%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA002-2 : TPTP v9.0.0. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:59:07 AM UTC 2025
% Result : Unsatisfiable 96.95s 97.20s
% Output : Proof 97.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA002-2 : TPTP v9.0.0. Bugfixed v1.0.1.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n005.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Thu Jun 19 11:17:50 EDT 2025
% 0.13/0.33 % CPUTime :
% 96.95/97.20 % SZS status Unsatisfiable
% 96.95/97.20 % SZS output start Proof
% 96.95/97.20 tff(less_than_or_equal_type, type, (
% 96.95/97.20 less_than_or_equal: ( $i * $i ) > $o)).
% 96.95/97.20 tff(f_type, type, (
% 96.95/97.20 f: $i > $i)).
% 96.95/97.20 tff(q_type, type, (
% 96.95/97.20 q: ( $i * $i ) > $i)).
% 96.95/97.20 tff(k_type, type, (
% 96.95/97.20 k: $i > $i)).
% 96.95/97.20 tff(l_type, type, (
% 96.95/97.20 l: $i)).
% 96.95/97.20 tff(h_type, type, (
% 96.95/97.20 h: $i > $i)).
% 96.95/97.20 tff(n0_type, type, (
% 96.95/97.20 n0: $i)).
% 96.95/97.20 tff(in_interval_type, type, (
% 96.95/97.20 in_interval: ( $i * $i * $i ) > $o)).
% 96.95/97.20 tff(upper_bound_type, type, (
% 96.95/97.20 upper_bound: $i)).
% 96.95/97.20 tff(lower_bound_type, type, (
% 96.95/97.20 lower_bound: $i)).
% 96.95/97.20 tff(g_type, type, (
% 96.95/97.20 g: $i > $i)).
% 96.95/97.20 tff(1,assumption,(~less_than_or_equal(f(l), n0)), introduced(assumption)).
% 96.95/97.20 tff(2,assumption,(~in_interval(lower_bound, l, upper_bound)), introduced(assumption)).
% 96.95/97.20 tff(3,assumption,(~less_than_or_equal(l, upper_bound)), introduced(assumption)).
% 96.95/97.20 tff(4,plain,
% 96.95/97.20 (^[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)))),
% 96.95/97.20 inference(bind,[status(th)],[])).
% 96.95/97.20 tff(5,plain,
% 96.95/97.20 (![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))),
% 96.95/97.20 inference(quant_intro,[status(thm)],[4])).
% 96.95/97.20 tff(6,plain,
% 96.95/97.20 (![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))),
% 96.95/97.20 inference(rewrite,[status(thm)],[])).
% 96.95/97.20 tff(7,axiom,(![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','crossover4_and_g_function3')).
% 96.95/97.20 tff(8,plain,
% 96.95/97.20 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[7, 6])).
% 96.95/97.20 tff(9,plain,(
% 96.95/97.20 ![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 96.95/97.20 inference(skolemize,[status(sab)],[8])).
% 96.95/97.20 tff(10,plain,
% 96.95/97.20 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[9, 5])).
% 96.95/97.20 tff(11,plain,
% 96.95/97.20 (((~![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))),
% 96.95/97.20 inference(rewrite,[status(thm)],[])).
% 96.95/97.20 tff(12,plain,
% 96.95/97.20 ((~![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))),
% 96.95/97.20 inference(quant_inst,[status(thm)],[])).
% 96.95/97.20 tff(13,plain,
% 96.95/97.20 ((~![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)),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[12, 11])).
% 96.95/97.20 tff(14,plain,
% 96.95/97.20 (~less_than_or_equal(g(upper_bound), upper_bound)),
% 96.95/97.20 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 96.95/97.20 tff(15,plain,
% 96.95/97.20 (^[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)))),
% 96.95/97.20 inference(bind,[status(th)],[])).
% 96.95/97.20 tff(16,plain,
% 96.95/97.20 (![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))),
% 96.95/97.20 inference(quant_intro,[status(thm)],[15])).
% 96.95/97.20 tff(17,plain,
% 96.95/97.20 (![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))),
% 96.95/97.20 inference(rewrite,[status(thm)],[])).
% 96.95/97.20 tff(18,plain,
% 96.95/97.20 (^[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)))),
% 96.95/97.20 inference(bind,[status(th)],[])).
% 96.95/97.20 tff(19,plain,
% 96.95/97.20 (![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))),
% 96.95/97.20 inference(quant_intro,[status(thm)],[18])).
% 96.95/97.20 tff(20,axiom,(![X: $i] : (less_than_or_equal(g(X), upper_bound) | less_than_or_equal(l, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','crossover2_and_g_function1')).
% 96.95/97.20 tff(21,plain,
% 96.95/97.20 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[20, 19])).
% 96.95/97.20 tff(22,plain,
% 96.95/97.20 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[21, 17])).
% 96.95/97.20 tff(23,plain,(
% 96.95/97.20 ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 96.95/97.20 inference(skolemize,[status(sab)],[22])).
% 96.95/97.20 tff(24,plain,
% 96.95/97.20 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[23, 16])).
% 96.95/97.20 tff(25,plain,
% 96.95/97.20 (((~![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))),
% 96.95/97.20 inference(rewrite,[status(thm)],[])).
% 96.95/97.20 tff(26,plain,
% 96.95/97.20 ((~![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))),
% 96.95/97.20 inference(quant_inst,[status(thm)],[])).
% 96.95/97.20 tff(27,plain,
% 96.95/97.20 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | less_than_or_equal(l, upper_bound) | less_than_or_equal(g(upper_bound), upper_bound)),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[26, 25])).
% 96.95/97.20 tff(28,plain,
% 96.95/97.20 ($false),
% 96.95/97.20 inference(unit_resolution,[status(thm)],[27, 24, 3, 14])).
% 96.95/97.20 tff(29,plain,(less_than_or_equal(l, upper_bound)), inference(lemma,lemma(discharge,[]))).
% 96.95/97.20 tff(30,plain,
% 96.95/97.20 (less_than_or_equal(f(lower_bound), n0) <=> less_than_or_equal(f(lower_bound), n0)),
% 96.95/97.20 inference(rewrite,[status(thm)],[])).
% 96.95/97.20 tff(31,axiom,(less_than_or_equal(f(lower_bound), n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lower_mapping')).
% 96.95/97.20 tff(32,plain,
% 96.95/97.20 (less_than_or_equal(f(lower_bound), n0)),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[31, 30])).
% 96.95/97.20 tff(33,plain,
% 96.95/97.20 (less_than_or_equal(lower_bound, upper_bound) <=> less_than_or_equal(lower_bound, upper_bound)),
% 96.95/97.20 inference(rewrite,[status(thm)],[])).
% 96.95/97.20 tff(34,axiom,(less_than_or_equal(lower_bound, upper_bound)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_interval')).
% 96.95/97.20 tff(35,plain,
% 96.95/97.20 (less_than_or_equal(lower_bound, upper_bound)),
% 96.95/97.20 inference(modus_ponens,[status(thm)],[34, 33])).
% 96.95/97.20 tff(36,plain,
% 96.95/97.20 (^[X: $i] : refl(((~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)))),
% 96.95/97.20 inference(bind,[status(th)],[])).
% 96.95/97.20 tff(37,plain,
% 96.95/97.20 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l)) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))),
% 96.95/97.20 inference(quant_intro,[status(thm)],[36])).
% 96.95/97.20 tff(38,plain,
% 96.95/97.20 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l)) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))),
% 96.95/97.20 inference(rewrite,[status(thm)],[])).
% 96.95/97.20 tff(39,plain,
% 96.95/97.20 (^[X: $i] : trans(monotonicity(rewrite((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | less_than_or_equal(X, l))), (((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, upper_bound)) | less_than_or_equal(X, l)) | (~less_than_or_equal(f(X), n0))))), rewrite((((~less_than_or_equal(X, upper_bound)) | less_than_or_equal(X, l)) | (~less_than_or_equal(f(X), n0))) <=> ((~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, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))))),
% 97.01/97.20 inference(bind,[status(th)],[])).
% 97.01/97.20 tff(40,plain,
% 97.01/97.20 (![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, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))),
% 97.01/97.20 inference(quant_intro,[status(thm)],[39])).
% 97.01/97.20 tff(41,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/sandbox/benchmark/theBenchmark.p','crossover1')).
% 97.01/97.20 tff(42,plain,
% 97.01/97.20 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[41, 40])).
% 97.01/97.20 tff(43,plain,
% 97.01/97.20 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[42, 38])).
% 97.01/97.20 tff(44,plain,(
% 97.01/97.20 ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))),
% 97.01/97.20 inference(skolemize,[status(sab)],[43])).
% 97.01/97.20 tff(45,plain,
% 97.01/97.20 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[44, 37])).
% 97.01/97.20 tff(46,plain,
% 97.01/97.20 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | ((~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)) | less_than_or_equal(lower_bound, l))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)) | less_than_or_equal(lower_bound, l))),
% 97.01/97.20 inference(rewrite,[status(thm)],[])).
% 97.01/97.20 tff(47,plain,
% 97.01/97.20 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | ((~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)) | less_than_or_equal(lower_bound, l))),
% 97.01/97.20 inference(quant_inst,[status(thm)],[])).
% 97.01/97.20 tff(48,plain,
% 97.01/97.20 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)) | less_than_or_equal(lower_bound, l)),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[47, 46])).
% 97.01/97.20 tff(49,plain,
% 97.01/97.20 (less_than_or_equal(lower_bound, l)),
% 97.01/97.20 inference(unit_resolution,[status(thm)],[48, 45, 35, 32])).
% 97.01/97.20 tff(50,plain,
% 97.01/97.20 (^[X: $i, Upper: $i, Lower: $i] : refl(((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper)) <=> ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper)))),
% 97.01/97.20 inference(bind,[status(th)],[])).
% 97.01/97.20 tff(51,plain,
% 97.01/97.20 (![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper)) <=> ![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))),
% 97.01/97.20 inference(quant_intro,[status(thm)],[50])).
% 97.01/97.20 tff(52,plain,
% 97.01/97.20 (![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper)) <=> ![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))),
% 97.01/97.20 inference(rewrite,[status(thm)],[])).
% 97.01/97.20 tff(53,plain,
% 97.01/97.20 (^[X: $i, Upper: $i, Lower: $i] : trans(monotonicity(rewrite((in_interval(Lower, X, Upper) | (~less_than_or_equal(Lower, X))) <=> ((~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))), (((in_interval(Lower, X, Upper) | (~less_than_or_equal(Lower, X))) | (~less_than_or_equal(X, Upper))) <=> (((~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper)) | (~less_than_or_equal(X, Upper))))), rewrite((((~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper)) | (~less_than_or_equal(X, Upper))) <=> ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))), (((in_interval(Lower, X, Upper) | (~less_than_or_equal(Lower, X))) | (~less_than_or_equal(X, Upper))) <=> ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))))),
% 97.01/97.20 inference(bind,[status(th)],[])).
% 97.01/97.20 tff(54,plain,
% 97.01/97.20 (![X: $i, Upper: $i, Lower: $i] : ((in_interval(Lower, X, Upper) | (~less_than_or_equal(Lower, X))) | (~less_than_or_equal(X, Upper))) <=> ![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))),
% 97.01/97.20 inference(quant_intro,[status(thm)],[53])).
% 97.01/97.20 tff(55,axiom,(![X: $i, Upper: $i, Lower: $i] : ((in_interval(Lower, X, Upper) | (~less_than_or_equal(Lower, X))) | (~less_than_or_equal(X, Upper)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','in_interval')).
% 97.01/97.20 tff(56,plain,
% 97.01/97.20 (![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[55, 54])).
% 97.01/97.20 tff(57,plain,
% 97.01/97.20 (![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[56, 52])).
% 97.01/97.20 tff(58,plain,(
% 97.01/97.20 ![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))),
% 97.01/97.20 inference(skolemize,[status(sab)],[57])).
% 97.01/97.20 tff(59,plain,
% 97.01/97.20 (![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[58, 51])).
% 97.01/97.20 tff(60,plain,
% 97.01/97.20 (((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | in_interval(lower_bound, l, upper_bound))) <=> ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | in_interval(lower_bound, l, upper_bound))),
% 97.01/97.20 inference(rewrite,[status(thm)],[])).
% 97.01/97.20 tff(61,plain,
% 97.01/97.20 ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | in_interval(lower_bound, l, upper_bound))),
% 97.01/97.20 inference(quant_inst,[status(thm)],[])).
% 97.01/97.20 tff(62,plain,
% 97.01/97.20 ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | in_interval(lower_bound, l, upper_bound)),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[61, 60])).
% 97.01/97.20 tff(63,plain,
% 97.01/97.20 ($false),
% 97.01/97.20 inference(unit_resolution,[status(thm)],[62, 59, 49, 29, 2])).
% 97.01/97.20 tff(64,plain,(in_interval(lower_bound, l, upper_bound)), inference(lemma,lemma(discharge,[]))).
% 97.01/97.20 tff(65,plain,
% 97.01/97.20 (^[X: $i] : refl(((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)))),
% 97.01/97.20 inference(bind,[status(th)],[])).
% 97.01/97.20 tff(66,plain,
% 97.01/97.20 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 97.01/97.20 inference(quant_intro,[status(thm)],[65])).
% 97.01/97.20 tff(67,plain,
% 97.01/97.20 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 97.01/97.20 inference(rewrite,[status(thm)],[])).
% 97.01/97.20 tff(68,plain,
% 97.01/97.20 (^[X: $i] : 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)))) | (~in_interval(lower_bound, X, upper_bound))) <=> (((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~in_interval(lower_bound, X, upper_bound))))), rewrite((((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~in_interval(lower_bound, X, upper_bound)) | (~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)))) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))))),
% 97.01/97.20 inference(bind,[status(th)],[])).
% 97.01/97.20 tff(69,plain,
% 97.01/97.20 (![X: $i] : ((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~in_interval(lower_bound, X, upper_bound))) <=> ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 97.01/97.20 inference(quant_intro,[status(thm)],[68])).
% 97.01/97.20 tff(70,axiom,(![X: $i] : ((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~in_interval(lower_bound, X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity1')).
% 97.01/97.20 tff(71,plain,
% 97.01/97.20 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[70, 69])).
% 97.01/97.20 tff(72,plain,
% 97.01/97.20 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[71, 67])).
% 97.01/97.20 tff(73,plain,(
% 97.01/97.20 ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 97.01/97.20 inference(skolemize,[status(sab)],[72])).
% 97.01/97.20 tff(74,plain,
% 97.01/97.20 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[73, 66])).
% 97.01/97.20 tff(75,plain,
% 97.01/97.20 (((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))) <=> ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))),
% 97.01/97.20 inference(rewrite,[status(thm)],[])).
% 97.01/97.20 tff(76,plain,
% 97.01/97.20 ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))),
% 97.01/97.20 inference(quant_inst,[status(thm)],[])).
% 97.01/97.20 tff(77,plain,
% 97.01/97.20 ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 97.01/97.20 inference(modus_ponens,[status(thm)],[76, 75])).
% 97.01/97.20 tff(78,plain,
% 97.01/97.20 ((~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 97.01/97.20 inference(unit_resolution,[status(thm)],[77, 74])).
% 97.01/97.20 tff(79,plain,
% 97.01/97.20 ((~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 97.01/97.20 inference(unit_resolution,[status(thm)],[78, 64])).
% 97.01/97.20 tff(80,plain,
% 97.01/97.20 (~less_than_or_equal(l, h(l))),
% 97.01/97.20 inference(unit_resolution,[status(thm)],[79, 1])).
% 97.01/97.21 tff(81,plain,
% 97.01/97.21 (^[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)))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(82,plain,
% 97.01/97.21 (![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))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[81])).
% 97.01/97.21 tff(83,plain,
% 97.01/97.21 (![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))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(84,plain,
% 97.01/97.21 (^[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)))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(85,plain,
% 97.01/97.21 (![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))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[84])).
% 97.01/97.21 tff(86,axiom,(![X: $i] : (less_than_or_equal(f(g(X)), n0) | less_than_or_equal(l, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','crossover3_and_g_function2')).
% 97.01/97.21 tff(87,plain,
% 97.01/97.21 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[86, 85])).
% 97.01/97.21 tff(88,plain,
% 97.01/97.21 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[87, 83])).
% 97.01/97.21 tff(89,plain,(
% 97.01/97.21 ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 97.01/97.21 inference(skolemize,[status(sab)],[88])).
% 97.01/97.21 tff(90,plain,
% 97.01/97.21 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[89, 82])).
% 97.01/97.21 tff(91,plain,
% 97.01/97.21 (((~![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))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(92,plain,
% 97.01/97.21 ((~![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))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(93,plain,
% 97.01/97.21 ((~![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)),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[92, 91])).
% 97.01/97.21 tff(94,plain,
% 97.01/97.21 (less_than_or_equal(f(g(h(l))), n0)),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[93, 90, 80])).
% 97.01/97.21 tff(95,plain,
% 97.01/97.21 (((~![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)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(96,plain,
% 97.01/97.21 ((~![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)))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(97,plain,
% 97.01/97.21 ((~![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))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[96, 95])).
% 97.01/97.21 tff(98,plain,
% 97.01/97.21 (~less_than_or_equal(g(h(l)), h(l))),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[97, 10, 80])).
% 97.01/97.21 tff(99,plain,
% 97.01/97.21 (^[Y: $i, X: $i] : refl(((~in_interval(lower_bound, X, upper_bound)) | 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))) <=> ((~in_interval(lower_bound, X, upper_bound)) | 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))))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(100,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[99])).
% 97.01/97.21 tff(101,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(102,plain,
% 97.01/97.21 (^[Y: $i, X: $i] : 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))) | (~in_interval(lower_bound, X, upper_bound))) <=> ((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))) | (~in_interval(lower_bound, X, upper_bound))))), 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))) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~in_interval(lower_bound, X, upper_bound)) | 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))) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~in_interval(lower_bound, X, upper_bound)) | 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)))))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(103,plain,
% 97.01/97.21 (![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))) | (~in_interval(lower_bound, X, upper_bound))) <=> ![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[102])).
% 97.01/97.21 tff(104,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))) | (~in_interval(lower_bound, X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity2')).
% 97.01/97.21 tff(105,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[104, 103])).
% 97.01/97.21 tff(106,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[105, 101])).
% 97.01/97.21 tff(107,plain,(
% 97.01/97.21 ![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))),
% 97.01/97.21 inference(skolemize,[status(sab)],[106])).
% 97.01/97.21 tff(108,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[107, 100])).
% 97.01/97.21 tff(109,plain,
% 97.01/97.21 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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) | (~in_interval(lower_bound, l, upper_bound)) | 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] : ((~in_interval(lower_bound, X, upper_bound)) | 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) | (~in_interval(lower_bound, l, upper_bound)) | 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)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(110,plain,
% 97.01/97.21 (((~in_interval(lower_bound, l, upper_bound)) | 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) | (~in_interval(lower_bound, l, upper_bound)) | 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)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(111,plain,
% 97.01/97.21 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, l, upper_bound)) | 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] : ((~in_interval(lower_bound, X, upper_bound)) | 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) | (~in_interval(lower_bound, l, upper_bound)) | 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))))),
% 97.01/97.21 inference(monotonicity,[status(thm)],[110])).
% 97.01/97.21 tff(112,plain,
% 97.01/97.21 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, l, upper_bound)) | 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] : ((~in_interval(lower_bound, X, upper_bound)) | 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) | (~in_interval(lower_bound, l, upper_bound)) | 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)))),
% 97.01/97.21 inference(transitivity,[status(thm)],[111, 109])).
% 97.01/97.21 tff(113,plain,
% 97.01/97.21 ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, l, upper_bound)) | 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)))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(114,plain,
% 97.01/97.21 ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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) | (~in_interval(lower_bound, l, upper_bound)) | 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))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[113, 112])).
% 97.01/97.21 tff(115,plain,
% 97.01/97.21 (~less_than_or_equal(g(h(l)), l)),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[114, 108, 1, 64, 98, 94])).
% 97.01/97.21 tff(116,plain,
% 97.01/97.21 (((~![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))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(117,plain,
% 97.01/97.21 ((~![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))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(118,plain,
% 97.01/97.21 ((~![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)),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[117, 116])).
% 97.01/97.21 tff(119,plain,
% 97.01/97.21 (less_than_or_equal(g(h(l)), upper_bound)),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[118, 24, 80])).
% 97.01/97.21 tff(120,plain,
% 97.01/97.21 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | ((~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(121,plain,
% 97.01/97.21 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | ((~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(122,plain,
% 97.01/97.21 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l)),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[121, 120])).
% 97.01/97.21 tff(123,plain,
% 97.01/97.21 ($false),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[122, 45, 119, 94, 115])).
% 97.01/97.21 tff(124,plain,(less_than_or_equal(f(l), n0)), inference(lemma,lemma(discharge,[]))).
% 97.01/97.21 tff(125,plain,
% 97.01/97.21 ((~in_interval(f(l), n0, f(l))) <=> (~in_interval(f(l), n0, f(l)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(126,axiom,(~in_interval(f(l), n0, f(l))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_there_is_x_which_crosses')).
% 97.01/97.21 tff(127,plain,
% 97.01/97.21 (~in_interval(f(l), n0, f(l))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[126, 125])).
% 97.01/97.21 tff(128,plain,
% 97.01/97.21 (((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(n0, f(l))) | (~less_than_or_equal(f(l), n0)) | in_interval(f(l), n0, f(l)))) <=> ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | (~less_than_or_equal(n0, f(l))) | (~less_than_or_equal(f(l), n0)) | in_interval(f(l), n0, f(l)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(129,plain,
% 97.01/97.21 ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(n0, f(l))) | (~less_than_or_equal(f(l), n0)) | in_interval(f(l), n0, f(l)))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(130,plain,
% 97.01/97.21 ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | (~less_than_or_equal(n0, f(l))) | (~less_than_or_equal(f(l), n0)) | in_interval(f(l), n0, f(l))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[129, 128])).
% 97.01/97.21 tff(131,plain,
% 97.01/97.21 ((~less_than_or_equal(n0, f(l))) | (~less_than_or_equal(f(l), n0))),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[130, 59, 127])).
% 97.01/97.21 tff(132,plain,
% 97.01/97.21 (~less_than_or_equal(n0, f(l))),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[131, 124])).
% 97.01/97.21 tff(133,assumption,(~less_than_or_equal(k(l), upper_bound)), introduced(assumption)).
% 97.01/97.21 tff(134,assumption,(~less_than_or_equal(n0, f(l))), introduced(assumption)).
% 97.01/97.21 tff(135,plain,
% 97.01/97.21 (less_than_or_equal(n0, f(upper_bound)) <=> less_than_or_equal(n0, f(upper_bound))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(136,axiom,(less_than_or_equal(n0, f(upper_bound))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','upper_mapping')).
% 97.01/97.21 tff(137,plain,
% 97.01/97.21 (less_than_or_equal(n0, f(upper_bound))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[136, 135])).
% 97.01/97.21 tff(138,plain,
% 97.01/97.21 (^[Y: $i, X: $i] : refl(((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(139,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[138])).
% 97.01/97.21 tff(140,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(141,plain,
% 97.01/97.21 (^[Y: $i, X: $i] : 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)) | (~in_interval(lower_bound, X, upper_bound))) <=> (((~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)))) | (~in_interval(lower_bound, X, upper_bound))))), 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)))) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(142,plain,
% 97.01/97.21 (![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)) | (~in_interval(lower_bound, X, upper_bound))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[141])).
% 97.01/97.21 tff(143,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)) | (~in_interval(lower_bound, X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity4')).
% 97.01/97.21 tff(144,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[143, 142])).
% 97.01/97.21 tff(145,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[144, 140])).
% 97.01/97.21 tff(146,plain,(
% 97.01/97.21 ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 97.01/97.21 inference(skolemize,[status(sab)],[145])).
% 97.01/97.21 tff(147,plain,
% 97.01/97.21 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[146, 139])).
% 97.01/97.21 tff(148,plain,
% 97.01/97.21 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), upper_bound))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), upper_bound))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(149,plain,
% 97.01/97.21 (((~less_than_or_equal(l, upper_bound)) | (~in_interval(lower_bound, l, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), upper_bound))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(150,plain,
% 97.01/97.21 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | 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)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), upper_bound)))),
% 97.01/97.21 inference(monotonicity,[status(thm)],[149])).
% 97.01/97.21 tff(151,plain,
% 97.01/97.21 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | 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)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), upper_bound))),
% 97.01/97.21 inference(transitivity,[status(thm)],[150, 148])).
% 97.01/97.21 tff(152,plain,
% 97.01/97.21 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound))))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(153,plain,
% 97.01/97.21 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), upper_bound)),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[152, 151])).
% 97.01/97.21 tff(154,plain,
% 97.01/97.21 ($false),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[153, 147, 137, 134, 29, 64, 133])).
% 97.01/97.21 tff(155,plain,(less_than_or_equal(k(l), upper_bound) | less_than_or_equal(n0, f(l))), inference(lemma,lemma(discharge,[]))).
% 97.01/97.21 tff(156,plain,
% 97.01/97.21 (less_than_or_equal(k(l), upper_bound)),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[155, 132])).
% 97.01/97.21 tff(157,plain,
% 97.01/97.21 (^[X: $i] : refl(((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) <=> ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(158,plain,
% 97.01/97.21 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) <=> ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[157])).
% 97.01/97.21 tff(159,plain,
% 97.01/97.21 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) <=> ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(160,plain,
% 97.01/97.21 (^[X: $i] : 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))) | (~in_interval(lower_bound, X, upper_bound))) <=> (((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) | (~in_interval(lower_bound, X, upper_bound))))), rewrite((((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~in_interval(lower_bound, X, upper_bound)) | (~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))) | (~in_interval(lower_bound, X, upper_bound))) <=> ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(161,plain,
% 97.01/97.21 (![X: $i] : ((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~in_interval(lower_bound, X, upper_bound))) <=> ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[160])).
% 97.01/97.21 tff(162,axiom,(![X: $i] : ((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~in_interval(lower_bound, X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity3')).
% 97.01/97.21 tff(163,plain,
% 97.01/97.21 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[162, 161])).
% 97.01/97.21 tff(164,plain,
% 97.01/97.21 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[163, 159])).
% 97.01/97.21 tff(165,plain,(
% 97.01/97.21 ![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))),
% 97.01/97.21 inference(skolemize,[status(sab)],[164])).
% 97.01/97.21 tff(166,plain,
% 97.01/97.21 (![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[165, 158])).
% 97.01/97.21 tff(167,plain,
% 97.01/97.21 (((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))) | ((~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(k(l), l)) | less_than_or_equal(n0, f(l)))) <=> ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))) | (~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(k(l), l)) | less_than_or_equal(n0, f(l)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(168,plain,
% 97.01/97.21 ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))) | ((~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(k(l), l)) | less_than_or_equal(n0, f(l)))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(169,plain,
% 97.01/97.21 ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))) | (~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(k(l), l)) | less_than_or_equal(n0, f(l))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[168, 167])).
% 97.01/97.21 tff(170,plain,
% 97.01/97.21 ((~in_interval(lower_bound, l, upper_bound)) | (~less_than_or_equal(k(l), l)) | less_than_or_equal(n0, f(l))),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[169, 166])).
% 97.01/97.21 tff(171,plain,
% 97.01/97.21 ((~less_than_or_equal(k(l), l)) | less_than_or_equal(n0, f(l))),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[170, 64])).
% 97.01/97.21 tff(172,plain,
% 97.01/97.21 (~less_than_or_equal(k(l), l)),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[171, 132])).
% 97.01/97.21 tff(173,plain,
% 97.01/97.21 (^[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)))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(174,plain,
% 97.01/97.21 (![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))),
% 97.01/97.21 inference(quant_intro,[status(thm)],[173])).
% 97.01/97.21 tff(175,plain,
% 97.01/97.21 (![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))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(176,axiom,(![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','totality_of_less')).
% 97.01/97.21 tff(177,plain,
% 97.01/97.21 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[176, 175])).
% 97.01/97.21 tff(178,plain,(
% 97.01/97.21 ![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 97.01/97.21 inference(skolemize,[status(sab)],[177])).
% 97.01/97.21 tff(179,plain,
% 97.01/97.21 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[178, 174])).
% 97.01/97.21 tff(180,plain,
% 97.01/97.21 (((~![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))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(181,plain,
% 97.01/97.21 ((~![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))),
% 97.01/97.21 inference(quant_inst,[status(thm)],[])).
% 97.01/97.21 tff(182,plain,
% 97.01/97.21 ((~![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)),
% 97.01/97.21 inference(modus_ponens,[status(thm)],[181, 180])).
% 97.01/97.21 tff(183,plain,
% 97.01/97.21 (less_than_or_equal(l, k(l))),
% 97.01/97.21 inference(unit_resolution,[status(thm)],[182, 179, 172])).
% 97.01/97.21 tff(184,plain,
% 97.01/97.21 (![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(185,plain,
% 97.01/97.21 (![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))),
% 97.01/97.21 inference(rewrite,[status(thm)],[])).
% 97.01/97.21 tff(186,plain,
% 97.01/97.21 (^[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, Z) | (~less_than_or_equal(X, Y)))), (((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> ((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))))), rewrite(((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))), (((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))))),
% 97.01/97.21 inference(bind,[status(th)],[])).
% 97.01/97.21 tff(187,plain,
% 97.01/97.21 (![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(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))),
% 97.01/97.22 inference(quant_intro,[status(thm)],[186])).
% 97.01/97.22 tff(188,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/sandbox/benchmark/theBenchmark.p','transitivity_of_less')).
% 97.01/97.22 tff(189,plain,
% 97.01/97.22 (![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[188, 187])).
% 97.01/97.22 tff(190,plain,
% 97.01/97.22 (![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[189, 185])).
% 97.01/97.22 tff(191,plain,(
% 97.01/97.22 ![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))),
% 97.01/97.22 inference(skolemize,[status(sab)],[190])).
% 97.01/97.22 tff(192,plain,
% 97.01/97.22 (![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[191, 184])).
% 97.01/97.22 tff(193,plain,
% 97.01/97.22 (((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | ((~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(194,plain,
% 97.01/97.22 ((less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l))) <=> ((~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(195,plain,
% 97.01/97.22 (((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l)))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | ((~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l)))))),
% 97.01/97.22 inference(monotonicity,[status(thm)],[194])).
% 97.01/97.22 tff(196,plain,
% 97.01/97.22 (((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l)))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))))),
% 97.01/97.22 inference(transitivity,[status(thm)],[195, 193])).
% 97.01/97.22 tff(197,plain,
% 97.01/97.22 ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l))) | (~less_than_or_equal(lower_bound, l)))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(198,plain,
% 97.01/97.22 ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(lower_bound, k(l)) | (~less_than_or_equal(l, k(l)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[197, 196])).
% 97.01/97.22 tff(199,plain,
% 97.01/97.22 (less_than_or_equal(lower_bound, k(l))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[198, 192, 49, 183])).
% 97.01/97.22 tff(200,assumption,(~in_interval(lower_bound, k(l), upper_bound)), introduced(assumption)).
% 97.01/97.22 tff(201,assumption,(less_than_or_equal(lower_bound, k(l))), introduced(assumption)).
% 97.01/97.22 tff(202,assumption,(less_than_or_equal(k(l), upper_bound)), introduced(assumption)).
% 97.01/97.22 tff(203,plain,
% 97.01/97.22 (((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(k(l), upper_bound)) | in_interval(lower_bound, k(l), upper_bound) | (~less_than_or_equal(lower_bound, k(l))))) <=> ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | (~less_than_or_equal(k(l), upper_bound)) | in_interval(lower_bound, k(l), upper_bound) | (~less_than_or_equal(lower_bound, k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(204,plain,
% 97.01/97.22 (((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | in_interval(lower_bound, k(l), upper_bound)) <=> ((~less_than_or_equal(k(l), upper_bound)) | in_interval(lower_bound, k(l), upper_bound) | (~less_than_or_equal(lower_bound, k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(205,plain,
% 97.01/97.22 (((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | in_interval(lower_bound, k(l), upper_bound))) <=> ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(k(l), upper_bound)) | in_interval(lower_bound, k(l), upper_bound) | (~less_than_or_equal(lower_bound, k(l)))))),
% 97.01/97.22 inference(monotonicity,[status(thm)],[204])).
% 97.01/97.22 tff(206,plain,
% 97.01/97.22 (((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | in_interval(lower_bound, k(l), upper_bound))) <=> ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | (~less_than_or_equal(k(l), upper_bound)) | in_interval(lower_bound, k(l), upper_bound) | (~less_than_or_equal(lower_bound, k(l))))),
% 97.01/97.22 inference(transitivity,[status(thm)],[205, 203])).
% 97.01/97.22 tff(207,plain,
% 97.01/97.22 ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l))) | in_interval(lower_bound, k(l), upper_bound))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(208,plain,
% 97.01/97.22 ((~![X: $i, Upper: $i, Lower: $i] : ((~less_than_or_equal(X, Upper)) | (~less_than_or_equal(Lower, X)) | in_interval(Lower, X, Upper))) | (~less_than_or_equal(k(l), upper_bound)) | in_interval(lower_bound, k(l), upper_bound) | (~less_than_or_equal(lower_bound, k(l)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[207, 206])).
% 97.01/97.22 tff(209,plain,
% 97.01/97.22 ($false),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[208, 59, 202, 201, 200])).
% 97.01/97.22 tff(210,plain,(in_interval(lower_bound, k(l), upper_bound) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(lower_bound, k(l)))), inference(lemma,lemma(discharge,[]))).
% 97.01/97.22 tff(211,plain,
% 97.01/97.22 (in_interval(lower_bound, k(l), upper_bound)),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[210, 199, 156])).
% 97.01/97.22 tff(212,plain,
% 97.01/97.22 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0)) | less_than_or_equal(k(l), l))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0)) | less_than_or_equal(k(l), l))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(213,plain,
% 97.01/97.22 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0)) | less_than_or_equal(k(l), l))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(214,plain,
% 97.01/97.22 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)) | less_than_or_equal(X, l))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(f(k(l)), n0)) | less_than_or_equal(k(l), l)),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[213, 212])).
% 97.01/97.22 tff(215,plain,
% 97.01/97.22 (~less_than_or_equal(f(k(l)), n0)),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[214, 45, 172, 156])).
% 97.01/97.22 tff(216,plain,
% 97.01/97.22 (((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0))) <=> ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(217,plain,
% 97.01/97.22 ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(218,plain,
% 97.01/97.22 ((~![X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(k(l), h(k(l)))) | less_than_or_equal(f(k(l)), n0)),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[217, 216])).
% 97.01/97.22 tff(219,plain,
% 97.01/97.22 ((~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(k(l), h(k(l))))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[218, 74, 215])).
% 97.01/97.22 tff(220,plain,
% 97.01/97.22 (~less_than_or_equal(k(l), h(k(l)))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[219, 211])).
% 97.01/97.22 tff(221,plain,
% 97.01/97.22 (^[Y: $i, X: $i] : refl(((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X)) <=> ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X)))),
% 97.01/97.22 inference(bind,[status(th)],[])).
% 97.01/97.22 tff(222,plain,
% 97.01/97.22 (![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))),
% 97.01/97.22 inference(quant_intro,[status(thm)],[221])).
% 97.01/97.22 tff(223,plain,
% 97.01/97.22 (![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))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(224,axiom,(![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','interpolation2')).
% 97.01/97.22 tff(225,plain,
% 97.01/97.22 (![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[224, 223])).
% 97.01/97.22 tff(226,plain,(
% 97.01/97.22 ![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
% 97.01/97.22 inference(skolemize,[status(sab)],[225])).
% 97.01/97.22 tff(227,plain,
% 97.01/97.22 (![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[226, 222])).
% 97.01/97.22 tff(228,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | ((~less_than_or_equal(q(h(k(l)), k(l)), h(k(l)))) | less_than_or_equal(k(l), h(k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | (~less_than_or_equal(q(h(k(l)), k(l)), h(k(l)))) | less_than_or_equal(k(l), h(k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(229,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | ((~less_than_or_equal(q(h(k(l)), k(l)), h(k(l)))) | less_than_or_equal(k(l), h(k(l))))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(230,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | (~less_than_or_equal(q(h(k(l)), k(l)), h(k(l)))) | less_than_or_equal(k(l), h(k(l)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[229, 228])).
% 97.01/97.22 tff(231,plain,
% 97.01/97.22 (~less_than_or_equal(q(h(k(l)), k(l)), h(k(l)))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[230, 227, 220])).
% 97.01/97.22 tff(232,plain,
% 97.01/97.22 (^[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)))),
% 97.01/97.22 inference(bind,[status(th)],[])).
% 97.01/97.22 tff(233,plain,
% 97.01/97.22 (![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))),
% 97.01/97.22 inference(quant_intro,[status(thm)],[232])).
% 97.01/97.22 tff(234,plain,
% 97.01/97.22 (![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))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(235,axiom,(![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','interpolation1')).
% 97.01/97.22 tff(236,plain,
% 97.01/97.22 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[235, 234])).
% 97.01/97.22 tff(237,plain,(
% 97.01/97.22 ![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 97.01/97.22 inference(skolemize,[status(sab)],[236])).
% 97.01/97.22 tff(238,plain,
% 97.01/97.22 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[237, 233])).
% 97.01/97.22 tff(239,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | ((~less_than_or_equal(k(l), q(h(k(l)), k(l)))) | less_than_or_equal(k(l), h(k(l))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | (~less_than_or_equal(k(l), q(h(k(l)), k(l)))) | less_than_or_equal(k(l), h(k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(240,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | ((~less_than_or_equal(k(l), q(h(k(l)), k(l)))) | less_than_or_equal(k(l), h(k(l))))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(241,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | (~less_than_or_equal(k(l), q(h(k(l)), k(l)))) | less_than_or_equal(k(l), h(k(l)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[240, 239])).
% 97.01/97.22 tff(242,plain,
% 97.01/97.22 (~less_than_or_equal(k(l), q(h(k(l)), k(l)))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[241, 238, 220])).
% 97.01/97.22 tff(243,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(k(l), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), 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), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), k(l)))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(244,plain,
% 97.01/97.22 ((less_than_or_equal(q(h(k(l)), k(l)), k(l)) | less_than_or_equal(k(l), q(h(k(l)), k(l)))) <=> (less_than_or_equal(k(l), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), k(l)))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(245,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(h(k(l)), k(l)), k(l)) | less_than_or_equal(k(l), q(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), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), k(l))))),
% 97.01/97.22 inference(monotonicity,[status(thm)],[244])).
% 97.01/97.22 tff(246,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(h(k(l)), k(l)), k(l)) | less_than_or_equal(k(l), q(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), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), k(l)))),
% 97.01/97.22 inference(transitivity,[status(thm)],[245, 243])).
% 97.01/97.22 tff(247,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(h(k(l)), k(l)), k(l)) | less_than_or_equal(k(l), q(h(k(l)), k(l))))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(248,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), k(l))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[247, 246])).
% 97.01/97.22 tff(249,plain,
% 97.01/97.22 (less_than_or_equal(q(h(k(l)), k(l)), k(l))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[248, 179, 242])).
% 97.01/97.22 tff(250,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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(k(l)), n0) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l))))) <=> ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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(k(l)), n0) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(251,plain,
% 97.01/97.22 (((~in_interval(lower_bound, k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l)))) <=> (less_than_or_equal(f(k(l)), n0) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(252,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l))))) <=> ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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(k(l)), n0) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l)))))),
% 97.01/97.22 inference(monotonicity,[status(thm)],[251])).
% 97.01/97.22 tff(253,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l))))) <=> ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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(k(l)), n0) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l))))),
% 97.01/97.22 inference(transitivity,[status(thm)],[252, 250])).
% 97.01/97.22 tff(254,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, k(l), upper_bound)) | less_than_or_equal(f(k(l)), n0) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l))))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(255,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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(k(l)), n0) | (~in_interval(lower_bound, k(l), upper_bound)) | (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))) | (~less_than_or_equal(q(h(k(l)), k(l)), k(l)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[254, 253])).
% 97.01/97.22 tff(256,plain,
% 97.01/97.22 (~less_than_or_equal(f(q(h(k(l)), k(l))), n0)),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[255, 108, 211, 215, 249, 231])).
% 97.01/97.22 tff(257,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(q(h(k(l)), k(l)))) | less_than_or_equal(f(q(h(k(l)), 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(h(k(l)), k(l)))) | less_than_or_equal(f(q(h(k(l)), k(l))), n0))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(258,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(q(h(k(l)), k(l)))) | less_than_or_equal(f(q(h(k(l)), k(l))), n0))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(259,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(q(h(k(l)), k(l)))) | less_than_or_equal(f(q(h(k(l)), k(l))), n0)),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[258, 257])).
% 97.01/97.22 tff(260,plain,
% 97.01/97.22 (less_than_or_equal(n0, f(q(h(k(l)), k(l))))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[259, 179, 256])).
% 97.01/97.22 tff(261,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(h(k(l)), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), 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(h(k(l)), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(262,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(h(k(l)), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l))))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(263,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(h(k(l)), q(h(k(l)), k(l))) | less_than_or_equal(q(h(k(l)), k(l)), h(k(l)))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[262, 261])).
% 97.01/97.22 tff(264,plain,
% 97.01/97.22 (less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[263, 179, 231])).
% 97.01/97.22 tff(265,assumption,(~less_than_or_equal(l, h(k(l)))), introduced(assumption)).
% 97.01/97.22 tff(266,assumption,(in_interval(lower_bound, k(l), upper_bound)), introduced(assumption)).
% 97.01/97.22 tff(267,assumption,(less_than_or_equal(l, k(l))), introduced(assumption)).
% 97.01/97.22 tff(268,assumption,(~less_than_or_equal(f(k(l)), n0)), introduced(assumption)).
% 97.01/97.22 tff(269,assumption,(less_than_or_equal(f(l), n0)), introduced(assumption)).
% 97.01/97.22 tff(270,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(l, h(k(l))) | (~in_interval(lower_bound, k(l), upper_bound)))) <=> ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(l, h(k(l))) | (~in_interval(lower_bound, k(l), upper_bound)))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(271,plain,
% 97.01/97.22 (((~in_interval(lower_bound, k(l), upper_bound)) | 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(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(l, h(k(l))) | (~in_interval(lower_bound, k(l), upper_bound)))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(272,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, k(l), upper_bound)) | 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] : ((~in_interval(lower_bound, X, upper_bound)) | 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(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(l, h(k(l))) | (~in_interval(lower_bound, k(l), upper_bound))))),
% 97.01/97.22 inference(monotonicity,[status(thm)],[271])).
% 97.01/97.22 tff(273,plain,
% 97.01/97.22 (((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, k(l), upper_bound)) | 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] : ((~in_interval(lower_bound, X, upper_bound)) | 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(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(l, h(k(l))) | (~in_interval(lower_bound, k(l), upper_bound)))),
% 97.01/97.22 inference(transitivity,[status(thm)],[272, 270])).
% 97.01/97.22 tff(274,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | 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)))) | ((~in_interval(lower_bound, k(l), upper_bound)) | 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))))),
% 97.01/97.22 inference(quant_inst,[status(thm)],[])).
% 97.01/97.22 tff(275,plain,
% 97.01/97.22 ((~![Y: $i, X: $i] : ((~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (~less_than_or_equal(f(l), n0)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | less_than_or_equal(l, h(k(l))) | (~in_interval(lower_bound, k(l), upper_bound))),
% 97.01/97.22 inference(modus_ponens,[status(thm)],[274, 273])).
% 97.01/97.22 tff(276,plain,
% 97.01/97.22 ($false),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[275, 108, 269, 268, 267, 266, 265])).
% 97.01/97.22 tff(277,plain,(less_than_or_equal(l, h(k(l))) | (~less_than_or_equal(f(l), n0)) | less_than_or_equal(f(k(l)), n0) | (~less_than_or_equal(l, k(l))) | (~in_interval(lower_bound, k(l), upper_bound))), inference(lemma,lemma(discharge,[]))).
% 97.01/97.22 tff(278,plain,
% 97.01/97.22 (less_than_or_equal(l, h(k(l)))),
% 97.01/97.22 inference(unit_resolution,[status(thm)],[277, 211, 215, 183, 124])).
% 97.01/97.22 tff(279,plain,
% 97.01/97.22 (((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | ((~less_than_or_equal(l, h(k(l)))) | less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (~less_than_or_equal(l, h(k(l)))) | less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))))),
% 97.01/97.22 inference(rewrite,[status(thm)],[])).
% 97.01/97.22 tff(280,plain,
% 97.01/97.22 ((less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))) | (~less_than_or_equal(l, h(k(l))))) <=> ((~less_than_or_equal(l, h(k(l)))) | less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))))),
% 97.01/97.23 inference(rewrite,[status(thm)],[])).
% 97.01/97.23 tff(281,plain,
% 97.01/97.23 (((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))) | (~less_than_or_equal(l, h(k(l)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | ((~less_than_or_equal(l, h(k(l)))) | less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l))))))),
% 97.01/97.23 inference(monotonicity,[status(thm)],[280])).
% 97.01/97.23 tff(282,plain,
% 97.01/97.23 (((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))) | (~less_than_or_equal(l, h(k(l)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (~less_than_or_equal(l, h(k(l)))) | less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))))),
% 97.01/97.23 inference(transitivity,[status(thm)],[281, 279])).
% 97.01/97.23 tff(283,plain,
% 97.01/97.23 ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l)))) | (~less_than_or_equal(l, h(k(l)))))),
% 97.01/97.23 inference(quant_inst,[status(thm)],[])).
% 97.01/97.23 tff(284,plain,
% 97.01/97.23 ((~![Z: $i, Y: $i, X: $i] : (less_than_or_equal(X, Z) | (~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)))) | (~less_than_or_equal(l, h(k(l)))) | less_than_or_equal(l, q(h(k(l)), k(l))) | (~less_than_or_equal(h(k(l)), q(h(k(l)), k(l))))),
% 97.01/97.23 inference(modus_ponens,[status(thm)],[283, 282])).
% 97.01/97.23 tff(285,plain,
% 97.01/97.23 (less_than_or_equal(l, q(h(k(l)), k(l)))),
% 97.01/97.23 inference(unit_resolution,[status(thm)],[284, 192, 278, 264])).
% 97.01/97.23 tff(286,plain,
% 97.01/97.23 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l))))))),
% 97.01/97.23 inference(rewrite,[status(thm)],[])).
% 97.01/97.23 tff(287,plain,
% 97.01/97.23 (((~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l)))))) <=> (less_than_or_equal(n0, f(l)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l))))))),
% 97.01/97.23 inference(rewrite,[status(thm)],[])).
% 97.01/97.23 tff(288,plain,
% 97.01/97.23 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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, q(h(k(l)), k(l)))) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l)))))))),
% 97.01/97.24 inference(monotonicity,[status(thm)],[287])).
% 97.01/97.24 tff(289,plain,
% 97.01/97.24 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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, q(h(k(l)), k(l)))) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l))))))),
% 97.01/97.24 inference(transitivity,[status(thm)],[288, 286])).
% 97.01/97.24 tff(290,plain,
% 97.01/97.24 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | 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, q(h(k(l)), k(l)))) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l))))))),
% 97.01/97.24 inference(quant_inst,[status(thm)],[])).
% 97.01/97.24 tff(291,plain,
% 97.01/97.24 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~in_interval(lower_bound, X, upper_bound)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~in_interval(lower_bound, l, upper_bound)) | less_than_or_equal(k(l), q(h(k(l)), k(l))) | (~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l)))))),
% 97.01/97.24 inference(modus_ponens,[status(thm)],[290, 289])).
% 97.01/97.24 tff(292,plain,
% 97.01/97.24 ((~less_than_or_equal(l, q(h(k(l)), k(l)))) | (~less_than_or_equal(n0, f(q(h(k(l)), k(l)))))),
% 97.01/97.24 inference(unit_resolution,[status(thm)],[291, 147, 132, 64, 242])).
% 97.01/97.24 tff(293,plain,
% 97.01/97.24 ($false),
% 97.01/97.24 inference(unit_resolution,[status(thm)],[292, 285, 260])).
% 97.01/97.24 % SZS output end Proof
% 97.01/97.24 % E exiting
%------------------------------------------------------------------------------