%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV019-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:31:21 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV019-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 09:21:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Unsatisfiable
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(less_than_type, type, (
% 0.13/0.37 less_than: ( $i * $i ) > $o)).
% 0.13/0.37 tff(successor_type, type, (
% 0.13/0.37 successor: $i > $i)).
% 0.13/0.37 tff(an_index_type, type, (
% 0.13/0.37 an_index: $i)).
% 0.13/0.37 tff(upper_bound_type, type, (
% 0.13/0.37 upper_bound: $i)).
% 0.13/0.37 tff(lower_bound_type, type, (
% 0.13/0.37 lower_bound: $i)).
% 0.13/0.37 tff(index_of_maximal_type, type, (
% 0.13/0.37 index_of_maximal: $i)).
% 0.13/0.37 tff(array_value_at_type, type, (
% 0.13/0.37 array_value_at: ( $i * $i ) > $i)).
% 0.13/0.37 tff(array_type, type, (
% 0.13/0.37 array: $i)).
% 0.13/0.37 tff(maximal_value_type, type, (
% 0.13/0.37 maximal_value: $i)).
% 0.13/0.37 tff(in_array_bounds_type, type, (
% 0.13/0.37 in_array_bounds: ( $i * $i ) > $o)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 (^[X: $i] : refl(less_than(X, successor(X)) <=> less_than(X, successor(X)))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 (![X: $i] : less_than(X, successor(X)) <=> ![X: $i] : less_than(X, successor(X))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.37 tff(3,plain,
% 0.13/0.37 (![X: $i] : less_than(X, successor(X)) <=> ![X: $i] : less_than(X, successor(X))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(4,axiom,(![X: $i] : less_than(X, successor(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_greater')).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (![X: $i] : less_than(X, successor(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.37 tff(6,plain,(
% 0.13/0.37 ![X: $i] : less_than(X, successor(X))),
% 0.13/0.37 inference(skolemize,[status(sab)],[5])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (![X: $i] : less_than(X, successor(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 ((~![X: $i] : less_than(X, successor(X))) | less_than(an_index, successor(an_index))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(9,plain,
% 0.13/0.37 (less_than(an_index, successor(an_index))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.37 tff(10,assumption,(~less_than(index_of_maximal, successor(an_index))), introduced(assumption)).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 (less_than(index_of_maximal, an_index) <=> less_than(index_of_maximal, an_index)),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(12,axiom,(less_than(index_of_maximal, an_index)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','maximal_before_somewhere')).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (less_than(index_of_maximal, an_index)),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 (^[Z: $i, Y: $i, X: $i] : rewrite((((~less_than(X, Y)) | (~less_than(Y, Z))) | less_than(X, Z)) <=> (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(17,plain,
% 0.13/0.37 (![Z: $i, Y: $i, X: $i] : (((~less_than(X, Y)) | (~less_than(Y, Z))) | less_than(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.37 tff(18,axiom,(![Z: $i, Y: $i, X: $i] : (((~less_than(X, Y)) | (~less_than(Y, Z))) | less_than(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity_of_less')).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.13/0.37 tff(21,plain,(
% 0.13/0.37 ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 0.13/0.37 inference(skolemize,[status(sab)],[20])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.37 tff(23,plain,
% 0.13/0.37 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(index_of_maximal, successor(an_index)) | (~less_than(an_index, successor(an_index))) | (~less_than(index_of_maximal, an_index)))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | less_than(index_of_maximal, successor(an_index)) | (~less_than(an_index, successor(an_index))) | (~less_than(index_of_maximal, an_index)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(24,plain,
% 0.13/0.37 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(index_of_maximal, successor(an_index)) | (~less_than(an_index, successor(an_index))) | (~less_than(index_of_maximal, an_index)))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | less_than(index_of_maximal, successor(an_index)) | (~less_than(an_index, successor(an_index))) | (~less_than(index_of_maximal, an_index))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.37 tff(26,plain,
% 0.13/0.37 ($false),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[25, 22, 13, 10, 9])).
% 0.13/0.37 tff(27,plain,(less_than(index_of_maximal, successor(an_index))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.37 tff(28,assumption,(less_than(successor(an_index), lower_bound)), introduced(assumption)).
% 0.13/0.37 tff(29,plain,
% 0.13/0.37 ((~less_than(index_of_maximal, lower_bound)) <=> (~less_than(index_of_maximal, lower_bound))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(30,axiom,(~less_than(index_of_maximal, lower_bound)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','maximal_above_lower_bound')).
% 0.13/0.37 tff(31,plain,
% 0.13/0.37 (~less_than(index_of_maximal, lower_bound)),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.37 tff(32,plain,
% 0.13/0.37 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(index_of_maximal, lower_bound) | (~less_than(index_of_maximal, successor(an_index))) | (~less_than(successor(an_index), lower_bound)))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | less_than(index_of_maximal, lower_bound) | (~less_than(index_of_maximal, successor(an_index))) | (~less_than(successor(an_index), lower_bound)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(33,plain,
% 0.13/0.37 ((less_than(index_of_maximal, lower_bound) | (~less_than(successor(an_index), lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) <=> (less_than(index_of_maximal, lower_bound) | (~less_than(index_of_maximal, successor(an_index))) | (~less_than(successor(an_index), lower_bound)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(34,plain,
% 0.13/0.37 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(index_of_maximal, lower_bound) | (~less_than(successor(an_index), lower_bound)) | (~less_than(index_of_maximal, successor(an_index))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(index_of_maximal, lower_bound) | (~less_than(index_of_maximal, successor(an_index))) | (~less_than(successor(an_index), lower_bound))))),
% 0.13/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.13/0.37 tff(35,plain,
% 0.13/0.37 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(index_of_maximal, lower_bound) | (~less_than(successor(an_index), lower_bound)) | (~less_than(index_of_maximal, successor(an_index))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | less_than(index_of_maximal, lower_bound) | (~less_than(index_of_maximal, successor(an_index))) | (~less_than(successor(an_index), lower_bound)))),
% 0.13/0.37 inference(transitivity,[status(thm)],[34, 32])).
% 0.13/0.37 tff(36,plain,
% 0.13/0.37 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(index_of_maximal, lower_bound) | (~less_than(successor(an_index), lower_bound)) | (~less_than(index_of_maximal, successor(an_index))))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(37,plain,
% 0.13/0.37 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | less_than(index_of_maximal, lower_bound) | (~less_than(index_of_maximal, successor(an_index))) | (~less_than(successor(an_index), lower_bound))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[37, 22, 31, 28, 27])).
% 0.13/0.38 tff(39,plain,(~less_than(successor(an_index), lower_bound)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(40,assumption,(less_than(upper_bound, index_of_maximal)), introduced(assumption)).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 ((~less_than(upper_bound, an_index)) <=> (~less_than(upper_bound, an_index))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(42,axiom,(~less_than(upper_bound, an_index)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','somewhere_below_upper_bound')).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (~less_than(upper_bound, an_index)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(upper_bound, an_index) | (~less_than(index_of_maximal, an_index)) | (~less_than(upper_bound, index_of_maximal)))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | less_than(upper_bound, an_index) | (~less_than(index_of_maximal, an_index)) | (~less_than(upper_bound, index_of_maximal)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(upper_bound, an_index) | (~less_than(index_of_maximal, an_index)) | (~less_than(upper_bound, index_of_maximal)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | less_than(upper_bound, an_index) | (~less_than(index_of_maximal, an_index)) | (~less_than(upper_bound, index_of_maximal))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[46, 22, 13, 43, 40])).
% 0.13/0.38 tff(48,plain,(~less_than(upper_bound, index_of_maximal)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 (^[X1: $i] : refl((in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound)) <=> (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(50,plain,
% 0.13/0.38 (![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound)) <=> ![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.38 tff(51,plain,
% 0.13/0.38 (![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound)) <=> ![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(52,plain,
% 0.13/0.38 (^[X1: $i] : trans(monotonicity(rewrite((less_than(X1, lower_bound) | less_than(upper_bound, X1)) <=> (less_than(upper_bound, X1) | less_than(X1, lower_bound))), (((less_than(X1, lower_bound) | less_than(upper_bound, X1)) | in_array_bounds(array, X1)) <=> ((less_than(upper_bound, X1) | less_than(X1, lower_bound)) | in_array_bounds(array, X1)))), rewrite(((less_than(upper_bound, X1) | less_than(X1, lower_bound)) | in_array_bounds(array, X1)) <=> (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))), (((less_than(X1, lower_bound) | less_than(upper_bound, X1)) | in_array_bounds(array, X1)) <=> (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(53,plain,
% 0.13/0.38 (![X1: $i] : ((less_than(X1, lower_bound) | less_than(upper_bound, X1)) | in_array_bounds(array, X1)) <=> ![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.13/0.38 tff(54,axiom,(![X1: $i] : ((less_than(X1, lower_bound) | less_than(upper_bound, X1)) | in_array_bounds(array, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','in_bounds')).
% 0.21/0.38 tff(55,plain,
% 0.21/0.38 (![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.38 tff(56,plain,
% 0.21/0.38 (![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.38 tff(57,plain,(
% 0.21/0.38 ![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))),
% 0.21/0.38 inference(skolemize,[status(sab)],[56])).
% 0.21/0.38 tff(58,plain,
% 0.21/0.38 (![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.21/0.38 tff(59,plain,
% 0.21/0.38 (((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, index_of_maximal) | less_than(index_of_maximal, lower_bound) | less_than(upper_bound, index_of_maximal))) <=> ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | in_array_bounds(array, index_of_maximal) | less_than(index_of_maximal, lower_bound) | less_than(upper_bound, index_of_maximal))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(60,plain,
% 0.21/0.38 ((in_array_bounds(array, index_of_maximal) | less_than(upper_bound, index_of_maximal) | less_than(index_of_maximal, lower_bound)) <=> (in_array_bounds(array, index_of_maximal) | less_than(index_of_maximal, lower_bound) | less_than(upper_bound, index_of_maximal))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(61,plain,
% 0.21/0.38 (((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, index_of_maximal) | less_than(upper_bound, index_of_maximal) | less_than(index_of_maximal, lower_bound))) <=> ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, index_of_maximal) | less_than(index_of_maximal, lower_bound) | less_than(upper_bound, index_of_maximal)))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.38 tff(62,plain,
% 0.21/0.38 (((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, index_of_maximal) | less_than(upper_bound, index_of_maximal) | less_than(index_of_maximal, lower_bound))) <=> ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | in_array_bounds(array, index_of_maximal) | less_than(index_of_maximal, lower_bound) | less_than(upper_bound, index_of_maximal))),
% 0.21/0.38 inference(transitivity,[status(thm)],[61, 59])).
% 0.21/0.38 tff(63,plain,
% 0.21/0.38 ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, index_of_maximal) | less_than(upper_bound, index_of_maximal) | less_than(index_of_maximal, lower_bound))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(64,plain,
% 0.21/0.38 ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | in_array_bounds(array, index_of_maximal) | less_than(index_of_maximal, lower_bound) | less_than(upper_bound, index_of_maximal)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.38 tff(65,plain,
% 0.21/0.38 (in_array_bounds(array, index_of_maximal) | less_than(upper_bound, index_of_maximal)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[64, 58, 31])).
% 0.21/0.38 tff(66,plain,
% 0.21/0.38 (in_array_bounds(array, index_of_maximal)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[65, 48])).
% 0.21/0.38 tff(67,plain,
% 0.21/0.38 (((~in_array_bounds(array, index_of_maximal)) | (maximal_value = array_value_at(array, index_of_maximal))) <=> ((~in_array_bounds(array, index_of_maximal)) | (maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(68,axiom,((~in_array_bounds(array, index_of_maximal)) | (maximal_value = array_value_at(array, index_of_maximal))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','this_is_maximal')).
% 0.21/0.38 tff(69,plain,
% 0.21/0.38 ((~in_array_bounds(array, index_of_maximal)) | (maximal_value = array_value_at(array, index_of_maximal))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.38 tff(70,plain,
% 0.21/0.38 (maximal_value = array_value_at(array, index_of_maximal)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.21/0.38 tff(71,plain,
% 0.21/0.38 ((~less_than(an_index, lower_bound)) <=> (~less_than(an_index, lower_bound))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(72,axiom,(~less_than(an_index, lower_bound)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','somewhere_above_lower_bound')).
% 0.21/0.38 tff(73,plain,
% 0.21/0.38 (~less_than(an_index, lower_bound)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.38 tff(74,plain,
% 0.21/0.38 (((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (less_than(an_index, lower_bound) | less_than(upper_bound, an_index) | in_array_bounds(array, an_index))) <=> ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | less_than(an_index, lower_bound) | less_than(upper_bound, an_index) | in_array_bounds(array, an_index))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(75,plain,
% 0.21/0.38 ((in_array_bounds(array, an_index) | less_than(upper_bound, an_index) | less_than(an_index, lower_bound)) <=> (less_than(an_index, lower_bound) | less_than(upper_bound, an_index) | in_array_bounds(array, an_index))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(76,plain,
% 0.21/0.38 (((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, an_index) | less_than(upper_bound, an_index) | less_than(an_index, lower_bound))) <=> ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (less_than(an_index, lower_bound) | less_than(upper_bound, an_index) | in_array_bounds(array, an_index)))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.38 tff(77,plain,
% 0.21/0.38 (((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, an_index) | less_than(upper_bound, an_index) | less_than(an_index, lower_bound))) <=> ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | less_than(an_index, lower_bound) | less_than(upper_bound, an_index) | in_array_bounds(array, an_index))),
% 0.21/0.38 inference(transitivity,[status(thm)],[76, 74])).
% 0.21/0.38 tff(78,plain,
% 0.21/0.38 ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | (in_array_bounds(array, an_index) | less_than(upper_bound, an_index) | less_than(an_index, lower_bound))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(79,plain,
% 0.21/0.38 ((~![X1: $i] : (in_array_bounds(array, X1) | less_than(upper_bound, X1) | less_than(X1, lower_bound))) | less_than(an_index, lower_bound) | less_than(upper_bound, an_index) | in_array_bounds(array, an_index)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.38 tff(80,plain,
% 0.21/0.38 (in_array_bounds(array, an_index)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[79, 58, 73, 43])).
% 0.21/0.38 tff(81,plain,
% 0.21/0.38 (((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))) <=> ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(82,plain,
% 0.21/0.38 ((((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index)))) | (~(maximal_value = array_value_at(array, index_of_maximal)))) <=> ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(83,plain,
% 0.21/0.38 (((less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index)))) | (~in_array_bounds(array, index_of_maximal))) <=> ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(84,plain,
% 0.21/0.38 (((less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index))) | (~less_than(index_of_maximal, successor(an_index)))) <=> (less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(85,plain,
% 0.21/0.38 ((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) <=> (less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(86,plain,
% 0.21/0.38 ((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) <=> ((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(87,plain,
% 0.21/0.38 (((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) <=> (((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.38 tff(88,plain,
% 0.21/0.38 (((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) <=> (less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)))),
% 0.21/0.38 inference(transitivity,[status(thm)],[87, 85])).
% 0.21/0.38 tff(89,plain,
% 0.21/0.38 ((((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) <=> ((less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index))) | (~less_than(index_of_maximal, successor(an_index))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.38 tff(90,plain,
% 0.21/0.38 ((((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) <=> (less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[89, 84])).
% 0.21/0.39 tff(91,plain,
% 0.21/0.39 (((((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) | (~in_array_bounds(array, index_of_maximal))) <=> ((less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index)))) | (~in_array_bounds(array, index_of_maximal)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.39 tff(92,plain,
% 0.21/0.39 (((((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) | (~in_array_bounds(array, index_of_maximal))) <=> ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[91, 83])).
% 0.21/0.39 tff(93,plain,
% 0.21/0.39 ((((((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) | (~in_array_bounds(array, index_of_maximal))) | (~(maximal_value = array_value_at(array, index_of_maximal)))) <=> (((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index)))) | (~(maximal_value = array_value_at(array, index_of_maximal))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.39 tff(94,plain,
% 0.21/0.39 ((((((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) | (~in_array_bounds(array, index_of_maximal))) | (~(maximal_value = array_value_at(array, index_of_maximal)))) <=> ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[93, 82])).
% 0.21/0.39 tff(95,axiom,(((((((~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound)) | less_than(successor(upper_bound), successor(an_index))) | less_than(index_of_maximal, lower_bound)) | (~less_than(index_of_maximal, successor(an_index)))) | (~in_array_bounds(array, index_of_maximal))) | (~(maximal_value = array_value_at(array, index_of_maximal)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.39 tff(96,plain,
% 0.21/0.39 ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.39 tff(97,plain,
% 0.21/0.39 ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[96, 81])).
% 0.21/0.39 tff(98,plain,
% 0.21/0.39 ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[97, 81])).
% 0.21/0.39 tff(99,plain,
% 0.21/0.39 ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[98, 81])).
% 0.21/0.39 tff(100,plain,
% 0.21/0.39 ((~in_array_bounds(array, index_of_maximal)) | less_than(index_of_maximal, lower_bound) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[99, 81])).
% 0.21/0.39 tff(101,plain,
% 0.21/0.39 ((~in_array_bounds(array, index_of_maximal)) | (~in_array_bounds(array, an_index)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[100, 31])).
% 0.21/0.39 tff(102,plain,
% 0.21/0.39 ((~in_array_bounds(array, index_of_maximal)) | less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index)) | (~less_than(index_of_maximal, successor(an_index))) | (~(maximal_value = array_value_at(array, index_of_maximal)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[101, 80])).
% 0.21/0.39 tff(103,plain,
% 0.21/0.39 (less_than(successor(an_index), lower_bound) | less_than(successor(upper_bound), successor(an_index))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[102, 66, 70, 27])).
% 0.21/0.39 tff(104,plain,
% 0.21/0.39 (less_than(successor(upper_bound), successor(an_index))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[103, 39])).
% 0.21/0.39 tff(105,plain,
% 0.21/0.39 (^[Y: $i, X: $i] : refl(((~less_than(successor(X), successor(Y))) | less_than(X, Y)) <=> ((~less_than(successor(X), successor(Y))) | less_than(X, Y)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(106,plain,
% 0.21/0.39 (![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y)) <=> ![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.39 tff(107,plain,
% 0.21/0.39 (![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y)) <=> ![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(108,axiom,(![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','predecessor_less')).
% 0.21/0.39 tff(109,plain,
% 0.21/0.39 (![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.39 tff(110,plain,(
% 0.21/0.39 ![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))),
% 0.21/0.39 inference(skolemize,[status(sab)],[109])).
% 0.21/0.39 tff(111,plain,
% 0.21/0.39 (![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.21/0.39 tff(112,plain,
% 0.21/0.39 (((~![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))) | ((~less_than(successor(upper_bound), successor(an_index))) | less_than(upper_bound, an_index))) <=> ((~![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))) | (~less_than(successor(upper_bound), successor(an_index))) | less_than(upper_bound, an_index))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(113,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))) | ((~less_than(successor(upper_bound), successor(an_index))) | less_than(upper_bound, an_index))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(114,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~less_than(successor(X), successor(Y))) | less_than(X, Y))) | (~less_than(successor(upper_bound), successor(an_index))) | less_than(upper_bound, an_index)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.39 tff(115,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[114, 111, 43, 104])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------