TSTP Solution File: SYN075-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN075-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 23:53:34 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN075-1 : TPTP v8.1.0. Released v1.0.0.
% 0.14/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Sep 5 01:32:16 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(h_type, type, (
% 0.21/0.44 h: ( $i * $i ) > $i)).
% 0.21/0.44 tff(a_type, type, (
% 0.21/0.44 a: $i)).
% 0.21/0.44 tff(b_type, type, (
% 0.21/0.44 b: $i)).
% 0.21/0.44 tff(big_f_type, type, (
% 0.21/0.44 big_f: ( $i * $i ) > $o)).
% 0.21/0.44 tff(f_type, type, (
% 0.21/0.44 f: $i > $i)).
% 0.21/0.44 tff(g_type, type, (
% 0.21/0.44 g: $i > $i)).
% 0.21/0.44 tff(1,assumption,(~(f(b) = b)), introduced(assumption)).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (^[Y: $i, X: $i] : refl(((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))) <=> ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))) <=> ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X))) <=> ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.44 tff(7,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')).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.44 tff(10,plain,(
% 0.21/0.44 ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[9])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | ((f(b) = b) | big_f(g(b), f(b)))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | (f(b) = b) | big_f(g(b), f(b)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (((f(b) = b) | $false | big_f(g(b), f(b))) <=> ((f(b) = b) | big_f(g(b), f(b)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 ((~$true) <=> $false),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 ((g(b) = g(b)) <=> $true),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 ((~(g(b) = g(b))) <=> (~$true)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 ((~(g(b) = g(b))) <=> $false),
% 0.21/0.44 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (((f(b) = b) | (~(g(b) = g(b))) | big_f(g(b), f(b))) <=> ((f(b) = b) | $false | big_f(g(b), f(b)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (((f(b) = b) | (~(g(b) = g(b))) | big_f(g(b), f(b))) <=> ((f(b) = b) | big_f(g(b), f(b)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[18, 13])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | ((f(b) = b) | (~(g(b) = g(b))) | big_f(g(b), f(b)))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | ((f(b) = b) | big_f(g(b), f(b))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[19])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | ((f(b) = b) | (~(g(b) = g(b))) | big_f(g(b), f(b)))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | (f(b) = b) | big_f(g(b), f(b)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[20, 12])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | ((f(b) = b) | (~(g(b) = g(b))) | big_f(g(b), f(b)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | big_f(Y, f(X)))) | (f(b) = b) | big_f(g(b), f(b))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 ((f(b) = b) | big_f(g(b), f(b))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[23, 11])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (big_f(g(b), f(b))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (^[Y: $i, X: $i] : refl(((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X)))) <=> ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X)))) <=> ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X)))) <=> ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (^[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))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.44 tff(31,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')).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.44 tff(34,plain,(
% 0.21/0.44 ![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[33])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | ((f(b) = b) | (~big_f(g(b), f(b))))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | (f(b) = b) | (~big_f(g(b), f(b))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (((f(b) = b) | $false | (~big_f(g(b), f(b)))) <=> ((f(b) = b) | (~big_f(g(b), f(b))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (((f(b) = b) | (~(g(b) = g(b))) | (~big_f(g(b), f(b)))) <=> ((f(b) = b) | $false | (~big_f(g(b), f(b))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (((f(b) = b) | (~(g(b) = g(b))) | (~big_f(g(b), f(b)))) <=> ((f(b) = b) | (~big_f(g(b), f(b))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[38, 37])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | ((f(b) = b) | (~(g(b) = g(b))) | (~big_f(g(b), f(b))))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | ((f(b) = b) | (~big_f(g(b), f(b)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | ((f(b) = b) | (~(g(b) = g(b))) | (~big_f(g(b), f(b))))) <=> ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | (f(b) = b) | (~big_f(g(b), f(b))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[40, 36])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | ((f(b) = b) | (~(g(b) = g(b))) | (~big_f(g(b), f(b))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : ((f(X) = X) | (~(Y = g(X))) | (~big_f(Y, f(X))))) | (f(b) = b) | (~big_f(g(b), f(b)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[43, 35, 1, 25])).
% 0.21/0.44 tff(45,plain,(f(b) = b), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (b = f(b)),
% 0.21/0.44 inference(symmetry,[status(thm)],[45])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (big_f(h(b, a), b) <=> big_f(h(b, a), f(b))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[46])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (big_f(h(b, a), f(b)) <=> big_f(h(b, a), b)),
% 0.21/0.44 inference(symmetry,[status(thm)],[47])).
% 0.21/0.44 tff(49,assumption,(~(h(b, a) = a)), introduced(assumption)).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.44 tff(55,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')).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.44 tff(58,plain,(
% 0.21/0.44 ![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[57])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (![Z: $i, X: $i] : ((h(X, Z) = Z) | (~(f(X) = X)) | big_f(h(X, Z), f(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (((~![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) | (~(f(b) = b)) | big_f(h(b, a), f(b)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 ((~![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)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 ((~![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))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 ((h(b, a) = a) | (~(f(b) = b)) | big_f(h(b, a), f(b))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 ((h(b, a) = a) | big_f(h(b, a), f(b))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[63, 45])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (big_f(h(b, a), f(b))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[64, 49])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (big_f(h(b, a), b)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[65, 48])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (^[Y: $i, X: $i] : refl(((~big_f(X, Y)) | (X = a)) <=> ((~big_f(X, Y)) | (X = a)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a)) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(70,axiom,(![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.44 tff(72,plain,(
% 0.21/0.45 ![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.21/0.45 inference(skolemize,[status(sab)],[71])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (((~![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))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | ((~big_f(h(b, a), b)) | (h(b, a) = a))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | (X = a))) | (~big_f(h(b, a), b)) | (h(b, a) = a)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (~big_f(h(b, a), b)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 73, 49])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[77, 66])).
% 0.21/0.45 tff(79,plain,(h(b, a) = a), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (h(b, h(b, a)) = h(b, a)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (big_f(h(b, h(b, a)), f(b)) <=> big_f(h(b, a), f(b))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (big_f(h(b, a), f(b)) <=> big_f(h(b, h(b, a)), f(b))),
% 0.21/0.45 inference(symmetry,[status(thm)],[81])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (a = h(b, a)),
% 0.21/0.45 inference(symmetry,[status(thm)],[79])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (big_f(a, b) <=> big_f(h(b, a), f(b))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[83, 46])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : refl((big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> (big_f(X, Y) | (~(Y = b)) | (~(X = a))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a))) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : rewrite((((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> (big_f(X, Y) | (~(Y = b)) | (~(X = a))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y)) <=> ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.45 tff(90,axiom,(![Y: $i, X: $i] : (((~(X = a)) | (~(Y = b))) | big_f(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.21/0.45 tff(93,plain,(
% 0.21/0.45 ![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[92])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (((~![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))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 ((big_f(a, b) | $false | $false) <=> big_f(a, b)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 ((a = a) <=> $true),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 ((~(a = a)) <=> (~$true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 ((~(a = a)) <=> $false),
% 0.21/0.45 inference(transitivity,[status(thm)],[98, 14])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 ((b = b) <=> $true),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 ((~(b = b)) <=> (~$true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 ((~(b = b)) <=> $false),
% 0.21/0.45 inference(transitivity,[status(thm)],[101, 14])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 ((big_f(a, b) | (~(b = b)) | (~(a = a))) <=> (big_f(a, b) | $false | $false)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[102, 99])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 ((big_f(a, b) | (~(b = b)) | (~(a = a))) <=> big_f(a, b)),
% 0.21/0.45 inference(transitivity,[status(thm)],[103, 96])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 (((~![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))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (((~![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))),
% 0.21/0.45 inference(transitivity,[status(thm)],[105, 95])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | (big_f(a, b) | (~(b = b)) | (~(a = a)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : (big_f(X, Y) | (~(Y = b)) | (~(X = a)))) | big_f(a, b)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 (big_f(a, b)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[108, 94])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (big_f(h(b, a), f(b))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[109, 84])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (big_f(h(b, h(b, a)), f(b))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[110, 82])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.45 tff(117,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')).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.21/0.45 tff(120,plain,(
% 0.21/0.45 ![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[119])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | ((~(f(b) = b)) | (~(h(b, h(b, a)) = h(b, a))) | (~big_f(h(b, h(b, a)), f(b))))) <=> ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | (~(f(b) = b)) | (~(h(b, h(b, a)) = h(b, a))) | (~big_f(h(b, h(b, a)), f(b))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (((~(f(b) = b)) | (~big_f(h(b, h(b, a)), f(b))) | (~(h(b, h(b, a)) = h(b, a)))) <=> ((~(f(b) = b)) | (~(h(b, h(b, a)) = h(b, a))) | (~big_f(h(b, h(b, a)), f(b))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (((~![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, h(b, a)), f(b))) | (~(h(b, h(b, a)) = h(b, a))))) <=> ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | ((~(f(b) = b)) | (~(h(b, h(b, a)) = h(b, a))) | (~big_f(h(b, h(b, a)), f(b)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (((~![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, h(b, a)), f(b))) | (~(h(b, h(b, a)) = h(b, a))))) <=> ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | (~(f(b) = b)) | (~(h(b, h(b, a)) = h(b, a))) | (~big_f(h(b, h(b, a)), f(b))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[124, 122])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 ((~![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, h(b, a)), f(b))) | (~(h(b, h(b, a)) = h(b, a))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 ((~![Z: $i, X: $i] : ((~(f(X) = X)) | (~big_f(h(X, Z), f(X))) | (~(h(X, Z) = Z)))) | (~(f(b) = b)) | (~(h(b, h(b, a)) = h(b, a))) | (~big_f(h(b, h(b, a)), f(b)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 ((~(h(b, h(b, a)) = h(b, a))) | (~big_f(h(b, h(b, a)), f(b)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[127, 121, 45])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[128, 111, 80])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------