%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA002-4 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 2.44s 2.59s
% Output : Proof 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : ANA002-4 : TPTP v9.0.0. Released v1.1.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 11:16:11 EDT 2025
% 0.14/0.36 % CPUTime :
% 2.44/2.59 % SZS status Unsatisfiable
% 2.44/2.59 % SZS output start Proof
% 2.44/2.59 tff(less_than_or_equal_type, type, (
% 2.44/2.59 less_than_or_equal: ( $i * $i ) > $o)).
% 2.44/2.59 tff(n0_type, type, (
% 2.44/2.59 n0: $i)).
% 2.44/2.59 tff(f_type, type, (
% 2.44/2.59 f: $i > $i)).
% 2.44/2.59 tff(q_type, type, (
% 2.44/2.59 q: ( $i * $i ) > $i)).
% 2.44/2.59 tff(k_type, type, (
% 2.44/2.59 k: $i > $i)).
% 2.44/2.59 tff(l_type, type, (
% 2.44/2.59 l: $i)).
% 2.44/2.59 tff(upper_bound_type, type, (
% 2.44/2.59 upper_bound: $i)).
% 2.44/2.59 tff(g_type, type, (
% 2.44/2.59 g: $i > $i)).
% 2.44/2.59 tff(h_type, type, (
% 2.44/2.59 h: $i > $i)).
% 2.44/2.59 tff(lower_bound_type, type, (
% 2.44/2.59 lower_bound: $i)).
% 2.44/2.59 tff(1,assumption,(~less_than_or_equal(f(l), n0)), introduced(assumption)).
% 2.44/2.59 tff(2,assumption,(~less_than_or_equal(l, upper_bound)), introduced(assumption)).
% 2.44/2.59 tff(3,plain,
% 2.44/2.59 (^[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)))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(4,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[3])).
% 2.44/2.59 tff(5,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(6,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')).
% 2.44/2.59 tff(7,plain,
% 2.44/2.59 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.44/2.59 tff(8,plain,(
% 2.44/2.59 ![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 2.44/2.59 inference(skolemize,[status(sab)],[7])).
% 2.44/2.59 tff(9,plain,
% 2.44/2.59 (![X: $i] : ((~less_than_or_equal(g(X), X)) | less_than_or_equal(l, X))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[8, 4])).
% 2.44/2.59 tff(10,plain,
% 2.44/2.59 (((~![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))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(11,plain,
% 2.44/2.59 ((~![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))),
% 2.44/2.59 inference(quant_inst,[status(thm)],[])).
% 2.44/2.59 tff(12,plain,
% 2.44/2.59 ((~![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)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[11, 10])).
% 2.44/2.59 tff(13,plain,
% 2.44/2.59 (~less_than_or_equal(g(upper_bound), upper_bound)),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[12, 9, 2])).
% 2.44/2.59 tff(14,plain,
% 2.44/2.59 (^[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)))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(15,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[14])).
% 2.44/2.59 tff(16,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(17,plain,
% 2.44/2.59 (^[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)))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(18,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[17])).
% 2.44/2.59 tff(19,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')).
% 2.44/2.59 tff(20,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.44/2.59 tff(21,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.44/2.59 tff(22,plain,(
% 2.44/2.59 ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 2.44/2.59 inference(skolemize,[status(sab)],[21])).
% 2.44/2.59 tff(23,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[22, 15])).
% 2.44/2.59 tff(24,plain,
% 2.44/2.59 (((~![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))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(25,plain,
% 2.44/2.59 ((~![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))),
% 2.44/2.59 inference(quant_inst,[status(thm)],[])).
% 2.44/2.59 tff(26,plain,
% 2.44/2.59 ((~![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(g(X), upper_bound))) | less_than_or_equal(l, upper_bound) | less_than_or_equal(g(upper_bound), upper_bound)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.44/2.59 tff(27,plain,
% 2.44/2.59 ($false),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[26, 23, 2, 13])).
% 2.44/2.59 tff(28,plain,(less_than_or_equal(l, upper_bound)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.59 tff(29,plain,
% 2.44/2.59 (less_than_or_equal(f(lower_bound), n0) <=> less_than_or_equal(f(lower_bound), n0)),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(30,axiom,(less_than_or_equal(f(lower_bound), n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lower_mapping')).
% 2.44/2.59 tff(31,plain,
% 2.44/2.59 (less_than_or_equal(f(lower_bound), n0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.44/2.59 tff(32,plain,
% 2.44/2.59 (less_than_or_equal(lower_bound, upper_bound) <=> less_than_or_equal(lower_bound, upper_bound)),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(33,axiom,(less_than_or_equal(lower_bound, upper_bound)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_interval')).
% 2.44/2.59 tff(34,plain,
% 2.44/2.59 (less_than_or_equal(lower_bound, upper_bound)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[33, 32])).
% 2.44/2.59 tff(35,plain,
% 2.44/2.59 (^[X: $i] : refl((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(36,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))) <=> ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[35])).
% 2.44/2.59 tff(37,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0))) <=> ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(38,plain,
% 2.44/2.59 (^[X: $i] : trans(monotonicity(rewrite((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)))), (((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> ((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))))), rewrite(((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))), (((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(39,plain,
% 2.44/2.59 (![X: $i] : ((less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound))) | (~less_than_or_equal(f(X), n0))) <=> ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[38])).
% 2.44/2.59 tff(40,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')).
% 2.44/2.59 tff(41,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.44/2.59 tff(42,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[41, 37])).
% 2.44/2.59 tff(43,plain,(
% 2.44/2.59 ![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(skolemize,[status(sab)],[42])).
% 2.44/2.59 tff(44,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[43, 36])).
% 2.44/2.59 tff(45,plain,
% 2.44/2.59 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(46,plain,
% 2.44/2.59 ((less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0))) <=> ((~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(47,plain,
% 2.44/2.59 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0))))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[46])).
% 2.44/2.59 tff(48,plain,
% 2.44/2.59 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0)))),
% 2.44/2.59 inference(transitivity,[status(thm)],[47, 45])).
% 2.44/2.59 tff(49,plain,
% 2.44/2.59 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(lower_bound, l) | (~less_than_or_equal(lower_bound, upper_bound)) | (~less_than_or_equal(f(lower_bound), n0)))),
% 2.44/2.59 inference(quant_inst,[status(thm)],[])).
% 2.44/2.59 tff(50,plain,
% 2.44/2.59 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(lower_bound, upper_bound)) | less_than_or_equal(lower_bound, l) | (~less_than_or_equal(f(lower_bound), n0))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[49, 48])).
% 2.44/2.59 tff(51,plain,
% 2.44/2.59 (less_than_or_equal(lower_bound, l)),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[50, 44, 34, 31])).
% 2.44/2.59 tff(52,plain,
% 2.44/2.59 (^[X: $i] : refl(((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(53,plain,
% 2.44/2.59 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[52])).
% 2.44/2.59 tff(54,plain,
% 2.44/2.59 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(55,plain,
% 2.44/2.59 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) <=> ((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) <=> (((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(lower_bound, X))))), rewrite((((~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0)) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(56,plain,
% 2.44/2.59 (![X: $i] : (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[55])).
% 2.44/2.59 tff(57,axiom,(![X: $i] : (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(X, h(X)))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity1')).
% 2.44/2.59 tff(58,plain,
% 2.44/2.59 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[57, 56])).
% 2.44/2.59 tff(59,plain,
% 2.44/2.59 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[58, 54])).
% 2.44/2.59 tff(60,plain,(
% 2.44/2.59 ![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 2.44/2.59 inference(skolemize,[status(sab)],[59])).
% 2.44/2.59 tff(61,plain,
% 2.44/2.59 (![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[60, 53])).
% 2.44/2.59 tff(62,plain,
% 2.44/2.59 (((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))) <=> ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(63,plain,
% 2.44/2.59 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0))),
% 2.44/2.59 inference(quant_inst,[status(thm)],[])).
% 2.44/2.59 tff(64,plain,
% 2.44/2.59 ((~![X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | (~less_than_or_equal(X, h(X))) | less_than_or_equal(f(X), n0))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.44/2.59 tff(65,plain,
% 2.44/2.59 ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[64, 61, 51])).
% 2.44/2.59 tff(66,plain,
% 2.44/2.59 ((~less_than_or_equal(l, h(l))) | less_than_or_equal(f(l), n0)),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[65, 28])).
% 2.44/2.59 tff(67,plain,
% 2.44/2.59 (~less_than_or_equal(l, h(l))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[66, 1])).
% 2.44/2.59 tff(68,plain,
% 2.44/2.59 (^[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)))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(69,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[68])).
% 2.44/2.59 tff(70,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(71,plain,
% 2.44/2.59 (^[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)))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(72,plain,
% 2.44/2.59 (![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))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[71])).
% 2.44/2.59 tff(73,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')).
% 2.44/2.59 tff(74,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.44/2.59 tff(75,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[74, 70])).
% 2.44/2.59 tff(76,plain,(
% 2.44/2.59 ![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 2.44/2.59 inference(skolemize,[status(sab)],[75])).
% 2.44/2.59 tff(77,plain,
% 2.44/2.59 (![X: $i] : (less_than_or_equal(l, X) | less_than_or_equal(f(g(X)), n0))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[76, 69])).
% 2.44/2.59 tff(78,plain,
% 2.44/2.59 (((~![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))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(79,plain,
% 2.44/2.59 ((~![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))),
% 2.44/2.59 inference(quant_inst,[status(thm)],[])).
% 2.44/2.59 tff(80,plain,
% 2.44/2.59 ((~![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)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.44/2.59 tff(81,plain,
% 2.44/2.59 (less_than_or_equal(f(g(h(l))), n0)),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[80, 77, 67])).
% 2.44/2.59 tff(82,plain,
% 2.44/2.59 (((~![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)))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(83,plain,
% 2.44/2.59 ((~![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)))),
% 2.44/2.59 inference(quant_inst,[status(thm)],[])).
% 2.44/2.59 tff(84,plain,
% 2.44/2.59 ((~![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))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.44/2.59 tff(85,plain,
% 2.44/2.59 (~less_than_or_equal(g(h(l)), h(l))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[84, 9, 67])).
% 2.44/2.59 tff(86,plain,
% 2.44/2.59 (^[Y: $i, X: $i] : refl(((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(87,plain,
% 2.44/2.59 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[86])).
% 2.44/2.59 tff(88,plain,
% 2.44/2.59 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 2.44/2.59 inference(rewrite,[status(thm)],[])).
% 2.44/2.59 tff(89,plain,
% 2.44/2.59 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) <=> (less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X)))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) <=> ((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))))), rewrite(((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) <=> (less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), (((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) <=> (less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) <=> ((less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | less_than_or_equal(Y, h(X))))), rewrite(((less_than_or_equal(f(X), n0) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | less_than_or_equal(Y, h(X))) <=> (less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), ((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) <=> (less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))), (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) <=> ((less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(lower_bound, X))))), rewrite(((less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))))), ((((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))), ((((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))))),
% 2.44/2.59 inference(bind,[status(th)],[])).
% 2.44/2.59 tff(90,plain,
% 2.44/2.59 (![Y: $i, X: $i] : (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 2.44/2.59 inference(quant_intro,[status(thm)],[89])).
% 2.44/2.59 tff(91,axiom,(![Y: $i, X: $i] : (((((less_than_or_equal(f(X), n0) | (~less_than_or_equal(Y, X))) | (~less_than_or_equal(f(Y), n0))) | less_than_or_equal(Y, h(X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity2')).
% 2.44/2.60 tff(92,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[91, 90])).
% 2.44/2.60 tff(93,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[92, 88])).
% 2.44/2.60 tff(94,plain,(
% 2.44/2.60 ![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 2.44/2.60 inference(skolemize,[status(sab)],[93])).
% 2.44/2.60 tff(95,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[94, 87])).
% 2.44/2.60 tff(96,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(97,plain,
% 2.44/2.60 (((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l))) <=> (less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(98,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | (less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[97])).
% 2.44/2.60 tff(99,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[98, 96])).
% 2.44/2.60 tff(100,plain,
% 2.44/2.60 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(f(l), n0) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l)))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(101,plain,
% 2.44/2.60 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(f(X), n0) | less_than_or_equal(Y, h(X)) | (~less_than_or_equal(f(Y), n0)) | (~less_than_or_equal(Y, X)))) | less_than_or_equal(f(l), n0) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(g(h(l)), h(l)) | (~less_than_or_equal(f(g(h(l))), n0)) | (~less_than_or_equal(g(h(l)), l))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[100, 99])).
% 2.44/2.60 tff(102,plain,
% 2.44/2.60 (~less_than_or_equal(g(h(l)), l)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[101, 95, 1, 51, 28, 85, 81])).
% 2.44/2.60 tff(103,plain,
% 2.44/2.60 (((~![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))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(104,plain,
% 2.44/2.60 ((~![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))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(105,plain,
% 2.44/2.60 ((~![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)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.44/2.60 tff(106,plain,
% 2.44/2.60 (less_than_or_equal(g(h(l)), upper_bound)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[105, 23, 67])).
% 2.44/2.60 tff(107,plain,
% 2.44/2.60 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(108,plain,
% 2.44/2.60 ((less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0))) <=> ((~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(109,plain,
% 2.44/2.60 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | ((~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[108])).
% 2.44/2.60 tff(110,plain,
% 2.44/2.60 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[109, 107])).
% 2.44/2.60 tff(111,plain,
% 2.44/2.60 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound)) | (~less_than_or_equal(f(g(h(l))), n0)))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(112,plain,
% 2.44/2.60 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (~less_than_or_equal(f(g(h(l))), n0)) | less_than_or_equal(g(h(l)), l) | (~less_than_or_equal(g(h(l)), upper_bound))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[111, 110])).
% 2.44/2.60 tff(113,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[112, 44, 106, 81, 102])).
% 2.44/2.60 tff(114,plain,(less_than_or_equal(f(l), n0)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(115,plain,
% 2.44/2.60 (((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))) <=> ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(116,axiom,((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_there_is_x_which_crosses')).
% 2.44/2.60 tff(117,plain,
% 2.44/2.60 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[116, 115])).
% 2.44/2.60 tff(118,plain,
% 2.44/2.60 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[117, 115])).
% 2.44/2.60 tff(119,plain,
% 2.44/2.60 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[118, 115])).
% 2.44/2.60 tff(120,plain,
% 2.44/2.60 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[119, 115])).
% 2.44/2.60 tff(121,plain,
% 2.44/2.60 ((~less_than_or_equal(f(l), n0)) | (~less_than_or_equal(n0, f(l)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[120, 115])).
% 2.44/2.60 tff(122,plain,
% 2.44/2.60 (~less_than_or_equal(n0, f(l))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[121, 114])).
% 2.44/2.60 tff(123,plain,
% 2.44/2.60 (^[X: $i] : refl(((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(124,plain,
% 2.44/2.60 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) <=> ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[123])).
% 2.44/2.60 tff(125,plain,
% 2.44/2.60 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) <=> ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(126,plain,
% 2.44/2.60 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) <=> ((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X)))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) <=> (((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(lower_bound, X))))), rewrite((((~less_than_or_equal(k(X), X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(127,plain,
% 2.44/2.60 (![X: $i] : (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[126])).
% 2.44/2.60 tff(128,axiom,(![X: $i] : (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(k(X), X))) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity3')).
% 2.44/2.60 tff(129,plain,
% 2.44/2.60 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[128, 127])).
% 2.44/2.60 tff(130,plain,
% 2.44/2.60 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[129, 125])).
% 2.44/2.60 tff(131,plain,(
% 2.44/2.60 ![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 2.44/2.60 inference(skolemize,[status(sab)],[130])).
% 2.44/2.60 tff(132,plain,
% 2.44/2.60 (![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[131, 124])).
% 2.44/2.60 tff(133,plain,
% 2.44/2.60 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(134,plain,
% 2.44/2.60 (((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l))) <=> (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(135,plain,
% 2.44/2.60 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[134])).
% 2.44/2.60 tff(136,plain,
% 2.44/2.60 (((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)))) <=> ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[135, 133])).
% 2.44/2.60 tff(137,plain,
% 2.44/2.60 ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | ((~less_than_or_equal(k(l), l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(138,plain,
% 2.44/2.60 ((~![X: $i] : ((~less_than_or_equal(k(X), X)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(k(l), l))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[137, 136])).
% 2.44/2.60 tff(139,plain,
% 2.44/2.60 (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(k(l), l))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[138, 132, 51])).
% 2.44/2.60 tff(140,plain,
% 2.44/2.60 (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(k(l), l))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[139, 28])).
% 2.44/2.60 tff(141,plain,
% 2.44/2.60 (~less_than_or_equal(k(l), l)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[140, 122])).
% 2.44/2.60 tff(142,plain,
% 2.44/2.60 (^[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)))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(143,plain,
% 2.44/2.60 (![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))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[142])).
% 2.44/2.60 tff(144,plain,
% 2.44/2.60 (![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))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(145,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')).
% 2.44/2.60 tff(146,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[145, 144])).
% 2.44/2.60 tff(147,plain,(
% 2.44/2.60 ![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 2.44/2.60 inference(skolemize,[status(sab)],[146])).
% 2.44/2.60 tff(148,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[147, 143])).
% 2.44/2.60 tff(149,plain,
% 2.44/2.60 (((~![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(l, k(l)))) | less_than_or_equal(k(l), l))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, q(Y, X))) | less_than_or_equal(X, Y))) | (~less_than_or_equal(k(l), q(l, k(l)))) | less_than_or_equal(k(l), l))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(150,plain,
% 2.44/2.60 ((~![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(l, k(l)))) | less_than_or_equal(k(l), l))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(151,plain,
% 2.44/2.60 ((~![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(l, k(l)))) | less_than_or_equal(k(l), l)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.44/2.60 tff(152,plain,
% 2.44/2.60 (~less_than_or_equal(k(l), q(l, k(l)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[151, 148, 141])).
% 2.44/2.60 tff(153,plain,
% 2.44/2.60 (^[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)))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(154,plain,
% 2.44/2.60 (![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))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[153])).
% 2.44/2.60 tff(155,plain,
% 2.44/2.60 (![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))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(156,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')).
% 2.44/2.60 tff(157,plain,
% 2.44/2.60 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[156, 155])).
% 2.44/2.60 tff(158,plain,(
% 2.44/2.60 ![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 2.44/2.60 inference(skolemize,[status(sab)],[157])).
% 2.44/2.60 tff(159,plain,
% 2.44/2.60 (![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[158, 154])).
% 2.44/2.60 tff(160,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(k(l), q(l, k(l))) | less_than_or_equal(q(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(l, k(l))) | less_than_or_equal(q(l, k(l)), k(l)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(161,plain,
% 2.44/2.60 ((less_than_or_equal(q(l, k(l)), k(l)) | less_than_or_equal(k(l), q(l, k(l)))) <=> (less_than_or_equal(k(l), q(l, k(l))) | less_than_or_equal(q(l, k(l)), k(l)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(162,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(l, k(l)), k(l)) | less_than_or_equal(k(l), q(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(l, k(l))) | less_than_or_equal(q(l, k(l)), k(l))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[161])).
% 2.44/2.60 tff(163,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(l, k(l)), k(l)) | less_than_or_equal(k(l), q(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(l, k(l))) | less_than_or_equal(q(l, k(l)), k(l)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[162, 160])).
% 2.44/2.60 tff(164,plain,
% 2.44/2.60 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(q(l, k(l)), k(l)) | less_than_or_equal(k(l), q(l, k(l))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(165,plain,
% 2.44/2.60 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(k(l), q(l, k(l))) | less_than_or_equal(q(l, k(l)), k(l))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[164, 163])).
% 2.44/2.60 tff(166,plain,
% 2.44/2.60 (less_than_or_equal(q(l, k(l)), k(l))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[165, 159, 152])).
% 2.44/2.60 tff(167,assumption,(~less_than_or_equal(k(l), upper_bound)), introduced(assumption)).
% 2.44/2.60 tff(168,plain,
% 2.44/2.60 (less_than_or_equal(n0, f(upper_bound)) <=> less_than_or_equal(n0, f(upper_bound))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(169,axiom,(less_than_or_equal(n0, f(upper_bound))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','upper_mapping')).
% 2.44/2.60 tff(170,plain,
% 2.44/2.60 (less_than_or_equal(n0, f(upper_bound))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[169, 168])).
% 2.44/2.60 tff(171,plain,
% 2.44/2.60 (^[Y: $i, X: $i] : refl(((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(172,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[171])).
% 2.44/2.60 tff(173,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(174,plain,
% 2.44/2.60 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(n0, f(Y)))))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X))) | (~less_than_or_equal(n0, f(Y)))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y))))), (((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y)))))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))), ((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))))), (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(lower_bound, X))))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))), (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))))), ((((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> (((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(X, upper_bound))))), rewrite((((~less_than_or_equal(X, Y)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y)))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))), ((((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(175,plain,
% 2.44/2.60 (![Y: $i, X: $i] : (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound))) <=> ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[174])).
% 2.44/2.60 tff(176,axiom,(![Y: $i, X: $i] : (((((less_than_or_equal(n0, f(X)) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(n0, f(Y)))) | less_than_or_equal(k(X), Y)) | (~less_than_or_equal(lower_bound, X))) | (~less_than_or_equal(X, upper_bound)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','continuity4')).
% 2.44/2.60 tff(177,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[176, 175])).
% 2.44/2.60 tff(178,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[177, 173])).
% 2.44/2.60 tff(179,plain,(
% 2.44/2.60 ![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 2.44/2.60 inference(skolemize,[status(sab)],[178])).
% 2.44/2.60 tff(180,plain,
% 2.44/2.60 (![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[179, 172])).
% 2.44/2.60 tff(181,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(182,plain,
% 2.44/2.60 (((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound)))) <=> (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(183,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[182])).
% 2.44/2.60 tff(184,plain,
% 2.44/2.60 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound))),
% 2.44/2.60 inference(transitivity,[status(thm)],[183, 181])).
% 2.44/2.60 tff(185,plain,
% 2.44/2.60 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), upper_bound) | (~less_than_or_equal(n0, f(upper_bound))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(186,plain,
% 2.44/2.60 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(n0, f(upper_bound))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(k(l), upper_bound)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[185, 184])).
% 2.44/2.60 tff(187,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[186, 180, 170, 122, 51, 28, 167])).
% 2.44/2.61 tff(188,plain,(less_than_or_equal(k(l), upper_bound)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(189,plain,
% 2.44/2.61 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(190,plain,
% 2.44/2.61 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(191,plain,
% 2.44/2.61 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) <=> ((~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))), (((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> (((~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) | (~less_than_or_equal(Y, Z))))), rewrite((((~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z)) | (~less_than_or_equal(Y, Z))) <=> ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))), (((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(192,plain,
% 2.44/2.61 (![Z: $i, Y: $i, X: $i] : ((less_than_or_equal(X, Z) | (~less_than_or_equal(X, Y))) | (~less_than_or_equal(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[191])).
% 2.44/2.61 tff(193,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')).
% 2.44/2.61 tff(194,plain,
% 2.44/2.61 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[193, 192])).
% 2.44/2.61 tff(195,plain,
% 2.44/2.61 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[194, 190])).
% 2.44/2.61 tff(196,plain,(
% 2.44/2.61 ![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 2.44/2.61 inference(skolemize,[status(sab)],[195])).
% 2.44/2.61 tff(197,plain,
% 2.44/2.61 (![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[196, 189])).
% 2.44/2.61 tff(198,plain,
% 2.44/2.61 (((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(q(l, k(l)), k(l))) | less_than_or_equal(q(l, k(l)), upper_bound))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(q(l, k(l)), k(l))) | less_than_or_equal(q(l, k(l)), upper_bound))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(199,plain,
% 2.44/2.61 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | ((~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(q(l, k(l)), k(l))) | less_than_or_equal(q(l, k(l)), upper_bound))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(200,plain,
% 2.44/2.61 ((~![Z: $i, Y: $i, X: $i] : ((~less_than_or_equal(Y, Z)) | (~less_than_or_equal(X, Y)) | less_than_or_equal(X, Z))) | (~less_than_or_equal(k(l), upper_bound)) | (~less_than_or_equal(q(l, k(l)), k(l))) | less_than_or_equal(q(l, k(l)), upper_bound)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[199, 198])).
% 2.44/2.61 tff(201,plain,
% 2.44/2.61 (less_than_or_equal(q(l, k(l)), upper_bound)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[200, 197, 188, 166])).
% 2.44/2.61 tff(202,plain,
% 2.44/2.61 (^[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)))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(203,plain,
% 2.44/2.61 (![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))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[202])).
% 2.44/2.61 tff(204,plain,
% 2.44/2.61 (![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))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(205,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')).
% 2.44/2.61 tff(206,plain,
% 2.44/2.61 (![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.44/2.61 tff(207,plain,(
% 2.44/2.61 ![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
% 2.44/2.61 inference(skolemize,[status(sab)],[206])).
% 2.44/2.61 tff(208,plain,
% 2.44/2.61 (![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[207, 203])).
% 2.44/2.61 tff(209,plain,
% 2.44/2.61 (((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | ((~less_than_or_equal(q(l, k(l)), l)) | less_than_or_equal(k(l), l))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | (~less_than_or_equal(q(l, k(l)), l)) | less_than_or_equal(k(l), l))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(210,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | ((~less_than_or_equal(q(l, k(l)), l)) | less_than_or_equal(k(l), l))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(211,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : ((~less_than_or_equal(q(X, Y), X)) | less_than_or_equal(Y, X))) | (~less_than_or_equal(q(l, k(l)), l)) | less_than_or_equal(k(l), l)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[210, 209])).
% 2.44/2.61 tff(212,plain,
% 2.44/2.61 (~less_than_or_equal(q(l, k(l)), l)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[211, 208, 141])).
% 2.44/2.61 tff(213,plain,
% 2.44/2.61 (((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(q(l, k(l)), l) | (~less_than_or_equal(q(l, k(l)), upper_bound)) | (~less_than_or_equal(f(q(l, k(l))), n0)))) <=> ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | less_than_or_equal(q(l, k(l)), l) | (~less_than_or_equal(q(l, k(l)), upper_bound)) | (~less_than_or_equal(f(q(l, k(l))), n0)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(214,plain,
% 2.44/2.61 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | (less_than_or_equal(q(l, k(l)), l) | (~less_than_or_equal(q(l, k(l)), upper_bound)) | (~less_than_or_equal(f(q(l, k(l))), n0)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(215,plain,
% 2.44/2.61 ((~![X: $i] : (less_than_or_equal(X, l) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(f(X), n0)))) | less_than_or_equal(q(l, k(l)), l) | (~less_than_or_equal(q(l, k(l)), upper_bound)) | (~less_than_or_equal(f(q(l, k(l))), n0))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[214, 213])).
% 2.44/2.61 tff(216,plain,
% 2.44/2.61 (~less_than_or_equal(f(q(l, k(l))), n0)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[215, 44, 212, 201])).
% 2.44/2.61 tff(217,plain,
% 2.44/2.61 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(l, q(l, k(l))) | less_than_or_equal(q(l, k(l)), l))) <=> ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(l, q(l, k(l))) | less_than_or_equal(q(l, k(l)), l))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(218,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(l, q(l, k(l))) | less_than_or_equal(q(l, k(l)), l))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(219,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(l, q(l, k(l))) | less_than_or_equal(q(l, k(l)), l)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[218, 217])).
% 2.44/2.61 tff(220,plain,
% 2.44/2.61 (less_than_or_equal(l, q(l, k(l)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[219, 159, 212])).
% 2.44/2.61 tff(221,plain,
% 2.44/2.61 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, q(l, k(l)))) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, q(l, k(l)))) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(222,plain,
% 2.44/2.61 (((~less_than_or_equal(l, q(l, k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l)))))) <=> (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, q(l, k(l)))) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(223,plain,
% 2.44/2.61 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, q(l, k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | (less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, q(l, k(l)))) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[222])).
% 2.44/2.61 tff(224,plain,
% 2.44/2.61 (((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, q(l, k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l))))))) <=> ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, q(l, k(l)))) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[223, 221])).
% 2.44/2.61 tff(225,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | ((~less_than_or_equal(l, q(l, k(l)))) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | less_than_or_equal(n0, f(l)) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(226,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : ((~less_than_or_equal(X, Y)) | (~less_than_or_equal(X, upper_bound)) | (~less_than_or_equal(lower_bound, X)) | less_than_or_equal(n0, f(X)) | less_than_or_equal(k(X), Y) | (~less_than_or_equal(n0, f(Y))))) | less_than_or_equal(n0, f(l)) | (~less_than_or_equal(l, upper_bound)) | (~less_than_or_equal(lower_bound, l)) | (~less_than_or_equal(l, q(l, k(l)))) | less_than_or_equal(k(l), q(l, k(l))) | (~less_than_or_equal(n0, f(q(l, k(l)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[225, 224])).
% 2.44/2.61 tff(227,plain,
% 2.44/2.61 ((~less_than_or_equal(l, q(l, k(l)))) | (~less_than_or_equal(n0, f(q(l, k(l)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[226, 180, 122, 51, 28, 152])).
% 2.44/2.61 tff(228,plain,
% 2.44/2.61 (~less_than_or_equal(n0, f(q(l, k(l))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[227, 220])).
% 2.44/2.61 tff(229,plain,
% 2.44/2.61 (((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(q(l, k(l)))) | less_than_or_equal(f(q(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(l, k(l)))) | less_than_or_equal(f(q(l, k(l))), n0))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(230,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | (less_than_or_equal(n0, f(q(l, k(l)))) | less_than_or_equal(f(q(l, k(l))), n0))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(231,plain,
% 2.44/2.61 ((~![Y: $i, X: $i] : (less_than_or_equal(X, Y) | less_than_or_equal(Y, X))) | less_than_or_equal(n0, f(q(l, k(l)))) | less_than_or_equal(f(q(l, k(l))), n0)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[230, 229])).
% 2.44/2.61 tff(232,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[231, 159, 228, 216])).
% 2.44/2.61 % SZS output end Proof
% 2.44/2.61 % E exiting
%------------------------------------------------------------------------------