TSTP Solution File: ANA002-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA002-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Tue Sep 6 16:23:19 EDT 2022
% Result : Unsatisfiable 1.98s 1.53s
% Output : Proof 2.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : ANA002-4 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Aug 29 17:55:28 EDT 2022
% 0.12/0.36 % CPUTime :
% 0.12/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.37 Usage: tptp [options] [-file:]file
% 0.12/0.37 -h, -? prints this message.
% 0.12/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.37 -m, -model generate model.
% 0.12/0.37 -p, -proof generate proof.
% 0.12/0.37 -c, -core generate unsat core of named formulas.
% 0.12/0.37 -st, -statistics display statistics.
% 0.12/0.37 -t:timeout set timeout (in second).
% 0.12/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.37 -<param>:<value> configuration parameter and value.
% 0.12/0.37 -o:<output-file> file to place output in.
% 1.98/1.53 % SZS status Unsatisfiable
% 1.98/1.53 % SZS output start Proof
% 1.98/1.53 tff(less_than_or_equal_type, type, (
% 1.98/1.53 less_than_or_equal: ( $i * $i ) > $o)).
% 1.98/1.53 tff(q_type, type, (
% 1.98/1.53 q: ( $i * $i ) > $i)).
% 1.98/1.53 tff(k_type, type, (
% 1.98/1.53 k: $i > $i)).
% 1.98/1.53 tff(h_type, type, (
% 1.98/1.53 h: $i > $i)).
% 1.98/1.53 tff(l_type, type, (
% 1.98/1.53 l: $i)).
% 1.98/1.53 tff(f_type, type, (
% 1.98/1.53 f: $i > $i)).
% 1.98/1.53 tff(n0_type, type, (
% 1.98/1.53 n0: $i)).
% 1.98/1.53 tff(lower_bound_type, type, (
% 1.98/1.53 lower_bound: $i)).
% 1.98/1.53 tff(g_type, type, (
% 1.98/1.53 g: $i > $i)).
% 1.98/1.53 tff(upper_bound_type, type, (
% 1.98/1.53 upper_bound: $i)).
% 1.98/1.53 tff(1,assumption,(less_than_or_equal(l, q(l, k(h(k(l)))))), introduced(assumption)).
% 1.98/1.53 tff(2,assumption,(~less_than_or_equal(k(h(k(l))), k(l))), introduced(assumption)).
% 1.98/1.53 tff(3,assumption,(~less_than_or_equal(l, h(k(l)))), introduced(assumption)).
% 1.98/1.53 tff(4,assumption,(~less_than_or_equal(f(l), n0)), introduced(assumption)).
% 1.98/1.53 tff(5,assumption,(~less_than_or_equal(l, upper_bound)), introduced(assumption)).
% 1.98/1.53 tff(6,plain,
% 1.98/1.53 (^[X: $i] : refl(((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X)) <=> ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X)))),
% 1.98/1.53 inference(bind,[status(th)],[])).
% 1.98/1.53 tff(7,plain,
% 1.98/1.53 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X)) <=> ![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 1.98/1.53 inference(quant_intro,[status(thm)],[6])).
% 1.98/1.53 tff(8,plain,
% 1.98/1.53 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X)) <=> ![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(9,axiom,(![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','crossover4_and_g_function3')).
% 1.98/1.53 tff(10,plain,
% 1.98/1.53 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.98/1.53 tff(11,plain,(
% 1.98/1.53 ![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 1.98/1.53 inference(skolemize,[status(sab)],[10])).
% 1.98/1.53 tff(12,plain,
% 1.98/1.53 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[11, 7])).
% 1.98/1.53 tff(13,plain,
% 1.98/1.53 (((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | ((~less_than_or_equal(g(upper_bound), upper_bound)) | less_than_or_equal(l, upper_bound))) <=> ((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | (~less_than_or_equal(g(upper_bound), upper_bound)) | less_than_or_equal(l, upper_bound))),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(14,plain,
% 1.98/1.53 ((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | ((~less_than_or_equal(g(upper_bound), upper_bound)) | less_than_or_equal(l, upper_bound))),
% 1.98/1.53 inference(quant_inst,[status(thm)],[])).
% 1.98/1.53 tff(15,plain,
% 1.98/1.53 ((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | (~less_than_or_equal(g(upper_bound), upper_bound)) | less_than_or_equal(l, upper_bound)),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.98/1.53 tff(16,plain,
% 1.98/1.53 (~less_than_or_equal(g(upper_bound), upper_bound)),
% 1.98/1.53 inference(unit_resolution,[status(thm)],[15, 12, 5])).
% 1.98/1.53 tff(17,plain,
% 1.98/1.53 (^[X: $i] : refl((less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound)) <=> (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound)))),
% 1.98/1.53 inference(bind,[status(th)],[])).
% 1.98/1.53 tff(18,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound)) <=> ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 1.98/1.53 inference(quant_intro,[status(thm)],[17])).
% 1.98/1.53 tff(19,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound)) <=> ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(20,plain,
% 1.98/1.53 (^[X: $i] : rewrite((less_than_or_equal(g(X), upper_bound) | less_than_or_equal(l, X)) <=> (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound)))),
% 1.98/1.53 inference(bind,[status(th)],[])).
% 1.98/1.53 tff(21,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(g(X), upper_bound) | less_than_or_equal(l, X)) <=> ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 1.98/1.53 inference(quant_intro,[status(thm)],[20])).
% 1.98/1.53 tff(22,axiom,(![X: $i] : (less_than_or_equal(g(X), upper_bound) | less_than_or_equal(l, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','crossover2_and_g_function1')).
% 1.98/1.53 tff(23,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.98/1.53 tff(24,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[23, 19])).
% 1.98/1.53 tff(25,plain,(
% 1.98/1.53 ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 1.98/1.53 inference(skolemize,[status(sab)],[24])).
% 1.98/1.53 tff(26,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[25, 18])).
% 1.98/1.53 tff(27,plain,
% 1.98/1.53 (((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | (less_than_or_equal(l, upper_bound) | less_than_or_equal(g(upper_bound), upper_bound))) <=> ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | less_than_or_equal(l, upper_bound) | less_than_or_equal(g(upper_bound), upper_bound))),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(28,plain,
% 1.98/1.53 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | (less_than_or_equal(l, upper_bound) | less_than_or_equal(g(upper_bound), upper_bound))),
% 1.98/1.53 inference(quant_inst,[status(thm)],[])).
% 1.98/1.53 tff(29,plain,
% 1.98/1.53 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | less_than_or_equal(l, upper_bound) | less_than_or_equal(g(upper_bound), upper_bound)),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.98/1.53 tff(30,plain,
% 1.98/1.53 ($false),
% 1.98/1.53 inference(unit_resolution,[status(thm)],[29, 26, 5, 16])).
% 1.98/1.53 tff(31,plain,(less_than_or_equal(l, upper_bound)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.53 tff(32,plain,
% 1.98/1.53 (less_than_or_equal(f(lower_bound), n0) <=> less_than_or_equal(f(lower_bound), n0)),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(33,axiom,(less_than_or_equal(f(lower_bound), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lower_mapping')).
% 1.98/1.53 tff(34,plain,
% 1.98/1.53 (less_than_or_equal(f(lower_bound), n0)),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.98/1.53 tff(35,plain,
% 1.98/1.53 (less_than_or_equal(lower_bound, upper_bound) <=> less_than_or_equal(lower_bound, upper_bound)),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(36,axiom,(less_than_or_equal(lower_bound, upper_bound)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_interval')).
% 1.98/1.53 tff(37,plain,
% 1.98/1.53 (less_than_or_equal(lower_bound, upper_bound)),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.98/1.53 tff(38,plain,
% 1.98/1.53 (^[X: $i] : refl((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))))),
% 1.98/1.53 inference(bind,[status(th)],[])).
% 1.98/1.53 tff(39,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))) <=> ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 1.98/1.53 inference(quant_intro,[status(thm)],[38])).
% 1.98/1.53 tff(40,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))) <=> ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(41,plain,
% 1.98/1.53 (^[X: $i] : trans(monotonicity(rewrite((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)))), (((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> ((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))))), rewrite(((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))), (((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))))),
% 1.98/1.53 inference(bind,[status(th)],[])).
% 1.98/1.53 tff(42,plain,
% 1.98/1.53 (![X: $i] : ((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 1.98/1.53 inference(quant_intro,[status(thm)],[41])).
% 1.98/1.53 tff(43,axiom,(![X: $i] : ((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','crossover1')).
% 1.98/1.53 tff(44,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.98/1.53 tff(45,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.98/1.53 tff(46,plain,(
% 1.98/1.53 ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 1.98/1.53 inference(skolemize,[status(sab)],[45])).
% 1.98/1.53 tff(47,plain,
% 1.98/1.53 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 1.98/1.53 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.98/1.53 tff(48,plain,
% 1.98/1.53 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(49,plain,
% 1.98/1.53 ((less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0))) <=> ((~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))),
% 1.98/1.53 inference(rewrite,[status(thm)],[])).
% 1.98/1.53 tff(50,plain,
% 1.98/1.53 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0))))),
% 1.98/1.53 inference(monotonicity,[status(thm)],[49])).
% 1.98/1.53 tff(51,plain,
% 1.98/1.53 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))),
% 1.98/1.53 inference(transitivity,[status(thm)],[50, 48])).
% 1.98/1.53 tff(52,plain,
% 1.98/1.53 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)))),
% 1.98/1.53 inference(quant_inst,[status(thm)],[])).
% 1.98/1.53 tff(53,plain,
% 1.98/1.53 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.98/1.54 tff(54,plain,
% 1.98/1.54 (less_than_or_equal(lower_bound, l)),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[53, 47, 37, 34])).
% 1.98/1.54 tff(55,plain,
% 1.98/1.54 (^[X: $i] : refl(((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(56,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[55])).
% 1.98/1.54 tff(57,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(58,plain,
% 1.98/1.54 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) <=> ((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) <=> (((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(lower_bound, X))))), rewrite((((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(59,plain,
% 1.98/1.54 (![X: $i] : (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[58])).
% 1.98/1.54 tff(60,axiom,(![X: $i] : (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','continuity1')).
% 1.98/1.54 tff(61,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.98/1.54 tff(62,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.98/1.54 tff(63,plain,(
% 1.98/1.54 ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 1.98/1.54 inference(skolemize,[status(sab)],[62])).
% 1.98/1.54 tff(64,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[63, 56])).
% 1.98/1.54 tff(65,plain,
% 1.98/1.54 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(66,plain,
% 1.98/1.54 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))),
% 1.98/1.54 inference(quant_inst,[status(thm)],[])).
% 1.98/1.54 tff(67,plain,
% 1.98/1.54 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.98/1.54 tff(68,plain,
% 1.98/1.54 ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 1.98/1.54 tff(69,plain,
% 1.98/1.54 ((~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[68, 31])).
% 1.98/1.54 tff(70,plain,
% 1.98/1.54 (~less_than_or_equal(l, h(l))),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[69, 4])).
% 1.98/1.54 tff(71,plain,
% 1.98/1.54 (^[X: $i] : refl((less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0)) <=> (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0)))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(72,plain,
% 1.98/1.54 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0)) <=> ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[71])).
% 1.98/1.54 tff(73,plain,
% 1.98/1.54 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0)) <=> ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(74,plain,
% 1.98/1.54 (^[X: $i] : rewrite((less_than_or_equal(f(g(X)), n0) | less_than_or_equal(l, X)) <=> (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0)))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(75,plain,
% 1.98/1.54 (![X: $i] : (less_than_or_equal(f(g(X)), n0) | less_than_or_equal(l, X)) <=> ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[74])).
% 1.98/1.54 tff(76,axiom,(![X: $i] : (less_than_or_equal(f(g(X)), n0) | less_than_or_equal(l, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','crossover3_and_g_function2')).
% 1.98/1.54 tff(77,plain,
% 1.98/1.54 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.98/1.54 tff(78,plain,
% 1.98/1.54 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[77, 73])).
% 1.98/1.54 tff(79,plain,(
% 1.98/1.54 ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 1.98/1.54 inference(skolemize,[status(sab)],[78])).
% 1.98/1.54 tff(80,plain,
% 1.98/1.54 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[79, 72])).
% 1.98/1.54 tff(81,plain,
% 1.98/1.54 (((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))) | (less_than_or_equal(l, h(l)) | less_than_or_equal(f(g(h(l))), n0))) <=> ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))) | less_than_or_equal(l, h(l)) | less_than_or_equal(f(g(h(l))), n0))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(82,plain,
% 1.98/1.54 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))) | (less_than_or_equal(l, h(l)) | less_than_or_equal(f(g(h(l))), n0))),
% 1.98/1.54 inference(quant_inst,[status(thm)],[])).
% 1.98/1.54 tff(83,plain,
% 1.98/1.54 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))) | less_than_or_equal(l, h(l)) | less_than_or_equal(f(g(h(l))), n0)),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.98/1.54 tff(84,plain,
% 1.98/1.54 (less_than_or_equal(f(g(h(l))), n0)),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[83, 80, 70])).
% 1.98/1.54 tff(85,plain,
% 1.98/1.54 (((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | ((~less_than_or_equal(g(h(l)), h(l))) | less_than_or_equal(l, h(l)))) <=> ((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | (~less_than_or_equal(g(h(l)), h(l))) | less_than_or_equal(l, h(l)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(86,plain,
% 1.98/1.54 ((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | ((~less_than_or_equal(g(h(l)), h(l))) | less_than_or_equal(l, h(l)))),
% 1.98/1.54 inference(quant_inst,[status(thm)],[])).
% 1.98/1.54 tff(87,plain,
% 1.98/1.54 ((~![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))) | (~less_than_or_equal(g(h(l)), h(l))) | less_than_or_equal(l, h(l))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.98/1.54 tff(88,plain,
% 1.98/1.54 (~less_than_or_equal(g(h(l)), h(l))),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[87, 12, 70])).
% 1.98/1.54 tff(89,plain,
% 1.98/1.54 (^[Y: $i, X: $i] : refl(((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(90,plain,
% 1.98/1.54 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[89])).
% 1.98/1.54 tff(91,plain,
% 1.98/1.54 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(92,plain,
% 1.98/1.54 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) <=> (less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X)))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) <=> ((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))))), rewrite(((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) <=> (less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) <=> (less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) <=> ((less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | less_than_or_equal(Y, h(X))))), rewrite(((less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | less_than_or_equal(Y, h(X))) <=> (less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) <=> (less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))), (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) <=> ((less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(lower_bound, X))))), rewrite(((less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))), ((((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), ((((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(93,plain,
% 1.98/1.54 (![Y: $i, X: $i] : (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[92])).
% 1.98/1.54 tff(94,axiom,(![Y: $i, X: $i] : (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','continuity2')).
% 1.98/1.54 tff(95,plain,
% 1.98/1.54 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.98/1.54 tff(96,plain,
% 1.98/1.54 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[95, 91])).
% 1.98/1.54 tff(97,plain,(
% 1.98/1.54 ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(skolemize,[status(sab)],[96])).
% 1.98/1.54 tff(98,plain,
% 1.98/1.54 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[97, 90])).
% 1.98/1.54 tff(99,plain,
% 1.98/1.54 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(100,plain,
% 1.98/1.54 (((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l))) <=> (less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(101,plain,
% 1.98/1.54 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l))))),
% 1.98/1.54 inference(monotonicity,[status(thm)],[100])).
% 1.98/1.54 tff(102,plain,
% 1.98/1.54 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 1.98/1.54 inference(transitivity,[status(thm)],[101, 99])).
% 1.98/1.54 tff(103,plain,
% 1.98/1.54 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 1.98/1.54 inference(quant_inst,[status(thm)],[])).
% 1.98/1.54 tff(104,plain,
% 1.98/1.54 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.98/1.54 tff(105,plain,
% 1.98/1.54 (~less_than_or_equal(g(h(l)), l)),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[104, 98, 4, 54, 31, 88, 84])).
% 1.98/1.54 tff(106,plain,
% 1.98/1.54 (((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | (less_than_or_equal(l, h(l)) | less_than_or_equal(g(h(l)), upper_bound))) <=> ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | less_than_or_equal(l, h(l)) | less_than_or_equal(g(h(l)), upper_bound))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(107,plain,
% 1.98/1.54 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | (less_than_or_equal(l, h(l)) | less_than_or_equal(g(h(l)), upper_bound))),
% 1.98/1.54 inference(quant_inst,[status(thm)],[])).
% 1.98/1.54 tff(108,plain,
% 1.98/1.54 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | less_than_or_equal(l, h(l)) | less_than_or_equal(g(h(l)), upper_bound)),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.98/1.54 tff(109,plain,
% 1.98/1.54 (less_than_or_equal(g(h(l)), upper_bound)),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[108, 26, 70])).
% 1.98/1.54 tff(110,plain,
% 1.98/1.54 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(111,plain,
% 1.98/1.54 ((less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0))) <=> ((~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(112,plain,
% 1.98/1.54 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound))))),
% 1.98/1.54 inference(monotonicity,[status(thm)],[111])).
% 1.98/1.54 tff(113,plain,
% 1.98/1.54 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))),
% 1.98/1.54 inference(transitivity,[status(thm)],[112, 110])).
% 1.98/1.54 tff(114,plain,
% 1.98/1.54 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)))),
% 1.98/1.54 inference(quant_inst,[status(thm)],[])).
% 1.98/1.54 tff(115,plain,
% 1.98/1.54 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.98/1.54 tff(116,plain,
% 1.98/1.54 ($false),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[115, 47, 109, 84, 105])).
% 1.98/1.54 tff(117,plain,(less_than_or_equal(f(l), n0)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.54 tff(118,plain,
% 1.98/1.54 (((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))) <=> ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l))))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(119,axiom,((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_x_which_crosses')).
% 1.98/1.54 tff(120,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.98/1.54 tff(121,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[120, 118])).
% 1.98/1.54 tff(122,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[121, 118])).
% 1.98/1.54 tff(123,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.98/1.54 tff(124,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[123, 118])).
% 1.98/1.54 tff(125,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[124, 118])).
% 1.98/1.54 tff(126,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.98/1.54 tff(127,plain,
% 1.98/1.54 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[126, 118])).
% 1.98/1.54 tff(128,plain,
% 1.98/1.54 (~less_than_or_equal(n0, f(l))),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[127, 117])).
% 1.98/1.54 tff(129,plain,
% 1.98/1.54 (^[X: $i] : refl(((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(130,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) <=> ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[129])).
% 1.98/1.54 tff(131,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) <=> ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(132,plain,
% 1.98/1.54 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) <=> ((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) <=> (((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(lower_bound, X))))), rewrite((((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(133,plain,
% 1.98/1.54 (![X: $i] : (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[132])).
% 1.98/1.54 tff(134,axiom,(![X: $i] : (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','continuity3')).
% 1.98/1.54 tff(135,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.98/1.54 tff(136,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[135, 131])).
% 1.98/1.54 tff(137,plain,(
% 1.98/1.54 ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 1.98/1.54 inference(skolemize,[status(sab)],[136])).
% 1.98/1.54 tff(138,plain,
% 1.98/1.54 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[137, 130])).
% 1.98/1.54 tff(139,plain,
% 1.98/1.54 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(140,plain,
% 1.98/1.54 (((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l))) <=> (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(141,plain,
% 1.98/1.54 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l))))),
% 1.98/1.54 inference(monotonicity,[status(thm)],[140])).
% 1.98/1.54 tff(142,plain,
% 1.98/1.54 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))),
% 1.98/1.54 inference(transitivity,[status(thm)],[141, 139])).
% 1.98/1.54 tff(143,plain,
% 1.98/1.54 ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)))),
% 1.98/1.54 inference(quant_inst,[status(thm)],[])).
% 1.98/1.54 tff(144,plain,
% 1.98/1.54 ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l))),
% 1.98/1.54 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.98/1.54 tff(145,plain,
% 1.98/1.54 (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(k(l), l))),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[144, 138, 54])).
% 1.98/1.54 tff(146,plain,
% 1.98/1.54 (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(k(l), l))),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[145, 31])).
% 1.98/1.54 tff(147,plain,
% 1.98/1.54 (~less_than_or_equal(k(l), l)),
% 1.98/1.54 inference(unit_resolution,[status(thm)],[146, 128])).
% 1.98/1.54 tff(148,plain,
% 1.98/1.54 (^[Y: $i, X: $i] : refl((less_than_or_equal(X, Y) | less_than_or_equal(Y, X)) <=> (less_than_or_equal(X, Y) | less_than_or_equal(Y, X)))),
% 1.98/1.54 inference(bind,[status(th)],[])).
% 1.98/1.54 tff(149,plain,
% 1.98/1.54 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X)) <=> ![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 1.98/1.54 inference(quant_intro,[status(thm)],[148])).
% 1.98/1.54 tff(150,plain,
% 1.98/1.54 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X)) <=> ![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 1.98/1.54 inference(rewrite,[status(thm)],[])).
% 1.98/1.54 tff(151,axiom,(![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','totality_of_less')).
% 1.98/1.54 tff(152,plain,
% 1.98/1.54 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.98/1.55 tff(153,plain,(
% 1.98/1.55 ![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 1.98/1.55 inference(skolemize,[status(sab)],[152])).
% 1.98/1.55 tff(154,plain,
% 1.98/1.55 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[153, 149])).
% 1.98/1.55 tff(155,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(l, k(l)) | less_than_or_equal(k(l), l))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(l, k(l)) | less_than_or_equal(k(l), l))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(156,plain,
% 1.98/1.55 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(l, k(l)) | less_than_or_equal(k(l), l))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(157,plain,
% 1.98/1.55 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(l, k(l)) | less_than_or_equal(k(l), l)),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.98/1.55 tff(158,plain,
% 1.98/1.55 (less_than_or_equal(l, k(l))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[157, 154, 147])).
% 1.98/1.55 tff(159,plain,
% 1.98/1.55 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(160,plain,
% 1.98/1.55 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(161,plain,
% 1.98/1.55 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))), (((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) | (~less_than_or_equal(Y, Z))))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) | (~less_than_or_equal(Y, Z))) <=> ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))), (((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))))),
% 1.98/1.55 inference(bind,[status(th)],[])).
% 1.98/1.55 tff(162,plain,
% 1.98/1.55 (![Z: $i, Y: $i, X: $i] : ((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 1.98/1.55 inference(quant_intro,[status(thm)],[161])).
% 1.98/1.55 tff(163,axiom,(![Z: $i, Y: $i, X: $i] : ((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_less')).
% 1.98/1.55 tff(164,plain,
% 1.98/1.55 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.98/1.55 tff(165,plain,
% 1.98/1.55 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[164, 160])).
% 1.98/1.55 tff(166,plain,(
% 1.98/1.55 ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 1.98/1.55 inference(skolemize,[status(sab)],[165])).
% 1.98/1.55 tff(167,plain,
% 1.98/1.55 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[166, 159])).
% 1.98/1.55 tff(168,plain,
% 1.98/1.55 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(lower_bound, k(l)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(lower_bound, k(l)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(169,plain,
% 1.98/1.55 (((~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l))) <=> ((~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(lower_bound, k(l)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(170,plain,
% 1.98/1.55 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(lower_bound, k(l))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[169])).
% 1.98/1.55 tff(171,plain,
% 1.98/1.55 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(lower_bound, k(l)))),
% 1.98/1.55 inference(transitivity,[status(thm)],[170, 168])).
% 1.98/1.55 tff(172,plain,
% 1.98/1.55 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(173,plain,
% 1.98/1.55 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(lower_bound, k(l))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.98/1.55 tff(174,plain,
% 1.98/1.55 (less_than_or_equal(lower_bound, k(l))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[173, 167, 54, 158])).
% 1.98/1.55 tff(175,assumption,(~less_than_or_equal(k(l), upper_bound)), introduced(assumption)).
% 1.98/1.55 tff(176,plain,
% 1.98/1.55 (less_than_or_equal(n0, f(upper_bound)) <=> less_than_or_equal(n0, f(upper_bound))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(177,axiom,(less_than_or_equal(n0, f(upper_bound))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','upper_mapping')).
% 1.98/1.55 tff(178,plain,
% 1.98/1.55 (less_than_or_equal(n0, f(upper_bound))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.98/1.55 tff(179,plain,
% 1.98/1.55 (^[Y: $i, X: $i] : refl(((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))))),
% 1.98/1.55 inference(bind,[status(th)],[])).
% 1.98/1.55 tff(180,plain,
% 1.98/1.55 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 1.98/1.55 inference(quant_intro,[status(thm)],[179])).
% 1.98/1.55 tff(181,plain,
% 1.98/1.55 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(182,plain,
% 1.98/1.55 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(n0, f(Y)))))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(n0, f(Y)))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y))))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y)))))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))))), (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(lower_bound, X))))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))), (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))))), ((((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))), ((((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))))),
% 1.98/1.55 inference(bind,[status(th)],[])).
% 1.98/1.55 tff(183,plain,
% 1.98/1.55 (![Y: $i, X: $i] : (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 1.98/1.55 inference(quant_intro,[status(thm)],[182])).
% 1.98/1.55 tff(184,axiom,(![Y: $i, X: $i] : (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','continuity4')).
% 1.98/1.55 tff(185,plain,
% 1.98/1.55 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.98/1.55 tff(186,plain,
% 1.98/1.55 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[185, 181])).
% 1.98/1.55 tff(187,plain,(
% 1.98/1.55 ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 1.98/1.55 inference(skolemize,[status(sab)],[186])).
% 1.98/1.55 tff(188,plain,
% 1.98/1.55 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.98/1.55 tff(189,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(190,plain,
% 1.98/1.55 (((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound)))) <=> (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(191,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound)))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[190])).
% 1.98/1.55 tff(192,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))),
% 1.98/1.55 inference(transitivity,[status(thm)],[191, 189])).
% 1.98/1.55 tff(193,plain,
% 1.98/1.55 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound))))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(194,plain,
% 1.98/1.55 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound)),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.98/1.55 tff(195,plain,
% 1.98/1.55 ($false),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[194, 188, 178, 128, 54, 31, 175])).
% 1.98/1.55 tff(196,plain,(less_than_or_equal(k(l), upper_bound)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.55 tff(197,plain,
% 1.98/1.55 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(k(l), l) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | less_than_or_equal(k(l), l) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(198,plain,
% 1.98/1.55 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(k(l), l) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0)))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(199,plain,
% 1.98/1.55 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | less_than_or_equal(k(l), l) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.98/1.55 tff(200,plain,
% 1.98/1.55 ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[199, 47, 147])).
% 1.98/1.55 tff(201,plain,
% 1.98/1.55 (~less_than_or_equal(f(k(l)), n0)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[200, 196])).
% 1.98/1.55 tff(202,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(l, h(k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(l, h(k(l))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(203,plain,
% 1.98/1.55 (((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(l, h(k(l))) | (~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(l, k(l)))) <=> ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(l, h(k(l))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(204,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(l, h(k(l))) | (~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(l, k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(l, h(k(l)))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[203])).
% 1.98/1.55 tff(205,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(l, h(k(l))) | (~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(l, k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(l, h(k(l))))),
% 1.98/1.55 inference(transitivity,[status(thm)],[204, 202])).
% 1.98/1.55 tff(206,plain,
% 1.98/1.55 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(l, h(k(l))) | (~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(l, k(l))))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(207,plain,
% 1.98/1.55 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(l, h(k(l)))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[206, 205])).
% 1.98/1.55 tff(208,plain,
% 1.98/1.55 ($false),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[207, 98, 117, 196, 201, 158, 174, 3])).
% 1.98/1.55 tff(209,plain,(less_than_or_equal(l, h(k(l)))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.55 tff(210,plain,
% 1.98/1.55 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))) | (~less_than_or_equal(l, h(k(l)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))) | (~less_than_or_equal(l, h(k(l)))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
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% 1.98/1.55 (((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l)))) <=> ((~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))) | (~less_than_or_equal(l, h(k(l)))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(212,plain,
% 1.98/1.55 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))) | (~less_than_or_equal(l, h(k(l))))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[211])).
% 1.98/1.55 tff(213,plain,
% 1.98/1.55 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))) | (~less_than_or_equal(l, h(k(l)))))),
% 1.98/1.55 inference(transitivity,[status(thm)],[212, 210])).
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% 1.98/1.55 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
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% 1.98/1.55 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, h(k(l))) | (~less_than_or_equal(l, h(k(l))))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.98/1.55 tff(216,plain,
% 1.98/1.55 (less_than_or_equal(lower_bound, h(k(l)))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[215, 167, 54, 209])).
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% 1.98/1.55 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
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% 1.98/1.55 (((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0)) <=> ((~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(219,plain,
% 1.98/1.55 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l))))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[218])).
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% 1.98/1.55 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))))),
% 1.98/1.55 inference(transitivity,[status(thm)],[219, 217])).
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% 1.98/1.55 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(222,plain,
% 1.98/1.55 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | (~less_than_or_equal(k(l), h(k(l))))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.98/1.55 tff(223,plain,
% 1.98/1.55 ((~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(k(l), h(k(l))))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[222, 64, 174])).
% 1.98/1.55 tff(224,plain,
% 1.98/1.55 (~less_than_or_equal(k(l), h(k(l)))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[223, 196, 201])).
% 1.98/1.55 tff(225,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(k(l), h(k(l))) | less_than_or_equal(h(k(l)), k(l)))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(l), h(k(l))) | less_than_or_equal(h(k(l)), k(l)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(226,plain,
% 1.98/1.55 ((less_than_or_equal(h(k(l)), k(l)) | less_than_or_equal(k(l), h(k(l)))) <=> (less_than_or_equal(k(l), h(k(l))) | less_than_or_equal(h(k(l)), k(l)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(227,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(h(k(l)), k(l)) | less_than_or_equal(k(l), h(k(l))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(k(l), h(k(l))) | less_than_or_equal(h(k(l)), k(l))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[226])).
% 1.98/1.55 tff(228,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(h(k(l)), k(l)) | less_than_or_equal(k(l), h(k(l))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(l), h(k(l))) | less_than_or_equal(h(k(l)), k(l)))),
% 1.98/1.55 inference(transitivity,[status(thm)],[227, 225])).
% 1.98/1.55 tff(229,plain,
% 1.98/1.55 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(h(k(l)), k(l)) | less_than_or_equal(k(l), h(k(l))))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
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% 1.98/1.55 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(l), h(k(l))) | less_than_or_equal(h(k(l)), k(l))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.98/1.55 tff(231,plain,
% 1.98/1.55 (less_than_or_equal(h(k(l)), k(l))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[230, 154, 224])).
% 1.98/1.55 tff(232,plain,
% 1.98/1.55 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(h(k(l)), k(l))) | less_than_or_equal(h(k(l)), upper_bound))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(h(k(l)), k(l))) | less_than_or_equal(h(k(l)), upper_bound))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(233,plain,
% 1.98/1.55 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(h(k(l)), k(l))) | less_than_or_equal(h(k(l)), upper_bound))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(234,plain,
% 1.98/1.55 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(h(k(l)), k(l))) | less_than_or_equal(h(k(l)), upper_bound)),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.98/1.55 tff(235,plain,
% 1.98/1.55 (less_than_or_equal(h(k(l)), upper_bound)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[234, 167, 196, 231])).
% 1.98/1.55 tff(236,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(n0, f(h(k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(n0, f(h(k(l))))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(237,plain,
% 1.98/1.55 (((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(n0, f(h(k(l)))))) <=> (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(n0, f(h(k(l))))))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(238,plain,
% 1.98/1.55 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(n0, f(h(k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(n0, f(h(k(l)))))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[237])).
% 1.98/1.56 tff(239,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(n0, f(h(k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(n0, f(h(k(l))))))),
% 1.98/1.56 inference(transitivity,[status(thm)],[238, 236])).
% 1.98/1.56 tff(240,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(n0, f(h(k(l))))))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(241,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), h(k(l))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.98/1.56 tff(242,plain,
% 1.98/1.56 ((~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[241, 188, 128, 54, 31, 224])).
% 1.98/1.56 tff(243,plain,
% 1.98/1.56 (~less_than_or_equal(n0, f(h(k(l))))),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[242, 209])).
% 1.98/1.56 tff(244,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(k(l))) | less_than_or_equal(f(k(l)), n0))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(k(l))) | less_than_or_equal(f(k(l)), n0))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(245,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(k(l))) | less_than_or_equal(f(k(l)), n0))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(246,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(k(l))) | less_than_or_equal(f(k(l)), n0)),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.98/1.56 tff(247,plain,
% 1.98/1.56 (less_than_or_equal(n0, f(k(l)))),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[246, 154, 201])).
% 1.98/1.56 tff(248,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | (~less_than_or_equal(n0, f(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(h(k(l)), k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | (~less_than_or_equal(n0, f(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(h(k(l)), k(l))))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(249,plain,
% 1.98/1.56 (((~less_than_or_equal(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(n0, f(k(l))))) <=> ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | (~less_than_or_equal(n0, f(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(h(k(l)), k(l))))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(250,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(n0, f(k(l)))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | (~less_than_or_equal(n0, f(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(h(k(l)), k(l)))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[249])).
% 1.98/1.56 tff(251,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(n0, f(k(l)))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | (~less_than_or_equal(n0, f(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(h(k(l)), k(l))))),
% 1.98/1.56 inference(transitivity,[status(thm)],[250, 248])).
% 1.98/1.56 tff(252,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(n0, f(k(l)))))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(253,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | (~less_than_or_equal(n0, f(k(l)))) | less_than_or_equal(k(h(k(l))), k(l)) | (~less_than_or_equal(h(k(l)), k(l)))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.98/1.56 tff(254,plain,
% 1.98/1.56 ($false),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[253, 188, 247, 243, 231, 235, 216, 2])).
% 1.98/1.56 tff(255,plain,(less_than_or_equal(k(h(k(l))), k(l))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.56 tff(256,plain,
% 1.98/1.56 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | (~less_than_or_equal(k(h(k(l))), h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | (~less_than_or_equal(k(h(k(l))), h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(257,plain,
% 1.98/1.56 (((~less_than_or_equal(k(h(k(l))), h(k(l)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l))))) <=> ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | (~less_than_or_equal(k(h(k(l))), h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(258,plain,
% 1.98/1.56 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(h(k(l))), h(k(l)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | (~less_than_or_equal(k(h(k(l))), h(k(l)))) | less_than_or_equal(n0, f(h(k(l))))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[257])).
% 1.98/1.56 tff(259,plain,
% 1.98/1.56 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(h(k(l))), h(k(l)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | (~less_than_or_equal(k(h(k(l))), h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.56 inference(transitivity,[status(thm)],[258, 256])).
% 1.98/1.56 tff(260,plain,
% 1.98/1.56 ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(h(k(l))), h(k(l)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(261,plain,
% 1.98/1.56 ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | (~less_than_or_equal(k(h(k(l))), h(k(l)))) | less_than_or_equal(n0, f(h(k(l))))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.98/1.56 tff(262,plain,
% 1.98/1.56 ((~less_than_or_equal(lower_bound, h(k(l)))) | (~less_than_or_equal(k(h(k(l))), h(k(l)))) | less_than_or_equal(n0, f(h(k(l))))),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[261, 138, 235])).
% 1.98/1.56 tff(263,plain,
% 1.98/1.56 (~less_than_or_equal(k(h(k(l))), h(k(l)))),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[262, 216, 243])).
% 1.98/1.56 tff(264,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(k(h(k(l))), k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(k(h(k(l))), k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(265,plain,
% 1.98/1.56 (((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)) | (~less_than_or_equal(k(h(k(l))), k(l)))) <=> ((~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(k(h(k(l))), k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(266,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)) | (~less_than_or_equal(k(h(k(l))), k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(k(h(k(l))), k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[265])).
% 1.98/1.56 tff(267,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)) | (~less_than_or_equal(k(h(k(l))), k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(k(h(k(l))), k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)))),
% 1.98/1.56 inference(transitivity,[status(thm)],[266, 264])).
% 1.98/1.56 tff(268,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0)) | (~less_than_or_equal(k(h(k(l))), k(l))))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(269,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (~less_than_or_equal(k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(lower_bound, k(l))) | less_than_or_equal(k(h(k(l))), h(k(l))) | (~less_than_or_equal(k(h(k(l))), k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.98/1.56 tff(270,plain,
% 1.98/1.56 ((~less_than_or_equal(k(h(k(l))), k(l))) | (~less_than_or_equal(f(k(h(k(l)))), n0))),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[269, 98, 196, 201, 174, 263])).
% 1.98/1.56 tff(271,plain,
% 1.98/1.56 (~less_than_or_equal(f(k(h(k(l)))), n0)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[270, 255])).
% 1.98/1.56 tff(272,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(k(h(k(l))))) | less_than_or_equal(f(k(h(k(l)))), n0))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(k(h(k(l))))) | less_than_or_equal(f(k(h(k(l)))), n0))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(273,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(k(h(k(l))))) | less_than_or_equal(f(k(h(k(l)))), n0))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
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% 1.98/1.56 inference(modus_ponens,[status(thm)],[273, 272])).
% 1.98/1.56 tff(275,plain,
% 1.98/1.56 (less_than_or_equal(n0, f(k(h(k(l)))))),
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% 1.98/1.56 tff(276,plain,
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% 1.98/1.56 inference(rewrite,[status(thm)],[])).
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% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(278,plain,
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% 1.98/1.56 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.98/1.56 tff(279,plain,
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% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(282,plain,
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% 1.98/1.56 inference(monotonicity,[status(thm)],[281])).
% 1.98/1.56 tff(283,plain,
% 1.98/1.56 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(h(k(l)), k(h(k(l))))) | (~less_than_or_equal(l, h(k(l)))) | less_than_or_equal(l, k(h(k(l)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(h(k(l)), k(h(k(l))))) | less_than_or_equal(l, k(h(k(l)))))),
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% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(285,plain,
% 1.98/1.56 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(l, h(k(l)))) | (~less_than_or_equal(h(k(l)), k(h(k(l))))) | less_than_or_equal(l, k(h(k(l))))),
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% 1.98/1.56 inference(rewrite,[status(thm)],[])).
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% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(289,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, k(h(k(l))))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), k(h(k(l)))) | (~less_than_or_equal(n0, f(k(h(k(l)))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), k(h(k(l)))) | (~less_than_or_equal(n0, f(k(h(k(l)))))) | (~less_than_or_equal(l, k(h(k(l)))))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[288])).
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% 1.98/1.56 inference(transitivity,[status(thm)],[289, 287])).
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% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
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% 1.98/1.56 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.98/1.56 tff(293,plain,
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% 1.98/1.56 inference(rewrite,[status(thm)],[])).
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% 1.98/1.56 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(h(k(l))), l)) | (~less_than_or_equal(k(l), k(h(k(l))))) | less_than_or_equal(k(l), l))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (less_than_or_equal(k(l), l) | (~less_than_or_equal(k(l), k(h(k(l))))) | (~less_than_or_equal(k(h(k(l))), l))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[296])).
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% 1.98/1.56 inference(transitivity,[status(thm)],[297, 295])).
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% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
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% 1.98/1.56 inference(modus_ponens,[status(thm)],[299, 298])).
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% 1.98/1.56 ($false),
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% 1.98/1.56 tff(303,plain,
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% 1.98/1.56 (![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X)) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
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% 1.98/1.56 tff(308,plain,(
% 1.98/1.56 ![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
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% 1.98/1.56 tff(310,plain,
% 1.98/1.56 (((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | ((~less_than_or_equal(q(l, k(h(k(l)))), l)) | less_than_or_equal(k(h(k(l))), l))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | (~less_than_or_equal(q(l, k(h(k(l)))), l)) | less_than_or_equal(k(h(k(l))), l))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
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% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | ((~less_than_or_equal(q(l, k(h(k(l)))), l)) | less_than_or_equal(k(h(k(l))), l))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(312,plain,
% 1.98/1.56 ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | (~less_than_or_equal(q(l, k(h(k(l)))), l)) | less_than_or_equal(k(h(k(l))), l)),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.98/1.56 tff(313,plain,
% 1.98/1.56 (~less_than_or_equal(q(l, k(h(k(l)))), l)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[312, 309, 302])).
% 1.98/1.56 tff(314,plain,
% 1.98/1.56 (^[Y: $i, X: $i] : refl(((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y)) <=> ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y)))),
% 1.98/1.56 inference(bind,[status(th)],[])).
% 1.98/1.56 tff(315,plain,
% 1.98/1.56 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 1.98/1.56 inference(quant_intro,[status(thm)],[314])).
% 1.98/1.56 tff(316,plain,
% 1.98/1.56 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(317,axiom,(![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','interpolation1')).
% 1.98/1.56 tff(318,plain,
% 1.98/1.56 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[317, 316])).
% 1.98/1.57 tff(319,plain,(
% 1.98/1.57 ![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 1.98/1.57 inference(skolemize,[status(sab)],[318])).
% 1.98/1.57 tff(320,plain,
% 1.98/1.57 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[319, 315])).
% 1.98/1.57 tff(321,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | ((~less_than_or_equal(k(h(k(l))), q(l, k(h(k(l)))))) | less_than_or_equal(k(h(k(l))), l))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | (~less_than_or_equal(k(h(k(l))), q(l, k(h(k(l)))))) | less_than_or_equal(k(h(k(l))), l))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(322,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | ((~less_than_or_equal(k(h(k(l))), q(l, k(h(k(l)))))) | less_than_or_equal(k(h(k(l))), l))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(323,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | (~less_than_or_equal(k(h(k(l))), q(l, k(h(k(l)))))) | less_than_or_equal(k(h(k(l))), l)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.98/1.57 tff(324,plain,
% 1.98/1.57 ((~less_than_or_equal(k(h(k(l))), q(l, k(h(k(l)))))) | less_than_or_equal(k(h(k(l))), l)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[323, 320])).
% 1.98/1.57 tff(325,plain,
% 1.98/1.57 (~less_than_or_equal(k(h(k(l))), q(l, k(h(k(l)))))),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[324, 302])).
% 1.98/1.57 tff(326,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(327,plain,
% 1.98/1.57 ((less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l)))))) <=> (less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(328,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[327])).
% 1.98/1.57 tff(329,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))))),
% 1.98/1.57 inference(transitivity,[status(thm)],[328, 326])).
% 1.98/1.57 tff(330,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(331,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.98/1.57 tff(332,plain,
% 1.98/1.57 (less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[331, 154, 325])).
% 1.98/1.57 tff(333,assumption,(~less_than_or_equal(q(l, k(h(k(l)))), upper_bound)), introduced(assumption)).
% 1.98/1.57 tff(334,assumption,(less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))), introduced(assumption)).
% 1.98/1.57 tff(335,plain,
% 1.98/1.57 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(k(h(k(l))), k(l))) | less_than_or_equal(k(h(k(l))), upper_bound))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(k(h(k(l))), k(l))) | less_than_or_equal(k(h(k(l))), upper_bound))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(336,plain,
% 1.98/1.57 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(k(h(k(l))), k(l))) | less_than_or_equal(k(h(k(l))), upper_bound))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(337,plain,
% 1.98/1.57 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(k(h(k(l))), k(l))) | less_than_or_equal(k(h(k(l))), upper_bound)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.98/1.57 tff(338,plain,
% 1.98/1.57 (less_than_or_equal(k(h(k(l))), upper_bound)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[337, 167, 196, 255])).
% 1.98/1.57 tff(339,plain,
% 1.98/1.57 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(h(k(l))), upper_bound)) | (~less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), upper_bound))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(h(k(l))), upper_bound)) | (~less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), upper_bound))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(340,plain,
% 1.98/1.57 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(h(k(l))), upper_bound)) | (~less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), upper_bound))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(341,plain,
% 1.98/1.57 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(h(k(l))), upper_bound)) | (~less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), upper_bound)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[340, 339])).
% 1.98/1.57 tff(342,plain,
% 1.98/1.57 ($false),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[341, 167, 338, 334, 333])).
% 1.98/1.57 tff(343,plain,(less_than_or_equal(q(l, k(h(k(l)))), upper_bound) | (~less_than_or_equal(q(l, k(h(k(l)))), k(h(k(l)))))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.57 tff(344,plain,
% 1.98/1.57 (less_than_or_equal(q(l, k(h(k(l)))), upper_bound)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[343, 332])).
% 1.98/1.57 tff(345,assumption,(less_than_or_equal(q(l, k(h(k(l)))), upper_bound)), introduced(assumption)).
% 1.98/1.57 tff(346,assumption,(less_than_or_equal(f(q(l, k(h(k(l))))), n0)), introduced(assumption)).
% 1.98/1.57 tff(347,assumption,(~less_than_or_equal(q(l, k(h(k(l)))), l)), introduced(assumption)).
% 1.98/1.57 tff(348,plain,
% 1.98/1.57 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(q(l, k(h(k(l)))), l) | (~less_than_or_equal(q(l, k(h(k(l)))), upper_bound)) | (~less_than_or_equal(f(q(l, k(h(k(l))))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | less_than_or_equal(q(l, k(h(k(l)))), l) | (~less_than_or_equal(q(l, k(h(k(l)))), upper_bound)) | (~less_than_or_equal(f(q(l, k(h(k(l))))), n0)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(349,plain,
% 1.98/1.57 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(q(l, k(h(k(l)))), l) | (~less_than_or_equal(q(l, k(h(k(l)))), upper_bound)) | (~less_than_or_equal(f(q(l, k(h(k(l))))), n0)))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(350,plain,
% 1.98/1.57 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | less_than_or_equal(q(l, k(h(k(l)))), l) | (~less_than_or_equal(q(l, k(h(k(l)))), upper_bound)) | (~less_than_or_equal(f(q(l, k(h(k(l))))), n0))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[349, 348])).
% 1.98/1.57 tff(351,plain,
% 1.98/1.57 ($false),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[350, 47, 347, 346, 345])).
% 1.98/1.57 tff(352,plain,((~less_than_or_equal(q(l, k(h(k(l)))), upper_bound)) | less_than_or_equal(q(l, k(h(k(l)))), l) | (~less_than_or_equal(f(q(l, k(h(k(l))))), n0))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.57 tff(353,plain,
% 1.98/1.57 (~less_than_or_equal(f(q(l, k(h(k(l))))), n0)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[352, 344, 313])).
% 1.98/1.57 tff(354,assumption,(~less_than_or_equal(f(q(l, k(h(k(l))))), n0)), introduced(assumption)).
% 1.98/1.57 tff(355,assumption,(~less_than_or_equal(n0, f(q(l, k(h(k(l))))))), introduced(assumption)).
% 1.98/1.57 tff(356,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(q(l, k(h(k(l)))))) | less_than_or_equal(f(q(l, k(h(k(l))))), n0))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(q(l, k(h(k(l)))))) | less_than_or_equal(f(q(l, k(h(k(l))))), n0))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(357,plain,
% 1.98/1.57 ((less_than_or_equal(f(q(l, k(h(k(l))))), n0) | less_than_or_equal(n0, f(q(l, k(h(k(l))))))) <=> (less_than_or_equal(n0, f(q(l, k(h(k(l)))))) | less_than_or_equal(f(q(l, k(h(k(l))))), n0))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(358,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(f(q(l, k(h(k(l))))), n0) | less_than_or_equal(n0, f(q(l, k(h(k(l)))))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(q(l, k(h(k(l)))))) | less_than_or_equal(f(q(l, k(h(k(l))))), n0)))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[357])).
% 1.98/1.57 tff(359,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(f(q(l, k(h(k(l))))), n0) | less_than_or_equal(n0, f(q(l, k(h(k(l)))))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(q(l, k(h(k(l)))))) | less_than_or_equal(f(q(l, k(h(k(l))))), n0))),
% 1.98/1.57 inference(transitivity,[status(thm)],[358, 356])).
% 1.98/1.57 tff(360,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(f(q(l, k(h(k(l))))), n0) | less_than_or_equal(n0, f(q(l, k(h(k(l)))))))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(361,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(q(l, k(h(k(l)))))) | less_than_or_equal(f(q(l, k(h(k(l))))), n0)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[360, 359])).
% 1.98/1.57 tff(362,plain,
% 1.98/1.57 ($false),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[361, 154, 355, 354])).
% 1.98/1.57 tff(363,plain,(less_than_or_equal(f(q(l, k(h(k(l))))), n0) | less_than_or_equal(n0, f(q(l, k(h(k(l))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.57 tff(364,plain,
% 1.98/1.57 (less_than_or_equal(n0, f(q(l, k(h(k(l))))))),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[363, 353])).
% 1.98/1.57 tff(365,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))) | (~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))) | (~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(366,plain,
% 1.98/1.57 (((~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l)))))))) <=> ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))) | (~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(367,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))) | (~less_than_or_equal(h(k(l)), q(l, k(h(k(l))))))))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[366])).
% 1.98/1.57 tff(368,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))) | (~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))))),
% 1.98/1.57 inference(transitivity,[status(thm)],[367, 365])).
% 1.98/1.57 tff(369,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(370,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(lower_bound, h(k(l)))) | less_than_or_equal(n0, f(h(k(l)))) | less_than_or_equal(k(h(k(l))), q(l, k(h(k(l))))) | (~less_than_or_equal(n0, f(q(l, k(h(k(l))))))) | (~less_than_or_equal(h(k(l)), q(l, k(h(k(l))))))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.98/1.57 tff(371,plain,
% 1.98/1.57 ((~less_than_or_equal(n0, f(q(l, k(h(k(l))))))) | (~less_than_or_equal(h(k(l)), q(l, k(h(k(l))))))),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[370, 188, 243, 235, 216, 325])).
% 1.98/1.57 tff(372,plain,
% 1.98/1.57 (~less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[371, 364])).
% 1.98/1.57 tff(373,plain,
% 1.98/1.57 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(f(h(k(l))), n0) | less_than_or_equal(n0, f(h(k(l)))))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(f(h(k(l))), n0) | less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(374,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(f(h(k(l))), n0) | less_than_or_equal(n0, f(h(k(l)))))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(375,plain,
% 1.98/1.57 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(f(h(k(l))), n0) | less_than_or_equal(n0, f(h(k(l))))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.98/1.57 tff(376,plain,
% 1.98/1.57 (less_than_or_equal(f(h(k(l))), n0)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[375, 154, 243])).
% 1.98/1.57 tff(377,plain,
% 1.98/1.57 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)) | less_than_or_equal(h(k(l)), l))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)) | less_than_or_equal(h(k(l)), l))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(378,plain,
% 1.98/1.57 ((less_than_or_equal(h(k(l)), l) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0))) <=> ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)) | less_than_or_equal(h(k(l)), l))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(379,plain,
% 1.98/1.57 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(h(k(l)), l) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)) | less_than_or_equal(h(k(l)), l)))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[378])).
% 1.98/1.57 tff(380,plain,
% 1.98/1.57 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(h(k(l)), l) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)) | less_than_or_equal(h(k(l)), l))),
% 1.98/1.57 inference(transitivity,[status(thm)],[379, 377])).
% 1.98/1.57 tff(381,plain,
% 1.98/1.57 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(h(k(l)), l) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(382,plain,
% 1.98/1.57 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(h(k(l)), upper_bound)) | (~less_than_or_equal(f(h(k(l))), n0)) | less_than_or_equal(h(k(l)), l)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[381, 380])).
% 1.98/1.57 tff(383,plain,
% 1.98/1.57 ((~less_than_or_equal(f(h(k(l))), n0)) | less_than_or_equal(h(k(l)), l)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[382, 47, 235])).
% 2.03/1.58 tff(384,plain,
% 2.03/1.58 (less_than_or_equal(h(k(l)), l)),
% 2.03/1.58 inference(unit_resolution,[status(thm)],[383, 376])).
% 2.03/1.58 tff(385,plain,
% 2.03/1.58 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))) | (~less_than_or_equal(l, q(l, k(h(k(l)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))) | (~less_than_or_equal(l, q(l, k(h(k(l)))))))),
% 2.03/1.58 inference(rewrite,[status(thm)],[])).
% 2.03/1.58 tff(386,plain,
% 2.03/1.58 (((~less_than_or_equal(l, q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l)))))) <=> ((~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))) | (~less_than_or_equal(l, q(l, k(h(k(l)))))))),
% 2.03/1.58 inference(rewrite,[status(thm)],[])).
% 2.03/1.58 tff(387,plain,
% 2.03/1.58 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))) | (~less_than_or_equal(l, q(l, k(h(k(l))))))))),
% 2.03/1.58 inference(monotonicity,[status(thm)],[386])).
% 2.03/1.58 tff(388,plain,
% 2.03/1.58 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))) | (~less_than_or_equal(l, q(l, k(h(k(l)))))))),
% 2.03/1.58 inference(transitivity,[status(thm)],[387, 385])).
% 2.03/1.58 tff(389,plain,
% 2.03/1.58 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(l, q(l, k(h(k(l)))))) | (~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))))),
% 2.03/1.58 inference(quant_inst,[status(thm)],[])).
% 2.03/1.58 tff(390,plain,
% 2.03/1.58 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(h(k(l)), l)) | less_than_or_equal(h(k(l)), q(l, k(h(k(l))))) | (~less_than_or_equal(l, q(l, k(h(k(l))))))),
% 2.03/1.58 inference(modus_ponens,[status(thm)],[389, 388])).
% 2.03/1.58 tff(391,plain,
% 2.03/1.58 ($false),
% 2.03/1.58 inference(unit_resolution,[status(thm)],[390, 167, 384, 372, 1])).
% 2.03/1.58 tff(392,plain,(~less_than_or_equal(l, q(l, k(h(k(l)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/1.58 tff(393,plain,
% 2.03/1.58 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(l, q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), l))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(l, q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), l))),
% 2.03/1.58 inference(rewrite,[status(thm)],[])).
% 2.03/1.58 tff(394,plain,
% 2.03/1.58 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(l, q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), l))),
% 2.03/1.58 inference(quant_inst,[status(thm)],[])).
% 2.03/1.58 tff(395,plain,
% 2.03/1.58 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(l, q(l, k(h(k(l))))) | less_than_or_equal(q(l, k(h(k(l)))), l)),
% 2.03/1.58 inference(modus_ponens,[status(thm)],[394, 393])).
% 2.03/1.58 tff(396,plain,
% 2.03/1.58 ($false),
% 2.03/1.58 inference(unit_resolution,[status(thm)],[395, 154, 313, 392])).
% 2.03/1.58 % SZS output end Proof
%------------------------------------------------------------------------------