TSTP Solution File: SYN077-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN077-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 23:53:37 EDT 2022
% Result : Unsatisfiable 23.35s 15.25s
% Output : Proof 23.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN077-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 01:48:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 23.35/15.25 % SZS status Unsatisfiable
% 23.35/15.25 % SZS output start Proof
% 23.35/15.25 tff(big_f_type, type, (
% 23.35/15.25 big_f: ( $i * $i ) > $o)).
% 23.35/15.25 tff(h_type, type, (
% 23.35/15.25 h: $i > $i)).
% 23.35/15.25 tff(a_type, type, (
% 23.35/15.25 a: $i)).
% 23.35/15.25 tff(g_type, type, (
% 23.35/15.25 g: ( $i * $i ) > $i)).
% 23.35/15.25 tff(i_type, type, (
% 23.35/15.25 i: ( $i * $i ) > $i)).
% 23.35/15.25 tff(f_type, type, (
% 23.35/15.25 f: $i > $i)).
% 23.35/15.25 tff(1,assumption,(~big_f(g(i(a, a), h(a)), h(a))), introduced(assumption)).
% 23.35/15.25 tff(2,assumption,(big_f(a, a)), introduced(assumption)).
% 23.35/15.25 tff(3,plain,
% 23.35/15.25 (^[Y: $i, X: $i] : refl(((~(X = Y)) | big_f(X, f(Y))) <=> ((~(X = Y)) | big_f(X, f(Y))))),
% 23.35/15.25 inference(bind,[status(th)],[])).
% 23.35/15.25 tff(4,plain,
% 23.35/15.25 (![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y))) <=> ![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))),
% 23.35/15.25 inference(quant_intro,[status(thm)],[3])).
% 23.35/15.25 tff(5,plain,
% 23.35/15.25 (![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y))) <=> ![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))),
% 23.35/15.25 inference(rewrite,[status(thm)],[])).
% 23.35/15.25 tff(6,axiom,(![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 23.35/15.25 tff(7,plain,
% 23.35/15.25 (![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))),
% 23.35/15.25 inference(modus_ponens,[status(thm)],[6, 5])).
% 23.35/15.25 tff(8,plain,(
% 23.35/15.25 ![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))),
% 23.35/15.25 inference(skolemize,[status(sab)],[7])).
% 23.35/15.25 tff(9,plain,
% 23.35/15.25 (![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))),
% 23.35/15.25 inference(modus_ponens,[status(thm)],[8, 4])).
% 23.35/15.25 tff(10,plain,
% 23.35/15.25 (((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | big_f(a, f(a))) <=> ((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | big_f(a, f(a)))),
% 23.35/15.25 inference(rewrite,[status(thm)],[])).
% 23.35/15.25 tff(11,plain,
% 23.35/15.25 (($false | big_f(a, f(a))) <=> big_f(a, f(a))),
% 23.35/15.25 inference(rewrite,[status(thm)],[])).
% 23.35/15.25 tff(12,plain,
% 23.35/15.25 ((~$true) <=> $false),
% 23.35/15.25 inference(rewrite,[status(thm)],[])).
% 23.35/15.25 tff(13,plain,
% 23.35/15.25 ((a = a) <=> $true),
% 23.35/15.25 inference(rewrite,[status(thm)],[])).
% 23.35/15.25 tff(14,plain,
% 23.35/15.25 ((~(a = a)) <=> (~$true)),
% 23.35/15.25 inference(monotonicity,[status(thm)],[13])).
% 23.35/15.25 tff(15,plain,
% 23.35/15.25 ((~(a = a)) <=> $false),
% 23.35/15.25 inference(transitivity,[status(thm)],[14, 12])).
% 23.35/15.25 tff(16,plain,
% 23.35/15.25 (((~(a = a)) | big_f(a, f(a))) <=> ($false | big_f(a, f(a)))),
% 23.35/15.25 inference(monotonicity,[status(thm)],[15])).
% 23.35/15.25 tff(17,plain,
% 23.35/15.25 (((~(a = a)) | big_f(a, f(a))) <=> big_f(a, f(a))),
% 23.35/15.25 inference(transitivity,[status(thm)],[16, 11])).
% 23.35/15.25 tff(18,plain,
% 23.35/15.25 (((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | ((~(a = a)) | big_f(a, f(a)))) <=> ((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | big_f(a, f(a)))),
% 23.35/15.25 inference(monotonicity,[status(thm)],[17])).
% 23.35/15.25 tff(19,plain,
% 23.35/15.25 (((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | ((~(a = a)) | big_f(a, f(a)))) <=> ((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | big_f(a, f(a)))),
% 23.35/15.25 inference(transitivity,[status(thm)],[18, 10])).
% 23.35/15.25 tff(20,plain,
% 23.35/15.25 ((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | ((~(a = a)) | big_f(a, f(a)))),
% 23.35/15.25 inference(quant_inst,[status(thm)],[])).
% 23.35/15.25 tff(21,plain,
% 23.35/15.25 ((~![Y: $i, X: $i] : ((~(X = Y)) | big_f(X, f(Y)))) | big_f(a, f(a))),
% 23.35/15.25 inference(modus_ponens,[status(thm)],[20, 19])).
% 23.35/15.25 tff(22,plain,
% 23.35/15.25 (big_f(a, f(a))),
% 23.35/15.25 inference(unit_resolution,[status(thm)],[21, 9])).
% 23.35/15.25 tff(23,plain,
% 23.35/15.25 (^[Y: $i, X: $i] : refl((big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a))) <=> (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a))))),
% 23.35/15.25 inference(bind,[status(th)],[])).
% 23.35/15.25 tff(24,plain,
% 23.35/15.25 (![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a))) <=> ![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))),
% 23.35/15.25 inference(quant_intro,[status(thm)],[23])).
% 23.35/15.25 tff(25,plain,
% 23.35/15.25 (![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a))) <=> ![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))),
% 23.35/15.25 inference(rewrite,[status(thm)],[])).
% 23.35/15.25 tff(26,plain,
% 23.35/15.25 (^[Y: $i, X: $i] : rewrite((((~big_f(X, a)) | (~big_f(X, Y))) | big_f(g(X, Y), Y)) <=> (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a))))),
% 23.35/15.25 inference(bind,[status(th)],[])).
% 23.35/15.25 tff(27,plain,
% 23.35/15.25 (![Y: $i, X: $i] : (((~big_f(X, a)) | (~big_f(X, Y))) | big_f(g(X, Y), Y)) <=> ![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[26])).
% 23.35/15.26 tff(28,axiom,(![Y: $i, X: $i] : (((~big_f(X, a)) | (~big_f(X, Y))) | big_f(g(X, Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 23.35/15.26 tff(29,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[28, 27])).
% 23.35/15.26 tff(30,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[29, 25])).
% 23.35/15.26 tff(31,plain,(
% 23.35/15.26 ![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))),
% 23.35/15.26 inference(skolemize,[status(sab)],[30])).
% 23.35/15.26 tff(32,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[31, 24])).
% 23.35/15.26 tff(33,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | ((~big_f(a, a)) | (~big_f(a, f(a))) | big_f(g(a, f(a)), f(a)))) <=> ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (~big_f(a, a)) | (~big_f(a, f(a))) | big_f(g(a, f(a)), f(a)))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(34,plain,
% 23.35/15.26 ((big_f(g(a, f(a)), f(a)) | (~big_f(a, f(a))) | (~big_f(a, a))) <=> ((~big_f(a, a)) | (~big_f(a, f(a))) | big_f(g(a, f(a)), f(a)))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(35,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (big_f(g(a, f(a)), f(a)) | (~big_f(a, f(a))) | (~big_f(a, a)))) <=> ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | ((~big_f(a, a)) | (~big_f(a, f(a))) | big_f(g(a, f(a)), f(a))))),
% 23.35/15.26 inference(monotonicity,[status(thm)],[34])).
% 23.35/15.26 tff(36,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (big_f(g(a, f(a)), f(a)) | (~big_f(a, f(a))) | (~big_f(a, a)))) <=> ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (~big_f(a, a)) | (~big_f(a, f(a))) | big_f(g(a, f(a)), f(a)))),
% 23.35/15.26 inference(transitivity,[status(thm)],[35, 33])).
% 23.35/15.26 tff(37,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (big_f(g(a, f(a)), f(a)) | (~big_f(a, f(a))) | (~big_f(a, a)))),
% 23.35/15.26 inference(quant_inst,[status(thm)],[])).
% 23.35/15.26 tff(38,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (~big_f(a, a)) | (~big_f(a, f(a))) | big_f(g(a, f(a)), f(a))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[37, 36])).
% 23.35/15.26 tff(39,plain,
% 23.35/15.26 ((~big_f(a, a)) | big_f(g(a, f(a)), f(a))),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[38, 32, 22])).
% 23.35/15.26 tff(40,plain,
% 23.35/15.26 (big_f(g(a, f(a)), f(a))),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[39, 2])).
% 23.35/15.26 tff(41,plain,
% 23.35/15.26 (^[Y: $i, X: $i] : refl(((~big_f(X, f(Y))) | (X = Y)) <=> ((~big_f(X, f(Y))) | (X = Y)))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(42,plain,
% 23.35/15.26 (![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[41])).
% 23.35/15.26 tff(43,plain,
% 23.35/15.26 (![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(44,axiom,(![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 23.35/15.26 tff(45,plain,
% 23.35/15.26 (![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[44, 43])).
% 23.35/15.26 tff(46,plain,(
% 23.35/15.26 ![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))),
% 23.35/15.26 inference(skolemize,[status(sab)],[45])).
% 23.35/15.26 tff(47,plain,
% 23.35/15.26 (![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[46, 42])).
% 23.35/15.26 tff(48,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))) | ((~big_f(g(a, f(a)), f(a))) | (g(a, f(a)) = a))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))) | (~big_f(g(a, f(a)), f(a))) | (g(a, f(a)) = a))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(49,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))) | ((~big_f(g(a, f(a)), f(a))) | (g(a, f(a)) = a))),
% 23.35/15.26 inference(quant_inst,[status(thm)],[])).
% 23.35/15.26 tff(50,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : ((~big_f(X, f(Y))) | (X = Y))) | (~big_f(g(a, f(a)), f(a))) | (g(a, f(a)) = a)),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[49, 48])).
% 23.35/15.26 tff(51,plain,
% 23.35/15.26 (g(a, f(a)) = a),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[50, 47, 40])).
% 23.35/15.26 tff(52,plain,
% 23.35/15.26 (big_f(a, g(a, f(a))) <=> big_f(a, a)),
% 23.35/15.26 inference(monotonicity,[status(thm)],[51])).
% 23.35/15.26 tff(53,plain,
% 23.35/15.26 (big_f(a, a) <=> big_f(a, g(a, f(a)))),
% 23.35/15.26 inference(symmetry,[status(thm)],[52])).
% 23.35/15.26 tff(54,plain,
% 23.35/15.26 (big_f(a, g(a, f(a)))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[2, 53])).
% 23.35/15.26 tff(55,plain,
% 23.35/15.26 (^[Z: $i, Y: $i, X: $i] : refl(((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y)))) <=> ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y)))))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(56,plain,
% 23.35/15.26 (![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[55])).
% 23.35/15.26 tff(57,plain,
% 23.35/15.26 (![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(58,plain,
% 23.35/15.26 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((((~big_f(X, a)) | (~big_f(X, Y))) | (~big_f(Z, g(X, Y)))) <=> ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, g(X, Y))))), (((((~big_f(X, a)) | (~big_f(X, Y))) | (~big_f(Z, g(X, Y)))) | (~big_f(Z, Y))) <=> (((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, g(X, Y)))) | (~big_f(Z, Y))))), rewrite((((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, g(X, Y)))) | (~big_f(Z, Y))) <=> ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))), (((((~big_f(X, a)) | (~big_f(X, Y))) | (~big_f(Z, g(X, Y)))) | (~big_f(Z, Y))) <=> ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(59,plain,
% 23.35/15.26 (![Z: $i, Y: $i, X: $i] : ((((~big_f(X, a)) | (~big_f(X, Y))) | (~big_f(Z, g(X, Y)))) | (~big_f(Z, Y))) <=> ![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[58])).
% 23.35/15.26 tff(60,axiom,(![Z: $i, Y: $i, X: $i] : ((((~big_f(X, a)) | (~big_f(X, Y))) | (~big_f(Z, g(X, Y)))) | (~big_f(Z, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 23.35/15.26 tff(61,plain,
% 23.35/15.26 (![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[60, 59])).
% 23.35/15.26 tff(62,plain,
% 23.35/15.26 (![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[61, 57])).
% 23.35/15.26 tff(63,plain,(
% 23.35/15.26 ![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))),
% 23.35/15.26 inference(skolemize,[status(sab)],[62])).
% 23.35/15.26 tff(64,plain,
% 23.35/15.26 (![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[63, 56])).
% 23.35/15.26 tff(65,plain,
% 23.35/15.26 (((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | (~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a)))))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(66,plain,
% 23.35/15.26 (((~big_f(a, f(a))) | (~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a))))) <=> ((~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a)))))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(67,plain,
% 23.35/15.26 (((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(a, f(a))) | (~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a))))))),
% 23.35/15.26 inference(monotonicity,[status(thm)],[66])).
% 23.35/15.26 tff(68,plain,
% 23.35/15.26 (((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(a, f(a))) | (~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | (~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a)))))),
% 23.35/15.26 inference(transitivity,[status(thm)],[67, 65])).
% 23.35/15.26 tff(69,plain,
% 23.35/15.26 ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(a, f(a))) | (~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a)))))),
% 23.35/15.26 inference(quant_inst,[status(thm)],[])).
% 23.35/15.26 tff(70,plain,
% 23.35/15.26 ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | (~big_f(a, a)) | (~big_f(a, f(a))) | (~big_f(a, g(a, f(a))))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[69, 68])).
% 23.35/15.26 tff(71,plain,
% 23.35/15.26 (~big_f(a, g(a, f(a)))),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[70, 64, 22, 2])).
% 23.35/15.26 tff(72,plain,
% 23.35/15.26 ($false),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[71, 54])).
% 23.35/15.26 tff(73,plain,(~big_f(a, a)), inference(lemma,lemma(discharge,[]))).
% 23.35/15.26 tff(74,plain,
% 23.35/15.26 (^[X: $i] : refl((big_f(X, h(X)) | big_f(X, a)) <=> (big_f(X, h(X)) | big_f(X, a)))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(75,plain,
% 23.35/15.26 (![X: $i] : (big_f(X, h(X)) | big_f(X, a)) <=> ![X: $i] : (big_f(X, h(X)) | big_f(X, a))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[74])).
% 23.35/15.26 tff(76,plain,
% 23.35/15.26 (![X: $i] : (big_f(X, h(X)) | big_f(X, a)) <=> ![X: $i] : (big_f(X, h(X)) | big_f(X, a))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(77,axiom,(![X: $i] : (big_f(X, h(X)) | big_f(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 23.35/15.26 tff(78,plain,
% 23.35/15.26 (![X: $i] : (big_f(X, h(X)) | big_f(X, a))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[77, 76])).
% 23.35/15.26 tff(79,plain,(
% 23.35/15.26 ![X: $i] : (big_f(X, h(X)) | big_f(X, a))),
% 23.35/15.26 inference(skolemize,[status(sab)],[78])).
% 23.35/15.26 tff(80,plain,
% 23.35/15.26 (![X: $i] : (big_f(X, h(X)) | big_f(X, a))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[79, 75])).
% 23.35/15.26 tff(81,plain,
% 23.35/15.26 (((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | (big_f(a, a) | big_f(a, h(a)))) <=> ((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | big_f(a, a) | big_f(a, h(a)))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(82,plain,
% 23.35/15.26 ((big_f(a, h(a)) | big_f(a, a)) <=> (big_f(a, a) | big_f(a, h(a)))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(83,plain,
% 23.35/15.26 (((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | (big_f(a, h(a)) | big_f(a, a))) <=> ((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | (big_f(a, a) | big_f(a, h(a))))),
% 23.35/15.26 inference(monotonicity,[status(thm)],[82])).
% 23.35/15.26 tff(84,plain,
% 23.35/15.26 (((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | (big_f(a, h(a)) | big_f(a, a))) <=> ((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | big_f(a, a) | big_f(a, h(a)))),
% 23.35/15.26 inference(transitivity,[status(thm)],[83, 81])).
% 23.35/15.26 tff(85,plain,
% 23.35/15.26 ((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | (big_f(a, h(a)) | big_f(a, a))),
% 23.35/15.26 inference(quant_inst,[status(thm)],[])).
% 23.35/15.26 tff(86,plain,
% 23.35/15.26 ((~![X: $i] : (big_f(X, h(X)) | big_f(X, a))) | big_f(a, a) | big_f(a, h(a))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[85, 84])).
% 23.35/15.26 tff(87,plain,
% 23.35/15.26 (big_f(a, a) | big_f(a, h(a))),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[86, 80])).
% 23.35/15.26 tff(88,plain,
% 23.35/15.26 (big_f(a, h(a))),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[87, 73])).
% 23.35/15.26 tff(89,plain,
% 23.35/15.26 (^[Y: $i, X: $i] : refl((big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X))) <=> (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X))))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(90,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X))) <=> ![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[89])).
% 23.35/15.26 tff(91,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X))) <=> ![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(92,plain,
% 23.35/15.26 (^[Y: $i, X: $i] : rewrite(((big_f(X, a) | big_f(i(X, Y), h(X))) | (~big_f(Y, h(X)))) <=> (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X))))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(93,plain,
% 23.35/15.26 (![Y: $i, X: $i] : ((big_f(X, a) | big_f(i(X, Y), h(X))) | (~big_f(Y, h(X)))) <=> ![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[92])).
% 23.35/15.26 tff(94,axiom,(![Y: $i, X: $i] : ((big_f(X, a) | big_f(i(X, Y), h(X))) | (~big_f(Y, h(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 23.35/15.26 tff(95,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[94, 93])).
% 23.35/15.26 tff(96,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[95, 91])).
% 23.35/15.26 tff(97,plain,(
% 23.35/15.26 ![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))),
% 23.35/15.26 inference(skolemize,[status(sab)],[96])).
% 23.35/15.26 tff(98,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[97, 90])).
% 23.35/15.26 tff(99,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | ((~big_f(a, h(a))) | big_f(i(a, a), h(a)) | big_f(a, a))) <=> ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (~big_f(a, h(a))) | big_f(i(a, a), h(a)) | big_f(a, a))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(100,plain,
% 23.35/15.26 ((big_f(a, a) | (~big_f(a, h(a))) | big_f(i(a, a), h(a))) <=> ((~big_f(a, h(a))) | big_f(i(a, a), h(a)) | big_f(a, a))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(101,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (big_f(a, a) | (~big_f(a, h(a))) | big_f(i(a, a), h(a)))) <=> ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | ((~big_f(a, h(a))) | big_f(i(a, a), h(a)) | big_f(a, a)))),
% 23.35/15.26 inference(monotonicity,[status(thm)],[100])).
% 23.35/15.26 tff(102,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (big_f(a, a) | (~big_f(a, h(a))) | big_f(i(a, a), h(a)))) <=> ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (~big_f(a, h(a))) | big_f(i(a, a), h(a)) | big_f(a, a))),
% 23.35/15.26 inference(transitivity,[status(thm)],[101, 99])).
% 23.35/15.26 tff(103,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (big_f(a, a) | (~big_f(a, h(a))) | big_f(i(a, a), h(a)))),
% 23.35/15.26 inference(quant_inst,[status(thm)],[])).
% 23.35/15.26 tff(104,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (~big_f(a, h(a))) | big_f(i(a, a), h(a)) | big_f(a, a)),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[103, 102])).
% 23.35/15.26 tff(105,plain,
% 23.35/15.26 (big_f(i(a, a), h(a))),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[104, 98, 73, 88])).
% 23.35/15.26 tff(106,plain,
% 23.35/15.26 (^[Y: $i, X: $i] : refl((big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y)))) <=> (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y)))))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(107,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y)))) <=> ![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[106])).
% 23.35/15.26 tff(108,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y)))) <=> ![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(109,plain,
% 23.35/15.26 (^[Y: $i, X: $i] : rewrite((((~big_f(X, h(Y))) | big_f(i(Y, X), X)) | big_f(Y, a)) <=> (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y)))))),
% 23.35/15.26 inference(bind,[status(th)],[])).
% 23.35/15.26 tff(110,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (((~big_f(X, h(Y))) | big_f(i(Y, X), X)) | big_f(Y, a)) <=> ![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))),
% 23.35/15.26 inference(quant_intro,[status(thm)],[109])).
% 23.35/15.26 tff(111,axiom,(![Y: $i, X: $i] : (((~big_f(X, h(Y))) | big_f(i(Y, X), X)) | big_f(Y, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 23.35/15.26 tff(112,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[111, 110])).
% 23.35/15.26 tff(113,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[112, 108])).
% 23.35/15.26 tff(114,plain,(
% 23.35/15.26 ![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))),
% 23.35/15.26 inference(skolemize,[status(sab)],[113])).
% 23.35/15.26 tff(115,plain,
% 23.35/15.26 (![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[114, 107])).
% 23.35/15.26 tff(116,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | ((~big_f(a, h(a))) | big_f(i(a, a), a) | big_f(a, a))) <=> ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (~big_f(a, h(a))) | big_f(i(a, a), a) | big_f(a, a))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(117,plain,
% 23.35/15.26 ((big_f(a, a) | big_f(i(a, a), a) | (~big_f(a, h(a)))) <=> ((~big_f(a, h(a))) | big_f(i(a, a), a) | big_f(a, a))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(118,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | big_f(i(a, a), a) | (~big_f(a, h(a))))) <=> ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | ((~big_f(a, h(a))) | big_f(i(a, a), a) | big_f(a, a)))),
% 23.35/15.26 inference(monotonicity,[status(thm)],[117])).
% 23.35/15.26 tff(119,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | big_f(i(a, a), a) | (~big_f(a, h(a))))) <=> ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (~big_f(a, h(a))) | big_f(i(a, a), a) | big_f(a, a))),
% 23.35/15.26 inference(transitivity,[status(thm)],[118, 116])).
% 23.35/15.26 tff(120,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | big_f(i(a, a), a) | (~big_f(a, h(a))))),
% 23.35/15.26 inference(quant_inst,[status(thm)],[])).
% 23.35/15.26 tff(121,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (~big_f(a, h(a))) | big_f(i(a, a), a) | big_f(a, a)),
% 23.35/15.26 inference(modus_ponens,[status(thm)],[120, 119])).
% 23.35/15.26 tff(122,plain,
% 23.35/15.26 (big_f(i(a, a), a)),
% 23.35/15.26 inference(unit_resolution,[status(thm)],[121, 115, 73, 88])).
% 23.35/15.26 tff(123,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | ((~big_f(i(a, a), h(a))) | big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), a)))) <=> ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (~big_f(i(a, a), h(a))) | big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), a)))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(124,plain,
% 23.35/15.26 ((big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a))) <=> ((~big_f(i(a, a), h(a))) | big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), a)))),
% 23.35/15.26 inference(rewrite,[status(thm)],[])).
% 23.35/15.26 tff(125,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a)))) <=> ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | ((~big_f(i(a, a), h(a))) | big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), a))))),
% 23.35/15.26 inference(monotonicity,[status(thm)],[124])).
% 23.35/15.26 tff(126,plain,
% 23.35/15.26 (((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a)))) <=> ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (~big_f(i(a, a), h(a))) | big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), a)))),
% 23.35/15.26 inference(transitivity,[status(thm)],[125, 123])).
% 23.35/15.26 tff(127,plain,
% 23.35/15.26 ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a)))),
% 23.35/15.27 inference(quant_inst,[status(thm)],[])).
% 23.35/15.27 tff(128,plain,
% 23.35/15.27 ((~![Y: $i, X: $i] : (big_f(g(X, Y), Y) | (~big_f(X, Y)) | (~big_f(X, a)))) | (~big_f(i(a, a), h(a))) | big_f(g(i(a, a), h(a)), h(a)) | (~big_f(i(a, a), a))),
% 23.35/15.27 inference(modus_ponens,[status(thm)],[127, 126])).
% 23.35/15.27 tff(129,plain,
% 23.35/15.27 ($false),
% 23.35/15.27 inference(unit_resolution,[status(thm)],[128, 32, 122, 105, 1])).
% 23.35/15.27 tff(130,plain,(big_f(g(i(a, a), h(a)), h(a))), inference(lemma,lemma(discharge,[]))).
% 23.35/15.27 tff(131,assumption,(big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))), introduced(assumption)).
% 23.35/15.27 tff(132,assumption,(~big_f(i(a, g(i(a, a), h(a))), h(a))), introduced(assumption)).
% 23.35/15.27 tff(133,plain,
% 23.35/15.27 (big_f(g(i(a, a), h(a)), h(a))),
% 23.35/15.27 inference(unit_resolution,[status(thm)],[128, 32, 122, 105])).
% 23.35/15.27 tff(134,plain,
% 23.35/15.27 (((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), h(a)))) <=> ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), h(a)))),
% 23.35/15.27 inference(rewrite,[status(thm)],[])).
% 23.35/15.27 tff(135,plain,
% 23.35/15.27 ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | (big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), h(a)))),
% 23.35/15.27 inference(quant_inst,[status(thm)],[])).
% 23.35/15.27 tff(136,plain,
% 23.35/15.27 ((~![Y: $i, X: $i] : (big_f(X, a) | (~big_f(Y, h(X))) | big_f(i(X, Y), h(X)))) | big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), h(a))),
% 23.35/15.27 inference(modus_ponens,[status(thm)],[135, 134])).
% 23.35/15.27 tff(137,plain,
% 23.35/15.27 ($false),
% 23.35/15.27 inference(unit_resolution,[status(thm)],[136, 98, 73, 133, 132])).
% 23.35/15.27 tff(138,plain,(big_f(i(a, g(i(a, a), h(a))), h(a))), inference(lemma,lemma(discharge,[]))).
% 23.35/15.27 tff(139,plain,
% 23.35/15.27 (((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(i(a, a), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))) | (~big_f(i(a, a), a)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | (~big_f(i(a, a), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))) | (~big_f(i(a, a), a)))),
% 23.35/15.27 inference(rewrite,[status(thm)],[])).
% 23.35/15.27 tff(140,plain,
% 23.35/15.27 (((~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a)) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))))) <=> ((~big_f(i(a, a), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))) | (~big_f(i(a, a), a)))),
% 23.35/15.27 inference(rewrite,[status(thm)],[])).
% 23.35/15.27 tff(141,plain,
% 23.35/15.27 (((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a)) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(i(a, a), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))) | (~big_f(i(a, a), a))))),
% 23.35/15.27 inference(monotonicity,[status(thm)],[140])).
% 23.35/15.27 tff(142,plain,
% 23.35/15.27 (((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a)) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | (~big_f(i(a, a), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))) | (~big_f(i(a, a), a)))),
% 23.35/15.27 inference(transitivity,[status(thm)],[141, 139])).
% 23.35/15.27 tff(143,plain,
% 23.35/15.27 ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | ((~big_f(i(a, a), h(a))) | (~big_f(i(a, a), a)) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))))),
% 23.35/15.27 inference(quant_inst,[status(thm)],[])).
% 23.35/15.27 tff(144,plain,
% 23.35/15.27 ((~![Z: $i, Y: $i, X: $i] : ((~big_f(X, Y)) | (~big_f(X, a)) | (~big_f(Z, Y)) | (~big_f(Z, g(X, Y))))) | (~big_f(i(a, a), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), h(a))) | (~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))) | (~big_f(i(a, a), a))),
% 23.35/15.27 inference(modus_ponens,[status(thm)],[143, 142])).
% 23.35/15.27 tff(145,plain,
% 23.35/15.27 ($false),
% 23.35/15.27 inference(unit_resolution,[status(thm)],[144, 64, 122, 105, 138, 131])).
% 23.35/15.27 tff(146,plain,(~big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))), inference(lemma,lemma(discharge,[]))).
% 23.35/15.27 tff(147,plain,
% 23.35/15.27 (((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))))) <=> ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))))),
% 23.35/15.27 inference(rewrite,[status(thm)],[])).
% 23.35/15.27 tff(148,plain,
% 23.35/15.27 ((big_f(a, a) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))) | (~big_f(g(i(a, a), h(a)), h(a)))) <=> (big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))))),
% 23.35/15.27 inference(rewrite,[status(thm)],[])).
% 23.35/15.27 tff(149,plain,
% 23.35/15.27 (((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))) | (~big_f(g(i(a, a), h(a)), h(a))))) <=> ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))))),
% 23.35/15.27 inference(monotonicity,[status(thm)],[148])).
% 23.35/15.27 tff(150,plain,
% 23.35/15.27 (((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))) | (~big_f(g(i(a, a), h(a)), h(a))))) <=> ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))))),
% 23.35/15.27 inference(transitivity,[status(thm)],[149, 147])).
% 23.35/15.27 tff(151,plain,
% 23.35/15.27 ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | (big_f(a, a) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a))) | (~big_f(g(i(a, a), h(a)), h(a))))),
% 23.35/15.27 inference(quant_inst,[status(thm)],[])).
% 23.35/15.27 tff(152,plain,
% 23.35/15.27 ((~![Y: $i, X: $i] : (big_f(Y, a) | big_f(i(Y, X), X) | (~big_f(X, h(Y))))) | big_f(a, a) | (~big_f(g(i(a, a), h(a)), h(a))) | big_f(i(a, g(i(a, a), h(a))), g(i(a, a), h(a)))),
% 23.35/15.27 inference(modus_ponens,[status(thm)],[151, 150])).
% 23.35/15.27 tff(153,plain,
% 23.35/15.27 ($false),
% 23.35/15.27 inference(unit_resolution,[status(thm)],[152, 115, 73, 146, 130])).
% 23.35/15.27 % SZS output end Proof
%------------------------------------------------------------------------------