TSTP Solution File: SEU244+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU244+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:58:09 EDT 2023
% Result : Theorem 66.84s 46.44s
% Output : CNFRefutation 66.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 220
% Syntax : Number of formulae : 303 ( 33 unt; 212 typ; 0 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 231 ( 113 ~; 94 |; 8 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 408 ( 198 >; 210 *; 0 +; 0 <<)
% Number of predicates : 29 ( 28 usr; 1 prp; 0-2 aty)
% Number of functors : 184 ( 184 usr; 14 con; 0-5 aty)
% Number of variables : 37 (; 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ well_orders > subset > proper_subset > ordinal_subset > is_well_founded_in > is_transitive_in > is_reflexive_in > is_connected_in > is_antisymmetric_in > in > element > disjoint > are_equipotent > well_ordering > well_founded_relation > transitive > relation_empty_yielding > relation > reflexive > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > connected > being_limit_ordinal > antisymmetric > unordered_triple > subset_difference > unordered_pair > union_of_subsets > subset_complement > set_union2 > set_intersection2 > set_difference > relation_rng_restriction > relation_inverse_image > relation_image > relation_dom_restriction > relation_composition > ordered_pair > meet_of_subsets > fiber > complements_of_subsets > cartesian_product2 > apply > #nlpp > union > succ > singleton > set_meet > relation_rng > relation_inverse > relation_field > relation_dom > powerset > identity_relation > function_inverse > cast_to_subset > empty_set > #skF_13 > #skF_118 > #skF_135 > #skF_76 > #skF_104 > #skF_24 > #skF_131 > #skF_37 > #skF_62 > #skF_35 > #skF_114 > #skF_75 > #skF_41 > #skF_73 > #skF_80 > #skF_17 > #skF_130 > #skF_109 > #skF_33 > #skF_148 > #skF_144 > #skF_106 > #skF_91 > #skF_120 > #skF_27 > #skF_93 > #skF_6 > #skF_152 > #skF_30 > #skF_44 > #skF_18 > #skF_47 > #skF_88 > #skF_127 > #skF_56 > #skF_45 > #skF_126 > #skF_63 > #skF_32 > #skF_150 > #skF_67 > #skF_111 > #skF_72 > #skF_140 > #skF_64 > #skF_70 > #skF_66 > #skF_82 > #skF_115 > #skF_99 > #skF_58 > #skF_52 > #skF_92 > #skF_31 > #skF_142 > #skF_128 > #skF_38 > #skF_79 > #skF_12 > #skF_78 > #skF_117 > #skF_3 > #skF_90 > #skF_124 > #skF_69 > #skF_34 > #skF_129 > #skF_77 > #skF_100 > #skF_29 > #skF_143 > #skF_48 > #skF_60 > #skF_85 > #skF_23 > #skF_26 > #skF_110 > #skF_147 > #skF_74 > #skF_5 > #skF_49 > #skF_19 > #skF_122 > #skF_65 > #skF_84 > #skF_97 > #skF_107 > #skF_113 > #skF_108 > #skF_98 > #skF_11 > #skF_36 > #skF_7 > #skF_39 > #skF_138 > #skF_121 > #skF_59 > #skF_9 > #skF_20 > #skF_51 > #skF_96 > #skF_137 > #skF_71 > #skF_86 > #skF_15 > #skF_103 > #skF_133 > #skF_149 > #skF_14 > #skF_28 > #skF_102 > #skF_151 > #skF_46 > #skF_81 > #skF_145 > #skF_95 > #skF_54 > #skF_55 > #skF_94 > #skF_87 > #skF_2 > #skF_57 > #skF_101 > #skF_136 > #skF_134 > #skF_105 > #skF_40 > #skF_83 > #skF_68 > #skF_8 > #skF_25 > #skF_89 > #skF_125 > #skF_43 > #skF_141 > #skF_132 > #skF_42 > #skF_21 > #skF_61 > #skF_50 > #skF_1 > #skF_119 > #skF_22 > #skF_123 > #skF_146 > #skF_139 > #skF_4 > #skF_53 > #skF_16 > #skF_112 > #skF_10 > #skF_116
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(well_ordering,type,
well_ordering: $i > $o ).
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(are_equipotent,type,
are_equipotent: ( $i * $i ) > $o ).
tff('#skF_118',type,
'#skF_118': $i ).
tff('#skF_135',type,
'#skF_135': $i > $i ).
tff('#skF_76',type,
'#skF_76': ( $i * $i ) > $i ).
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_104',type,
'#skF_104': ( $i * $i ) > $i ).
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff('#skF_131',type,
'#skF_131': ( $i * $i * $i ) > $i ).
tff(complements_of_subsets,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i ) > $i ).
tff('#skF_62',type,
'#skF_62': ( $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff('#skF_114',type,
'#skF_114': $i > $i ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_75',type,
'#skF_75': ( $i * $i ) > $i ).
tff(cast_to_subset,type,
cast_to_subset: $i > $i ).
tff(union,type,
union: $i > $i ).
tff('#skF_41',type,
'#skF_41': ( $i * $i ) > $i ).
tff('#skF_73',type,
'#skF_73': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_80',type,
'#skF_80': ( $i * $i ) > $i ).
tff(unordered_triple,type,
unordered_triple: ( $i * $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_130',type,
'#skF_130': $i > $i ).
tff('#skF_109',type,
'#skF_109': $i > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff(connected,type,
connected: $i > $o ).
tff('#skF_148',type,
'#skF_148': ( $i * $i * $i ) > $i ).
tff(relation_inverse,type,
relation_inverse: $i > $i ).
tff('#skF_144',type,
'#skF_144': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_106',type,
'#skF_106': $i > $i ).
tff('#skF_91',type,
'#skF_91': ( $i * $i ) > $i ).
tff('#skF_120',type,
'#skF_120': $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i * $i ) > $i ).
tff('#skF_93',type,
'#skF_93': ( $i * $i ) > $i ).
tff(is_reflexive_in,type,
is_reflexive_in: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_152',type,
'#skF_152': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i ) > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_44',type,
'#skF_44': ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff('#skF_47',type,
'#skF_47': ( $i * $i * $i ) > $i ).
tff('#skF_88',type,
'#skF_88': ( $i * $i ) > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff('#skF_127',type,
'#skF_127': $i ).
tff('#skF_56',type,
'#skF_56': ( $i * $i * $i ) > $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i ) > $i ).
tff('#skF_126',type,
'#skF_126': $i ).
tff('#skF_63',type,
'#skF_63': ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_32',type,
'#skF_32': ( $i * $i ) > $i ).
tff('#skF_150',type,
'#skF_150': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_67',type,
'#skF_67': ( $i * $i * $i ) > $i ).
tff('#skF_111',type,
'#skF_111': $i > $i ).
tff('#skF_72',type,
'#skF_72': ( $i * $i ) > $i ).
tff('#skF_140',type,
'#skF_140': $i > $i ).
tff('#skF_64',type,
'#skF_64': ( $i * $i ) > $i ).
tff(relation_rng_restriction,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff('#skF_70',type,
'#skF_70': ( $i * $i ) > $i ).
tff('#skF_66',type,
'#skF_66': ( $i * $i * $i ) > $i ).
tff('#skF_82',type,
'#skF_82': ( $i * $i ) > $i ).
tff('#skF_115',type,
'#skF_115': ( $i * $i ) > $i ).
tff('#skF_99',type,
'#skF_99': ( $i * $i * $i ) > $i ).
tff('#skF_58',type,
'#skF_58': ( $i * $i * $i * $i ) > $i ).
tff(relation_inverse_image,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff('#skF_52',type,
'#skF_52': ( $i * $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_92',type,
'#skF_92': ( $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff('#skF_142',type,
'#skF_142': ( $i * $i ) > $i ).
tff('#skF_128',type,
'#skF_128': $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i ) > $i ).
tff('#skF_79',type,
'#skF_79': ( $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i * $i ) > $i ).
tff('#skF_78',type,
'#skF_78': ( $i * $i * $i ) > $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_117',type,
'#skF_117': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_90',type,
'#skF_90': ( $i * $i ) > $i ).
tff('#skF_124',type,
'#skF_124': $i > $i ).
tff('#skF_69',type,
'#skF_69': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff('#skF_129',type,
'#skF_129': $i ).
tff('#skF_77',type,
'#skF_77': ( $i * $i * $i ) > $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff('#skF_100',type,
'#skF_100': ( $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': $i > $i ).
tff(well_founded_relation,type,
well_founded_relation: $i > $o ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_143',type,
'#skF_143': ( $i * $i ) > $i ).
tff('#skF_48',type,
'#skF_48': ( $i * $i * $i ) > $i ).
tff('#skF_60',type,
'#skF_60': $i > $i ).
tff('#skF_85',type,
'#skF_85': ( $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i * $i ) > $i ).
tff('#skF_110',type,
'#skF_110': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(is_well_founded_in,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff(identity_relation,type,
identity_relation: $i > $i ).
tff(function_inverse,type,
function_inverse: $i > $i ).
tff('#skF_147',type,
'#skF_147': $i > $i ).
tff('#skF_74',type,
'#skF_74': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_122',type,
'#skF_122': $i ).
tff('#skF_65',type,
'#skF_65': ( $i * $i * $i ) > $i ).
tff('#skF_84',type,
'#skF_84': ( $i * $i ) > $i ).
tff(relation_image,type,
relation_image: ( $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff('#skF_97',type,
'#skF_97': ( $i * $i * $i ) > $i ).
tff('#skF_107',type,
'#skF_107': $i > $i ).
tff('#skF_113',type,
'#skF_113': $i > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_108',type,
'#skF_108': $i > $i ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_98',type,
'#skF_98': ( $i * $i * $i ) > $i ).
tff(relation_dom_restriction,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(well_orders,type,
well_orders: ( $i * $i ) > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_39',type,
'#skF_39': $i > $i ).
tff('#skF_138',type,
'#skF_138': ( $i * $i ) > $i ).
tff('#skF_121',type,
'#skF_121': $i ).
tff('#skF_59',type,
'#skF_59': $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff('#skF_51',type,
'#skF_51': ( $i * $i * $i ) > $i ).
tff('#skF_96',type,
'#skF_96': ( $i * $i * $i * $i * $i ) > $i ).
tff(set_meet,type,
set_meet: $i > $i ).
tff('#skF_137',type,
'#skF_137': ( $i * $i ) > $i ).
tff('#skF_71',type,
'#skF_71': ( $i * $i * $i ) > $i ).
tff('#skF_86',type,
'#skF_86': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff(being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
tff('#skF_103',type,
'#skF_103': ( $i * $i ) > $i ).
tff('#skF_133',type,
'#skF_133': ( $i * $i ) > $i ).
tff('#skF_149',type,
'#skF_149': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i * $i ) > $i ).
tff('#skF_102',type,
'#skF_102': ( $i * $i ) > $i ).
tff('#skF_151',type,
'#skF_151': $i > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i ) > $i ).
tff('#skF_81',type,
'#skF_81': ( $i * $i ) > $i ).
tff('#skF_145',type,
'#skF_145': ( $i * $i ) > $i ).
tff('#skF_95',type,
'#skF_95': $i > $i ).
tff('#skF_54',type,
'#skF_54': ( $i * $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': ( $i * $i * $i ) > $i ).
tff('#skF_94',type,
'#skF_94': $i > $i ).
tff('#skF_87',type,
'#skF_87': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_57',type,
'#skF_57': ( $i * $i * $i * $i ) > $i ).
tff(transitive,type,
transitive: $i > $o ).
tff('#skF_101',type,
'#skF_101': ( $i * $i * $i ) > $i ).
tff('#skF_136',type,
'#skF_136': ( $i * $i ) > $i ).
tff('#skF_134',type,
'#skF_134': ( $i * $i ) > $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(is_connected_in,type,
is_connected_in: ( $i * $i ) > $o ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_105',type,
'#skF_105': ( $i * $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(reflexive,type,
reflexive: $i > $o ).
tff('#skF_83',type,
'#skF_83': ( $i * $i * $i ) > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_68',type,
'#skF_68': ( $i * $i ) > $i ).
tff(is_transitive_in,type,
is_transitive_in: ( $i * $i ) > $o ).
tff(ordinal_subset,type,
ordinal_subset: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(is_antisymmetric_in,type,
is_antisymmetric_in: ( $i * $i ) > $o ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_89',type,
'#skF_89': ( $i * $i ) > $i ).
tff('#skF_125',type,
'#skF_125': $i ).
tff('#skF_43',type,
'#skF_43': ( $i * $i ) > $i ).
tff('#skF_141',type,
'#skF_141': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_132',type,
'#skF_132': ( $i * $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': $i > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff('#skF_61',type,
'#skF_61': ( $i * $i ) > $i ).
tff('#skF_50',type,
'#skF_50': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(succ,type,
succ: $i > $i ).
tff('#skF_119',type,
'#skF_119': $i > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff('#skF_123',type,
'#skF_123': $i ).
tff('#skF_146',type,
'#skF_146': $i > $i ).
tff('#skF_139',type,
'#skF_139': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_53',type,
'#skF_53': ( $i * $i * $i ) > $i ).
tff(fiber,type,
fiber: ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff('#skF_112',type,
'#skF_112': $i > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff('#skF_116',type,
'#skF_116': $i ).
tff(f_2022,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
tff(f_505,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
tff(f_158,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
tff(f_204,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
tff(f_210,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
tff(f_1864,lemma,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
tff(f_692,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
tff(f_562,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_reflexive_in(A,B)
& is_transitive_in(A,B)
& is_antisymmetric_in(A,B)
& is_connected_in(A,B)
& is_well_founded_in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
tff(c_1402,plain,
relation('#skF_150'),
inference(cnfTransformation,[status(thm)],[f_2022]) ).
tff(c_1404,plain,
( ~ well_ordering('#skF_150')
| ~ well_orders('#skF_150',relation_field('#skF_150')) ),
inference(cnfTransformation,[status(thm)],[f_2022]) ).
tff(c_1462,plain,
~ well_orders('#skF_150',relation_field('#skF_150')),
inference(splitLeft,[status(thm)],[c_1404]) ).
tff(c_1410,plain,
( well_orders('#skF_150',relation_field('#skF_150'))
| well_ordering('#skF_150') ),
inference(cnfTransformation,[status(thm)],[f_2022]) ).
tff(c_1463,plain,
well_ordering('#skF_150'),
inference(splitLeft,[status(thm)],[c_1410]) ).
tff(c_2527,plain,
! [A_1434] :
( antisymmetric(A_1434)
| ~ well_ordering(A_1434)
| ~ relation(A_1434) ),
inference(cnfTransformation,[status(thm)],[f_505]) ).
tff(c_2530,plain,
( antisymmetric('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_1463,c_2527]) ).
tff(c_2533,plain,
antisymmetric('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2530]) ).
tff(c_122,plain,
! [A_108] :
( is_antisymmetric_in(A_108,relation_field(A_108))
| ~ antisymmetric(A_108)
| ~ relation(A_108) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_2541,plain,
! [A_1436] :
( connected(A_1436)
| ~ well_ordering(A_1436)
| ~ relation(A_1436) ),
inference(cnfTransformation,[status(thm)],[f_505]) ).
tff(c_2544,plain,
( connected('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_1463,c_2541]) ).
tff(c_2547,plain,
connected('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2544]) ).
tff(c_180,plain,
! [A_205] :
( is_connected_in(A_205,relation_field(A_205))
| ~ connected(A_205)
| ~ relation(A_205) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_2534,plain,
! [A_1435] :
( transitive(A_1435)
| ~ well_ordering(A_1435)
| ~ relation(A_1435) ),
inference(cnfTransformation,[status(thm)],[f_505]) ).
tff(c_2537,plain,
( transitive('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_1463,c_2534]) ).
tff(c_2540,plain,
transitive('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2537]) ).
tff(c_184,plain,
! [A_206] :
( is_transitive_in(A_206,relation_field(A_206))
| ~ transitive(A_206)
| ~ relation(A_206) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_2549,plain,
! [A_1439] :
( well_founded_relation(A_1439)
| ~ well_ordering(A_1439)
| ~ relation(A_1439) ),
inference(cnfTransformation,[status(thm)],[f_505]) ).
tff(c_2552,plain,
( well_founded_relation('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_1463,c_2549]) ).
tff(c_2555,plain,
well_founded_relation('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2552]) ).
tff(c_1322,plain,
! [A_1198] :
( is_well_founded_in(A_1198,relation_field(A_1198))
| ~ well_founded_relation(A_1198)
| ~ relation(A_1198) ),
inference(cnfTransformation,[status(thm)],[f_1864]) ).
tff(c_2753,plain,
! [A_1450] :
( reflexive(A_1450)
| ~ well_ordering(A_1450)
| ~ relation(A_1450) ),
inference(cnfTransformation,[status(thm)],[f_505]) ).
tff(c_2756,plain,
( reflexive('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_1463,c_2753]) ).
tff(c_2759,plain,
reflexive('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2756]) ).
tff(c_656,plain,
! [A_775] :
( is_reflexive_in(A_775,relation_field(A_775))
| ~ reflexive(A_775)
| ~ relation(A_775) ),
inference(cnfTransformation,[status(thm)],[f_692]) ).
tff(c_131036,plain,
! [A_1633101,B_1633102] :
( well_orders(A_1633101,B_1633102)
| ~ is_well_founded_in(A_1633101,B_1633102)
| ~ is_connected_in(A_1633101,B_1633102)
| ~ is_antisymmetric_in(A_1633101,B_1633102)
| ~ is_transitive_in(A_1633101,B_1633102)
| ~ is_reflexive_in(A_1633101,B_1633102)
| ~ relation(A_1633101) ),
inference(cnfTransformation,[status(thm)],[f_562]) ).
tff(c_131054,plain,
( ~ is_well_founded_in('#skF_150',relation_field('#skF_150'))
| ~ is_connected_in('#skF_150',relation_field('#skF_150'))
| ~ is_antisymmetric_in('#skF_150',relation_field('#skF_150'))
| ~ is_transitive_in('#skF_150',relation_field('#skF_150'))
| ~ is_reflexive_in('#skF_150',relation_field('#skF_150'))
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_131036,c_1462]) ).
tff(c_131062,plain,
( ~ is_well_founded_in('#skF_150',relation_field('#skF_150'))
| ~ is_connected_in('#skF_150',relation_field('#skF_150'))
| ~ is_antisymmetric_in('#skF_150',relation_field('#skF_150'))
| ~ is_transitive_in('#skF_150',relation_field('#skF_150'))
| ~ is_reflexive_in('#skF_150',relation_field('#skF_150')) ),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_131054]) ).
tff(c_131871,plain,
~ is_reflexive_in('#skF_150',relation_field('#skF_150')),
inference(splitLeft,[status(thm)],[c_131062]) ).
tff(c_131877,plain,
( ~ reflexive('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_656,c_131871]) ).
tff(c_131884,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2759,c_131877]) ).
tff(c_131885,plain,
( ~ is_transitive_in('#skF_150',relation_field('#skF_150'))
| ~ is_antisymmetric_in('#skF_150',relation_field('#skF_150'))
| ~ is_connected_in('#skF_150',relation_field('#skF_150'))
| ~ is_well_founded_in('#skF_150',relation_field('#skF_150')) ),
inference(splitRight,[status(thm)],[c_131062]) ).
tff(c_132209,plain,
~ is_well_founded_in('#skF_150',relation_field('#skF_150')),
inference(splitLeft,[status(thm)],[c_131885]) ).
tff(c_132215,plain,
( ~ well_founded_relation('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_1322,c_132209]) ).
tff(c_132222,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2555,c_132215]) ).
tff(c_132223,plain,
( ~ is_connected_in('#skF_150',relation_field('#skF_150'))
| ~ is_antisymmetric_in('#skF_150',relation_field('#skF_150'))
| ~ is_transitive_in('#skF_150',relation_field('#skF_150')) ),
inference(splitRight,[status(thm)],[c_131885]) ).
tff(c_132751,plain,
~ is_transitive_in('#skF_150',relation_field('#skF_150')),
inference(splitLeft,[status(thm)],[c_132223]) ).
tff(c_132760,plain,
( ~ transitive('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_184,c_132751]) ).
tff(c_132770,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2540,c_132760]) ).
tff(c_132771,plain,
( ~ is_antisymmetric_in('#skF_150',relation_field('#skF_150'))
| ~ is_connected_in('#skF_150',relation_field('#skF_150')) ),
inference(splitRight,[status(thm)],[c_132223]) ).
tff(c_133144,plain,
~ is_connected_in('#skF_150',relation_field('#skF_150')),
inference(splitLeft,[status(thm)],[c_132771]) ).
tff(c_133153,plain,
( ~ connected('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_180,c_133144]) ).
tff(c_133163,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2547,c_133153]) ).
tff(c_133164,plain,
~ is_antisymmetric_in('#skF_150',relation_field('#skF_150')),
inference(splitRight,[status(thm)],[c_132771]) ).
tff(c_133183,plain,
( ~ antisymmetric('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_122,c_133164]) ).
tff(c_133196,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_2533,c_133183]) ).
tff(c_133197,plain,
well_orders('#skF_150',relation_field('#skF_150')),
inference(splitRight,[status(thm)],[c_1410]) ).
tff(c_133199,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1462,c_133197]) ).
tff(c_133200,plain,
~ well_ordering('#skF_150'),
inference(splitRight,[status(thm)],[c_1404]) ).
tff(c_133202,plain,
well_orders('#skF_150',relation_field('#skF_150')),
inference(negUnitSimplification,[status(thm)],[c_133200,c_1410]) ).
tff(c_141060,plain,
! [A_1666669,B_1666670] :
( is_reflexive_in(A_1666669,B_1666670)
| ~ well_orders(A_1666669,B_1666670)
| ~ relation(A_1666669) ),
inference(cnfTransformation,[status(thm)],[f_562]) ).
tff(c_141063,plain,
( is_reflexive_in('#skF_150',relation_field('#skF_150'))
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_133202,c_141060]) ).
tff(c_141066,plain,
is_reflexive_in('#skF_150',relation_field('#skF_150')),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_141063]) ).
tff(c_147929,plain,
! [A_1666895] :
( reflexive(A_1666895)
| ~ is_reflexive_in(A_1666895,relation_field(A_1666895))
| ~ relation(A_1666895) ),
inference(cnfTransformation,[status(thm)],[f_692]) ).
tff(c_147932,plain,
( reflexive('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_141066,c_147929]) ).
tff(c_147938,plain,
reflexive('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_147932]) ).
tff(c_139969,plain,
! [A_1666620,B_1666621] :
( is_transitive_in(A_1666620,B_1666621)
| ~ well_orders(A_1666620,B_1666621)
| ~ relation(A_1666620) ),
inference(cnfTransformation,[status(thm)],[f_562]) ).
tff(c_139972,plain,
( is_transitive_in('#skF_150',relation_field('#skF_150'))
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_133202,c_139969]) ).
tff(c_139975,plain,
is_transitive_in('#skF_150',relation_field('#skF_150')),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_139972]) ).
tff(c_147384,plain,
! [A_1666882] :
( transitive(A_1666882)
| ~ is_transitive_in(A_1666882,relation_field(A_1666882))
| ~ relation(A_1666882) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_147390,plain,
( transitive('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_139975,c_147384]) ).
tff(c_147394,plain,
transitive('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_147390]) ).
tff(c_140141,plain,
! [A_1666630,B_1666631] :
( is_antisymmetric_in(A_1666630,B_1666631)
| ~ well_orders(A_1666630,B_1666631)
| ~ relation(A_1666630) ),
inference(cnfTransformation,[status(thm)],[f_562]) ).
tff(c_140144,plain,
( is_antisymmetric_in('#skF_150',relation_field('#skF_150'))
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_133202,c_140141]) ).
tff(c_140147,plain,
is_antisymmetric_in('#skF_150',relation_field('#skF_150')),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_140144]) ).
tff(c_145843,plain,
! [A_1666826] :
( antisymmetric(A_1666826)
| ~ is_antisymmetric_in(A_1666826,relation_field(A_1666826))
| ~ relation(A_1666826) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_145846,plain,
( antisymmetric('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_140147,c_145843]) ).
tff(c_145849,plain,
antisymmetric('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_145846]) ).
tff(c_142708,plain,
! [A_1666737,B_1666738] :
( is_connected_in(A_1666737,B_1666738)
| ~ well_orders(A_1666737,B_1666738)
| ~ relation(A_1666737) ),
inference(cnfTransformation,[status(thm)],[f_562]) ).
tff(c_142711,plain,
( is_connected_in('#skF_150',relation_field('#skF_150'))
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_133202,c_142708]) ).
tff(c_142714,plain,
is_connected_in('#skF_150',relation_field('#skF_150')),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_142711]) ).
tff(c_178,plain,
! [A_205] :
( connected(A_205)
| ~ is_connected_in(A_205,relation_field(A_205))
| ~ relation(A_205) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_142717,plain,
( connected('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_142714,c_178]) ).
tff(c_142720,plain,
connected('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_142717]) ).
tff(c_142163,plain,
! [A_1666711,B_1666712] :
( is_well_founded_in(A_1666711,B_1666712)
| ~ well_orders(A_1666711,B_1666712)
| ~ relation(A_1666711) ),
inference(cnfTransformation,[status(thm)],[f_562]) ).
tff(c_142166,plain,
( is_well_founded_in('#skF_150',relation_field('#skF_150'))
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_133202,c_142163]) ).
tff(c_142169,plain,
is_well_founded_in('#skF_150',relation_field('#skF_150')),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_142166]) ).
tff(c_144289,plain,
! [A_1666775] :
( well_founded_relation(A_1666775)
| ~ is_well_founded_in(A_1666775,relation_field(A_1666775))
| ~ relation(A_1666775) ),
inference(cnfTransformation,[status(thm)],[f_1864]) ).
tff(c_144295,plain,
( well_founded_relation('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_142169,c_144289]) ).
tff(c_144299,plain,
well_founded_relation('#skF_150'),
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_144295]) ).
tff(c_199498,plain,
! [A_2081331] :
( well_ordering(A_2081331)
| ~ well_founded_relation(A_2081331)
| ~ connected(A_2081331)
| ~ antisymmetric(A_2081331)
| ~ transitive(A_2081331)
| ~ reflexive(A_2081331)
| ~ relation(A_2081331) ),
inference(cnfTransformation,[status(thm)],[f_505]) ).
tff(c_199516,plain,
( ~ well_founded_relation('#skF_150')
| ~ connected('#skF_150')
| ~ antisymmetric('#skF_150')
| ~ transitive('#skF_150')
| ~ reflexive('#skF_150')
| ~ relation('#skF_150') ),
inference(resolution,[status(thm)],[c_199498,c_133200]) ).
tff(c_199525,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1402,c_147938,c_147394,c_145849,c_142720,c_144299,c_199516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU244+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.36 % Computer : n002.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 3 12:15:16 EDT 2023
% 0.13/0.36 % CPUTime :
% 66.84/46.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 66.84/46.45
% 66.84/46.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 66.99/46.49
% 66.99/46.49 Inference rules
% 66.99/46.49 ----------------------
% 66.99/46.49 #Ref : 12
% 66.99/46.49 #Sup : 36241
% 66.99/46.49 #Fact : 12
% 66.99/46.49 #Define : 0
% 66.99/46.49 #Split : 63
% 66.99/46.49 #Chain : 0
% 66.99/46.49 #Close : 0
% 66.99/46.49
% 66.99/46.49 Ordering : KBO
% 66.99/46.49
% 66.99/46.49 Simplification rules
% 66.99/46.49 ----------------------
% 66.99/46.49 #Subsume : 9892
% 66.99/46.49 #Demod : 9012
% 66.99/46.49 #Tautology : 6659
% 66.99/46.49 #SimpNegUnit : 1144
% 66.99/46.49 #BackRed : 318
% 66.99/46.49
% 66.99/46.49 #Partial instantiations: 1040888
% 66.99/46.49 #Strategies tried : 1
% 66.99/46.49
% 66.99/46.49 Timing (in seconds)
% 66.99/46.49 ----------------------
% 66.99/46.50 Preprocessing : 1.37
% 66.99/46.50 Parsing : 0.63
% 66.99/46.50 CNF conversion : 0.15
% 66.99/46.50 Main loop : 44.02
% 66.99/46.50 Inferencing : 12.23
% 66.99/46.50 Reduction : 16.64
% 66.99/46.50 Demodulation : 11.23
% 66.99/46.50 BG Simplification : 0.31
% 66.99/46.50 Subsumption : 12.30
% 66.99/46.50 Abstraction : 0.34
% 66.99/46.50 MUC search : 0.00
% 66.99/46.50 Cooper : 0.00
% 66.99/46.50 Total : 45.46
% 66.99/46.50 Index Insertion : 0.00
% 66.99/46.50 Index Deletion : 0.00
% 66.99/46.50 Index Matching : 0.00
% 66.99/46.50 BG Taut test : 0.00
%------------------------------------------------------------------------------