TSTP Solution File: SEU230+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU230+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n015.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 10:58:06 EDT 2023
% Result : Theorem 11.68s 3.73s
% Output : CNFRefutation 11.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 169
% Syntax : Number of formulae : 178 ( 12 unt; 164 typ; 0 def)
% Number of atoms : 16 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 342 ( 153 >; 189 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 153 ( 153 usr; 11 con; 0-5 aty)
% Number of variables : 19 (; 19 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > relation_empty_yielding > relation > one_to_one > function > empty > 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 > 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_104 > #skF_91 > #skF_76 > #skF_32 > #skF_49 > #skF_24 > #skF_106 > #skF_37 > #skF_69 > #skF_62 > #skF_35 > #skF_111 > #skF_75 > #skF_41 > #skF_80 > #skF_17 > #skF_117 > #skF_105 > #skF_57 > #skF_56 > #skF_114 > #skF_63 > #skF_113 > #skF_94 > #skF_27 > #skF_6 > #skF_30 > #skF_44 > #skF_122 > #skF_53 > #skF_18 > #skF_47 > #skF_112 > #skF_84 > #skF_103 > #skF_67 > #skF_72 > #skF_118 > #skF_64 > #skF_70 > #skF_115 > #skF_52 > #skF_60 > #skF_92 > #skF_31 > #skF_65 > #skF_108 > #skF_12 > #skF_3 > #skF_34 > #skF_77 > #skF_90 > #skF_29 > #skF_48 > #skF_78 > #skF_68 > #skF_23 > #skF_45 > #skF_26 > #skF_100 > #skF_89 > #skF_88 > #skF_83 > #skF_107 > #skF_119 > #skF_54 > #skF_74 > #skF_33 > #skF_5 > #skF_19 > #skF_102 > #skF_82 > #skF_38 > #skF_58 > #skF_66 > #skF_110 > #skF_42 > #skF_11 > #skF_36 > #skF_71 > #skF_97 > #skF_7 > #skF_9 > #skF_20 > #skF_51 > #skF_15 > #skF_14 > #skF_28 > #skF_81 > #skF_121 > #skF_95 > #skF_50 > #skF_99 > #skF_93 > #skF_59 > #skF_55 > #skF_87 > #skF_46 > #skF_2 > #skF_98 > #skF_40 > #skF_116 > #skF_96 > #skF_8 > #skF_101 > #skF_25 > #skF_43 > #skF_85 > #skF_86 > #skF_120 > #skF_21 > #skF_61 > #skF_1 > #skF_22 > #skF_73 > #skF_4 > #skF_16 > #skF_10 > #skF_79 > #skF_39 > #skF_109
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_104',type,
'#skF_104': $i ).
tff('#skF_91',type,
'#skF_91': $i > $i ).
tff(are_equipotent,type,
are_equipotent: ( $i * $i ) > $o ).
tff('#skF_76',type,
'#skF_76': ( $i * $i ) > $i ).
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff('#skF_106',type,
'#skF_106': ( $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_69',type,
'#skF_69': ( $i * $i * $i ) > $i ).
tff('#skF_62',type,
'#skF_62': ( $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff('#skF_111',type,
'#skF_111': ( $i * $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(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_117',type,
'#skF_117': $i > $i ).
tff('#skF_105',type,
'#skF_105': $i > $i ).
tff('#skF_57',type,
'#skF_57': ( $i * $i ) > $i ).
tff('#skF_56',type,
'#skF_56': ( $i * $i ) > $i ).
tff(relation_inverse,type,
relation_inverse: $i > $i ).
tff('#skF_114',type,
'#skF_114': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_63',type,
'#skF_63': ( $i * $i * $i ) > $i ).
tff('#skF_113',type,
'#skF_113': ( $i * $i ) > $i ).
tff('#skF_94',type,
'#skF_94': $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $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('#skF_122',type,
'#skF_122': ( $i * $i ) > $i ).
tff('#skF_53',type,
'#skF_53': ( $i * $i * $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(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff('#skF_112',type,
'#skF_112': ( $i * $i ) > $i ).
tff('#skF_84',type,
'#skF_84': ( $i * $i * $i * $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_103',type,
'#skF_103': $i ).
tff('#skF_67',type,
'#skF_67': ( $i * $i * $i ) > $i ).
tff('#skF_72',type,
'#skF_72': ( $i * $i ) > $i ).
tff('#skF_118',type,
'#skF_118': $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_115',type,
'#skF_115': ( $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('#skF_60',type,
'#skF_60': ( $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_65',type,
'#skF_65': ( $i * $i ) > $i ).
tff('#skF_108',type,
'#skF_108': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i * $i ) > $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff('#skF_77',type,
'#skF_77': ( $i * $i * $i ) > $i ).
tff('#skF_90',type,
'#skF_90': ( $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': $i > $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_48',type,
'#skF_48': ( $i * $i * $i ) > $i ).
tff('#skF_78',type,
'#skF_78': ( $i * $i ) > $i ).
tff('#skF_68',type,
'#skF_68': ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i * $i ) > $i ).
tff('#skF_100',type,
'#skF_100': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_89',type,
'#skF_89': ( $i * $i * $i ) > $i ).
tff(identity_relation,type,
identity_relation: $i > $i ).
tff(function_inverse,type,
function_inverse: $i > $i ).
tff('#skF_88',type,
'#skF_88': ( $i * $i * $i ) > $i ).
tff('#skF_83',type,
'#skF_83': $i > $i ).
tff('#skF_107',type,
'#skF_107': ( $i * $i * $i ) > $i ).
tff('#skF_119',type,
'#skF_119': ( $i * $i * $i ) > $i ).
tff('#skF_54',type,
'#skF_54': ( $i * $i * $i * $i ) > $i ).
tff('#skF_74',type,
'#skF_74': ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff('#skF_102',type,
'#skF_102': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_82',type,
'#skF_82': $i > $i ).
tff('#skF_38',type,
'#skF_38': $i > $i ).
tff('#skF_58',type,
'#skF_58': ( $i * $i * $i ) > $i ).
tff('#skF_66',type,
'#skF_66': ( $i * $i ) > $i ).
tff(relation_image,type,
relation_image: ( $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff('#skF_110',type,
'#skF_110': ( $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
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_71',type,
'#skF_71': ( $i * $i ) > $i ).
tff('#skF_97',type,
'#skF_97': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $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(set_meet,type,
set_meet: $i > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $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_81',type,
'#skF_81': ( $i * $i ) > $i ).
tff('#skF_121',type,
'#skF_121': $i > $i ).
tff('#skF_95',type,
'#skF_95': $i > $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i * $i ) > $i ).
tff('#skF_99',type,
'#skF_99': $i > $i ).
tff('#skF_93',type,
'#skF_93': $i ).
tff('#skF_59',type,
'#skF_59': ( $i * $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': ( $i * $i ) > $i ).
tff('#skF_87',type,
'#skF_87': ( $i * $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff('#skF_98',type,
'#skF_98': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_116',type,
'#skF_116': ( $i * $i ) > $i ).
tff('#skF_96',type,
'#skF_96': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_101',type,
'#skF_101': $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_43',type,
'#skF_43': ( $i * $i ) > $i ).
tff('#skF_85',type,
'#skF_85': ( $i * $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_86',type,
'#skF_86': ( $i * $i * $i ) > $i ).
tff('#skF_120',type,
'#skF_120': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff('#skF_61',type,
'#skF_61': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(succ,type,
succ: $i > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff('#skF_73',type,
'#skF_73': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff('#skF_79',type,
'#skF_79': ( $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i ) > $i ).
tff('#skF_109',type,
'#skF_109': ( $i * $i ) > $i ).
tff(f_181,axiom,
! [A] : ( succ(A) = set_union2(A,singleton(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
tff(f_60,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_1529,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(f_1176,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
tff(f_856,negated_conjecture,
~ ! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
tff(c_1890,plain,
! [A_1212] : ( set_union2(A_1212,singleton(A_1212)) = succ(A_1212) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_1720,plain,
! [B_1193,A_1194] : ( set_union2(B_1193,A_1194) = set_union2(A_1194,B_1193) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_1094,plain,
! [A_1048,B_1049] : subset(A_1048,set_union2(A_1048,B_1049)),
inference(cnfTransformation,[status(thm)],[f_1529]) ).
tff(c_1735,plain,
! [A_1194,B_1193] : subset(A_1194,set_union2(B_1193,A_1194)),
inference(superposition,[status(thm),theory(equality)],[c_1720,c_1094]) ).
tff(c_1896,plain,
! [A_1212] : subset(singleton(A_1212),succ(A_1212)),
inference(superposition,[status(thm),theory(equality)],[c_1890,c_1735]) ).
tff(c_4908,plain,
! [A_1406,B_1407] :
( in(A_1406,B_1407)
| ~ subset(singleton(A_1406),B_1407) ),
inference(cnfTransformation,[status(thm)],[f_1176]) ).
tff(c_4949,plain,
! [A_1212] : in(A_1212,succ(A_1212)),
inference(resolution,[status(thm)],[c_1896,c_4908]) ).
tff(c_774,plain,
~ in('#skF_104',succ('#skF_104')),
inference(cnfTransformation,[status(thm)],[f_856]) ).
tff(c_4958,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4949,c_774]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU230+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 12:28:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 11.68/3.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.68/3.73
% 11.68/3.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.76/3.76
% 11.76/3.76 Inference rules
% 11.76/3.76 ----------------------
% 11.76/3.76 #Ref : 0
% 11.76/3.76 #Sup : 893
% 11.76/3.76 #Fact : 0
% 11.76/3.76 #Define : 0
% 11.76/3.76 #Split : 8
% 11.76/3.76 #Chain : 0
% 11.76/3.76 #Close : 0
% 11.76/3.76
% 11.76/3.76 Ordering : KBO
% 11.76/3.76
% 11.76/3.76 Simplification rules
% 11.76/3.76 ----------------------
% 11.76/3.76 #Subsume : 198
% 11.76/3.76 #Demod : 439
% 11.76/3.76 #Tautology : 501
% 11.76/3.76 #SimpNegUnit : 13
% 11.76/3.76 #BackRed : 23
% 11.76/3.76
% 11.76/3.76 #Partial instantiations: 0
% 11.76/3.76 #Strategies tried : 1
% 11.76/3.76
% 11.76/3.76 Timing (in seconds)
% 11.76/3.76 ----------------------
% 11.76/3.77 Preprocessing : 1.23
% 11.76/3.77 Parsing : 0.56
% 11.76/3.77 CNF conversion : 0.14
% 11.76/3.77 Main loop : 1.45
% 11.76/3.77 Inferencing : 0.31
% 11.76/3.77 Reduction : 0.59
% 11.76/3.77 Demodulation : 0.42
% 11.76/3.77 BG Simplification : 0.11
% 11.76/3.77 Subsumption : 0.33
% 11.76/3.77 Abstraction : 0.04
% 11.76/3.77 MUC search : 0.00
% 11.76/3.77 Cooper : 0.00
% 11.76/3.77 Total : 2.72
% 11.76/3.77 Index Insertion : 0.00
% 11.76/3.77 Index Deletion : 0.00
% 11.76/3.77 Index Matching : 0.00
% 11.76/3.77 BG Taut test : 0.00
%------------------------------------------------------------------------------