))) | (~(h(a, b) = b))) <=> ((~(f(a) = a)) | (~(h(a, b) = b)) | (~big_f(f(a), h(a, b))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(103,plain,
% 0.18/0.44 (((~![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)) | (~(h(a, b) = b)) | (~big_f(f(a), h(a, b)))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[102])).
% 0.18/0.44 tff(104,plain,
% 0.18/0.44 (((~![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)) | (~(h(a, b) = b)) | (~big_f(f(a), h(a, b))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[103, 101])).
% 0.18/0.44 tff(105,plain,
% 0.18/0.44 ((~![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)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(106,plain,
% 0.18/0.44 ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(f(X), h(X, Z))) | (~(h(X, Z) = Z)))) | (~(f(a) = a)) | (~(h(a, b) = b)) | (~big_f(f(a), h(a, b)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.18/0.44 tff(107,plain,
% 0.18/0.44 (~(h(a, b) = b)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[106, 100, 37, 89])).
% 0.18/0.44 tff(108,plain,
% 0.18/0.44 (^[Y: $i, X: $i] : refl(((~big_f(X, Y)) | (Y = b)) <=> ((~big_f(X, Y)) | (Y = b)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(109,plain,
% 0.18/0.44 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.18/0.44 tff(110,plain,
% 0.18/0.44 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(111,axiom,(![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.18/0.44 tff(112,plain,
% 0.18/0.44 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.44 tff(113,plain,(
% 0.18/0.44 ![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.18/0.44 inference(skolemize,[status(sab)],[112])).
% 0.18/0.44 tff(114,plain,
% 0.18/0.44 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.18/0.44 tff(115,plain,
% 0.18/0.44 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | ((~big_f(a, h(a, b))) | (h(a, b) = b))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | (~big_f(a, h(a, b))) | (h(a, b) = b))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(116,plain,
% 0.18/0.44 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | ((~big_f(a, h(a, b))) | (h(a, b) = b))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(117,plain,
% 0.18/0.44 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (Y = b))) | (~big_f(a, h(a, b))) | (h(a, b) = b)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.44 tff(118,plain,
% 0.18/0.44 ((~big_f(a, h(a, b))) | (h(a, b) = b)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.18/0.44 tff(119,plain,
% 0.18/0.44 (~big_f(a, h(a, b))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[118, 107])).
% 0.18/0.44 tff(120,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[119, 90])).
% 0.18/0.44 % SZS output end Proof
%------------------------------------------------------------------------------