TSTP Solution File: SEU230+2 by Beagle---0.9.51

View Problem - 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
%------------------------------------------------------------------------------