TSTP Solution File: SEU250+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU250+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 : Thu Aug 31 16:23:48 EDT 2023

% Result   : Theorem 1.29s 1.39s
% Output   : CNFRefutation 1.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  187
% Syntax   : Number of formulae    :  203 (   3 unt; 184 typ;   0 def)
%            Number of atoms       :   54 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   57 (  22   ~;  22   |;   7   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  333 ( 169   >; 164   *;   0   +;   0  <<)
%            Number of predicates  :   29 (  28 usr;   1 prp; 0-2 aty)
%            Number of functors    :  156 ( 156 usr;  15 con; 0-5 aty)
%            Number of variables   :   38 (   2 sgn;  18   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    in: ( $i * $i ) > $o ).

tff(decl_23,type,
    proper_subset: ( $i * $i ) > $o ).

tff(decl_24,type,
    empty: $i > $o ).

tff(decl_25,type,
    function: $i > $o ).

tff(decl_26,type,
    ordinal: $i > $o ).

tff(decl_27,type,
    epsilon_transitive: $i > $o ).

tff(decl_28,type,
    epsilon_connected: $i > $o ).

tff(decl_29,type,
    relation: $i > $o ).

tff(decl_30,type,
    one_to_one: $i > $o ).

tff(decl_31,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_32,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_33,type,
    set_intersection2: ( $i * $i ) > $i ).

tff(decl_34,type,
    ordinal_subset: ( $i * $i ) > $o ).

tff(decl_35,type,
    identity_relation: $i > $i ).

tff(decl_36,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_37,type,
    subset: ( $i * $i ) > $o ).

tff(decl_38,type,
    relation_dom_restriction: ( $i * $i ) > $i ).

tff(decl_39,type,
    relation_image: ( $i * $i ) > $i ).

tff(decl_40,type,
    relation_dom: $i > $i ).

tff(decl_41,type,
    apply: ( $i * $i ) > $i ).

tff(decl_42,type,
    relation_rng_restriction: ( $i * $i ) > $i ).

tff(decl_43,type,
    antisymmetric: $i > $o ).

tff(decl_44,type,
    relation_field: $i > $i ).

tff(decl_45,type,
    is_antisymmetric_in: ( $i * $i ) > $o ).

tff(decl_46,type,
    relation_inverse_image: ( $i * $i ) > $i ).

tff(decl_47,type,
    connected: $i > $o ).

tff(decl_48,type,
    is_connected_in: ( $i * $i ) > $o ).

tff(decl_49,type,
    transitive: $i > $o ).

tff(decl_50,type,
    is_transitive_in: ( $i * $i ) > $o ).

tff(decl_51,type,
    unordered_triple: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    succ: $i > $i ).

tff(decl_53,type,
    singleton: $i > $i ).

tff(decl_54,type,
    is_reflexive_in: ( $i * $i ) > $o ).

tff(decl_55,type,
    empty_set: $i ).

tff(decl_56,type,
    set_meet: $i > $i ).

tff(decl_57,type,
    powerset: $i > $i ).

tff(decl_58,type,
    element: ( $i * $i ) > $o ).

tff(decl_59,type,
    well_founded_relation: $i > $o ).

tff(decl_60,type,
    fiber: ( $i * $i ) > $i ).

tff(decl_61,type,
    disjoint: ( $i * $i ) > $o ).

tff(decl_62,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_63,type,
    is_well_founded_in: ( $i * $i ) > $o ).

tff(decl_64,type,
    cast_to_subset: $i > $i ).

tff(decl_65,type,
    union: $i > $i ).

tff(decl_66,type,
    well_ordering: $i > $o ).

tff(decl_67,type,
    reflexive: $i > $o ).

tff(decl_68,type,
    set_difference: ( $i * $i ) > $i ).

tff(decl_69,type,
    relation_rng: $i > $i ).

tff(decl_70,type,
    subset_complement: ( $i * $i ) > $i ).

tff(decl_71,type,
    well_orders: ( $i * $i ) > $o ).

tff(decl_72,type,
    being_limit_ordinal: $i > $o ).

tff(decl_73,type,
    relation_restriction: ( $i * $i ) > $i ).

tff(decl_74,type,
    relation_inverse: $i > $i ).

tff(decl_75,type,
    relation_composition: ( $i * $i ) > $i ).

tff(decl_76,type,
    complements_of_subsets: ( $i * $i ) > $i ).

tff(decl_77,type,
    function_inverse: $i > $i ).

tff(decl_78,type,
    union_of_subsets: ( $i * $i ) > $i ).

tff(decl_79,type,
    meet_of_subsets: ( $i * $i ) > $i ).

tff(decl_80,type,
    subset_difference: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    relation_empty_yielding: $i > $o ).

tff(decl_82,type,
    are_equipotent: ( $i * $i ) > $o ).

tff(decl_83,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_84,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_85,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk5_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_96,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk17_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_100,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_101,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_102,type,
    esk20_1: $i > $i ).

tff(decl_103,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_104,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_105,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_106,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_107,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk26_1: $i > $i ).

tff(decl_109,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_110,type,
    esk28_1: $i > $i ).

tff(decl_111,type,
    esk29_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk30_2: ( $i * $i ) > $i ).

tff(decl_113,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_114,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_115,type,
    esk33_1: $i > $i ).

tff(decl_116,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_117,type,
    esk35_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_118,type,
    esk36_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_119,type,
    esk37_3: ( $i * $i * $i ) > $i ).

tff(decl_120,type,
    esk38_3: ( $i * $i * $i ) > $i ).

tff(decl_121,type,
    esk39_3: ( $i * $i * $i ) > $i ).

tff(decl_122,type,
    esk40_1: $i > $i ).

tff(decl_123,type,
    esk41_1: $i > $i ).

tff(decl_124,type,
    esk42_2: ( $i * $i ) > $i ).

tff(decl_125,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_126,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_127,type,
    esk45_3: ( $i * $i * $i ) > $i ).

tff(decl_128,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_129,type,
    esk47_3: ( $i * $i * $i ) > $i ).

tff(decl_130,type,
    esk48_3: ( $i * $i * $i ) > $i ).

tff(decl_131,type,
    esk49_2: ( $i * $i ) > $i ).

tff(decl_132,type,
    esk50_2: ( $i * $i ) > $i ).

tff(decl_133,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_134,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_135,type,
    esk53_3: ( $i * $i * $i ) > $i ).

tff(decl_136,type,
    esk54_2: ( $i * $i ) > $i ).

tff(decl_137,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_138,type,
    esk56_3: ( $i * $i * $i ) > $i ).

tff(decl_139,type,
    esk57_3: ( $i * $i * $i ) > $i ).

tff(decl_140,type,
    esk58_2: ( $i * $i ) > $i ).

tff(decl_141,type,
    esk59_2: ( $i * $i ) > $i ).

tff(decl_142,type,
    esk60_3: ( $i * $i * $i ) > $i ).

tff(decl_143,type,
    esk61_2: ( $i * $i ) > $i ).

tff(decl_144,type,
    esk62_2: ( $i * $i ) > $i ).

tff(decl_145,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_146,type,
    esk64_2: ( $i * $i ) > $i ).

tff(decl_147,type,
    esk65_2: ( $i * $i ) > $i ).

tff(decl_148,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_149,type,
    esk67_1: $i > $i ).

tff(decl_150,type,
    esk68_1: $i > $i ).

tff(decl_151,type,
    esk69_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_152,type,
    esk70_3: ( $i * $i * $i ) > $i ).

tff(decl_153,type,
    esk71_3: ( $i * $i * $i ) > $i ).

tff(decl_154,type,
    esk72_3: ( $i * $i * $i ) > $i ).

tff(decl_155,type,
    esk73_2: ( $i * $i ) > $i ).

tff(decl_156,type,
    esk74_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk75_2: ( $i * $i ) > $i ).

tff(decl_158,type,
    esk76_3: ( $i * $i * $i ) > $i ).

tff(decl_159,type,
    esk77_1: $i > $i ).

tff(decl_160,type,
    esk78_1: $i > $i ).

tff(decl_161,type,
    esk79_1: $i > $i ).

tff(decl_162,type,
    esk80_1: $i > $i ).

tff(decl_163,type,
    esk81_1: $i > $i ).

tff(decl_164,type,
    esk82_1: $i > $i ).

tff(decl_165,type,
    esk83_1: $i > $i ).

tff(decl_166,type,
    esk84_1: $i > $i ).

tff(decl_167,type,
    esk85_1: $i > $i ).

tff(decl_168,type,
    esk86_2: ( $i * $i ) > $i ).

tff(decl_169,type,
    esk87_0: $i ).

tff(decl_170,type,
    esk88_0: $i ).

tff(decl_171,type,
    esk89_0: $i ).

tff(decl_172,type,
    esk90_1: $i > $i ).

tff(decl_173,type,
    esk91_0: $i ).

tff(decl_174,type,
    esk92_0: $i ).

tff(decl_175,type,
    esk93_0: $i ).

tff(decl_176,type,
    esk94_0: $i ).

tff(decl_177,type,
    esk95_1: $i > $i ).

tff(decl_178,type,
    esk96_0: $i ).

tff(decl_179,type,
    esk97_0: $i ).

tff(decl_180,type,
    esk98_0: $i ).

tff(decl_181,type,
    esk99_0: $i ).

tff(decl_182,type,
    esk100_0: $i ).

tff(decl_183,type,
    esk101_1: $i > $i ).

tff(decl_184,type,
    esk102_3: ( $i * $i * $i ) > $i ).

tff(decl_185,type,
    esk103_3: ( $i * $i * $i ) > $i ).

tff(decl_186,type,
    esk104_0: $i ).

tff(decl_187,type,
    esk105_0: $i ).

tff(decl_188,type,
    esk106_2: ( $i * $i ) > $i ).

tff(decl_189,type,
    esk107_1: $i > $i ).

tff(decl_190,type,
    esk108_2: ( $i * $i ) > $i ).

tff(decl_191,type,
    esk109_2: ( $i * $i ) > $i ).

tff(decl_192,type,
    esk110_2: ( $i * $i ) > $i ).

tff(decl_193,type,
    esk111_1: $i > $i ).

tff(decl_194,type,
    esk112_1: $i > $i ).

tff(decl_195,type,
    esk113_2: ( $i * $i ) > $i ).

tff(decl_196,type,
    esk114_2: ( $i * $i ) > $i ).

tff(decl_197,type,
    esk115_2: ( $i * $i ) > $i ).

tff(decl_198,type,
    esk116_2: ( $i * $i ) > $i ).

tff(decl_199,type,
    esk117_2: ( $i * $i ) > $i ).

tff(decl_200,type,
    esk118_1: $i > $i ).

tff(decl_201,type,
    esk119_1: $i > $i ).

tff(decl_202,type,
    esk120_3: ( $i * $i * $i ) > $i ).

tff(decl_203,type,
    esk121_2: ( $i * $i ) > $i ).

tff(decl_204,type,
    esk122_1: $i > $i ).

tff(decl_205,type,
    esk123_2: ( $i * $i ) > $i ).

fof(t19_wellord1,lemma,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(X1,relation_field(relation_restriction(X3,X2)))
       => ( in(X1,relation_field(X3))
          & in(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(t20_wellord1,conjecture,
    ! [X1,X2] :
      ( relation(X2)
     => ( subset(relation_field(relation_restriction(X2,X1)),relation_field(X2))
        & subset(relation_field(relation_restriction(X2,X1)),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).

fof(c_0_3,lemma,
    ! [X603,X604,X605] :
      ( ( in(X603,relation_field(X605))
        | ~ in(X603,relation_field(relation_restriction(X605,X604)))
        | ~ relation(X605) )
      & ( in(X603,X604)
        | ~ in(X603,relation_field(relation_restriction(X605,X604)))
        | ~ relation(X605) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_wellord1])])]) ).

fof(c_0_4,plain,
    ! [X222,X223,X224,X225,X226] :
      ( ( ~ subset(X222,X223)
        | ~ in(X224,X222)
        | in(X224,X223) )
      & ( in(esk44_2(X225,X226),X225)
        | subset(X225,X226) )
      & ( ~ in(esk44_2(X225,X226),X226)
        | subset(X225,X226) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2] :
        ( relation(X2)
       => ( subset(relation_field(relation_restriction(X2,X1)),relation_field(X2))
          & subset(relation_field(relation_restriction(X2,X1)),X1) ) ),
    inference(assume_negation,[status(cth)],[t20_wellord1]) ).

cnf(c_0_6,lemma,
    ( in(X1,relation_field(X2))
    | ~ in(X1,relation_field(relation_restriction(X2,X3)))
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_7,plain,
    ( in(esk44_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_8,negated_conjecture,
    ( relation(esk105_0)
    & ( ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),relation_field(esk105_0))
      | ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),esk104_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | ~ in(esk44_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_10,lemma,
    ( subset(relation_field(relation_restriction(X1,X2)),X3)
    | in(esk44_2(relation_field(relation_restriction(X1,X2)),X3),relation_field(X1))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_11,lemma,
    ( in(X1,X2)
    | ~ in(X1,relation_field(relation_restriction(X3,X2)))
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_12,negated_conjecture,
    ( ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),relation_field(esk105_0))
    | ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),esk104_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,lemma,
    ( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    relation(esk105_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,lemma,
    ( subset(relation_field(relation_restriction(X1,X2)),X3)
    | in(esk44_2(relation_field(relation_restriction(X1,X2)),X3),X2)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_7]) ).

cnf(c_0_16,negated_conjecture,
    ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),esk104_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).

cnf(c_0_17,lemma,
    ( subset(relation_field(relation_restriction(X1,X2)),X2)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_15]) ).

cnf(c_0_18,lemma,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU250+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 01:32:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 1.29/1.39  % Version  : CSE_E---1.5
% 1.29/1.39  % Problem  : theBenchmark.p
% 1.29/1.39  % Proof found
% 1.29/1.39  % SZS status Theorem for theBenchmark.p
% 1.29/1.39  % SZS output start Proof
% See solution above
% 1.29/1.40  % Total time : 0.815000 s
% 1.29/1.40  % SZS output end Proof
% 1.29/1.40  % Total time : 0.821000 s
%------------------------------------------------------------------------------