TSTP Solution File: SEU265+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU265+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/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 16:23:57 EDT 2023

% Result   : Theorem 73.09s 73.30s
% Output   : CNFRefutation 73.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :  210
% Syntax   : Number of formulae    :  267 (  17 unt; 197 typ;   0 def)
%            Number of atoms       :  186 (  50 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  197 (  81   ~;  81   |;  18   &)
%                                         (   7 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  361 ( 180   >; 181   *;   0   +;   0  <<)
%            Number of predicates  :   34 (  32 usr;   1 prp; 0-3 aty)
%            Number of functors    :  165 ( 165 usr;  17 con; 0-5 aty)
%            Number of variables   :  138 (  11 sgn;  80   !;   1   ?;   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,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_31,type,
    powerset: $i > $i ).

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

tff(decl_33,type,
    one_to_one: $i > $o ).

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

tff(decl_35,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_36,type,
    set_intersection2: ( $i * $i ) > $i ).

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

tff(decl_38,type,
    identity_relation: $i > $i ).

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

tff(decl_40,type,
    subset: ( $i * $i ) > $o ).

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

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

tff(decl_43,type,
    relation_dom: $i > $i ).

tff(decl_44,type,
    apply: ( $i * $i ) > $i ).

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

tff(decl_46,type,
    antisymmetric: $i > $o ).

tff(decl_47,type,
    relation_field: $i > $i ).

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

tff(decl_49,type,
    relation_inverse_image: ( $i * $i ) > $i ).

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

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

tff(decl_52,type,
    transitive: $i > $o ).

tff(decl_53,type,
    is_transitive_in: ( $i * $i ) > $o ).

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

tff(decl_55,type,
    succ: $i > $i ).

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

tff(decl_57,type,
    is_reflexive_in: ( $i * $i ) > $o ).

tff(decl_58,type,
    relation_of2: ( $i * $i * $i ) > $o ).

tff(decl_59,type,
    empty_set: $i ).

tff(decl_60,type,
    set_meet: $i > $i ).

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

tff(decl_62,type,
    well_founded_relation: $i > $o ).

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

tff(decl_64,type,
    is_well_founded_in: ( $i * $i ) > $o ).

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

tff(decl_66,type,
    union: $i > $i ).

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

tff(decl_68,type,
    reflexive: $i > $o ).

tff(decl_69,type,
    set_difference: ( $i * $i ) > $i ).

tff(decl_70,type,
    relation_rng: $i > $i ).

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

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

tff(decl_73,type,
    being_limit_ordinal: $i > $o ).

tff(decl_74,type,
    relation_restriction: ( $i * $i ) > $i ).

tff(decl_75,type,
    relation_inverse: $i > $i ).

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

tff(decl_77,type,
    relation_composition: ( $i * $i ) > $i ).

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

tff(decl_79,type,
    function_inverse: $i > $i ).

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

tff(decl_81,type,
    union_of_subsets: ( $i * $i ) > $i ).

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

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

tff(decl_84,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

tff(decl_85,type,
    relation_empty_yielding: $i > $o ).

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

tff(decl_87,type,
    epred1_2: ( $i * $i ) > $o ).

tff(decl_88,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_89,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_90,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk5_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_96,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_100,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_101,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_102,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_103,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk17_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_105,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_106,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_107,type,
    esk20_1: $i > $i ).

tff(decl_108,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_109,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_110,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_111,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_113,type,
    esk26_3: ( $i * $i * $i ) > $i ).

tff(decl_114,type,
    esk27_1: $i > $i ).

tff(decl_115,type,
    esk28_2: ( $i * $i ) > $i ).

tff(decl_116,type,
    esk29_1: $i > $i ).

tff(decl_117,type,
    esk30_2: ( $i * $i ) > $i ).

tff(decl_118,type,
    esk31_2: ( $i * $i ) > $i ).

tff(decl_119,type,
    esk32_3: ( $i * $i * $i ) > $i ).

tff(decl_120,type,
    esk33_2: ( $i * $i ) > $i ).

tff(decl_121,type,
    esk34_1: $i > $i ).

tff(decl_122,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_123,type,
    esk36_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_124,type,
    esk37_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_125,type,
    esk38_3: ( $i * $i * $i ) > $i ).

tff(decl_126,type,
    esk39_3: ( $i * $i * $i ) > $i ).

tff(decl_127,type,
    esk40_3: ( $i * $i * $i ) > $i ).

tff(decl_128,type,
    esk41_1: $i > $i ).

tff(decl_129,type,
    esk42_1: $i > $i ).

tff(decl_130,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_131,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_132,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_133,type,
    esk46_3: ( $i * $i * $i ) > $i ).

tff(decl_134,type,
    esk47_2: ( $i * $i ) > $i ).

tff(decl_135,type,
    esk48_3: ( $i * $i * $i ) > $i ).

tff(decl_136,type,
    esk49_3: ( $i * $i * $i ) > $i ).

tff(decl_137,type,
    esk50_2: ( $i * $i ) > $i ).

tff(decl_138,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_139,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_140,type,
    esk53_2: ( $i * $i ) > $i ).

tff(decl_141,type,
    esk54_3: ( $i * $i * $i ) > $i ).

tff(decl_142,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_143,type,
    esk56_2: ( $i * $i ) > $i ).

tff(decl_144,type,
    esk57_3: ( $i * $i * $i ) > $i ).

tff(decl_145,type,
    esk58_3: ( $i * $i * $i ) > $i ).

tff(decl_146,type,
    esk59_2: ( $i * $i ) > $i ).

tff(decl_147,type,
    esk60_2: ( $i * $i ) > $i ).

tff(decl_148,type,
    esk61_3: ( $i * $i * $i ) > $i ).

tff(decl_149,type,
    esk62_2: ( $i * $i ) > $i ).

tff(decl_150,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_151,type,
    esk64_2: ( $i * $i ) > $i ).

tff(decl_152,type,
    esk65_2: ( $i * $i ) > $i ).

tff(decl_153,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_154,type,
    esk67_2: ( $i * $i ) > $i ).

tff(decl_155,type,
    esk68_3: ( $i * $i * $i ) > $i ).

tff(decl_156,type,
    esk69_3: ( $i * $i * $i ) > $i ).

tff(decl_157,type,
    esk70_1: $i > $i ).

tff(decl_158,type,
    esk71_1: $i > $i ).

tff(decl_159,type,
    esk72_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_160,type,
    esk73_3: ( $i * $i * $i ) > $i ).

tff(decl_161,type,
    esk74_3: ( $i * $i * $i ) > $i ).

tff(decl_162,type,
    esk75_3: ( $i * $i * $i ) > $i ).

tff(decl_163,type,
    esk76_2: ( $i * $i ) > $i ).

tff(decl_164,type,
    esk77_2: ( $i * $i ) > $i ).

tff(decl_165,type,
    esk78_2: ( $i * $i ) > $i ).

tff(decl_166,type,
    esk79_3: ( $i * $i * $i ) > $i ).

tff(decl_167,type,
    esk80_2: ( $i * $i ) > $i ).

tff(decl_168,type,
    esk81_1: $i > $i ).

tff(decl_169,type,
    esk82_2: ( $i * $i ) > $i ).

tff(decl_170,type,
    esk83_1: $i > $i ).

tff(decl_171,type,
    esk84_1: $i > $i ).

tff(decl_172,type,
    esk85_1: $i > $i ).

tff(decl_173,type,
    esk86_1: $i > $i ).

tff(decl_174,type,
    esk87_1: $i > $i ).

tff(decl_175,type,
    esk88_1: $i > $i ).

tff(decl_176,type,
    esk89_1: $i > $i ).

tff(decl_177,type,
    esk90_1: $i > $i ).

tff(decl_178,type,
    esk91_2: ( $i * $i ) > $i ).

tff(decl_179,type,
    esk92_0: $i ).

tff(decl_180,type,
    esk93_0: $i ).

tff(decl_181,type,
    esk94_0: $i ).

tff(decl_182,type,
    esk95_1: $i > $i ).

tff(decl_183,type,
    esk96_0: $i ).

tff(decl_184,type,
    esk97_0: $i ).

tff(decl_185,type,
    esk98_0: $i ).

tff(decl_186,type,
    esk99_0: $i ).

tff(decl_187,type,
    esk100_1: $i > $i ).

tff(decl_188,type,
    esk101_0: $i ).

tff(decl_189,type,
    esk102_0: $i ).

tff(decl_190,type,
    esk103_0: $i ).

tff(decl_191,type,
    esk104_0: $i ).

tff(decl_192,type,
    esk105_0: $i ).

tff(decl_193,type,
    esk106_1: $i > $i ).

tff(decl_194,type,
    esk107_3: ( $i * $i * $i ) > $i ).

tff(decl_195,type,
    esk108_3: ( $i * $i * $i ) > $i ).

tff(decl_196,type,
    esk109_0: $i ).

tff(decl_197,type,
    esk110_0: $i ).

tff(decl_198,type,
    esk111_0: $i ).

tff(decl_199,type,
    esk112_0: $i ).

tff(decl_200,type,
    esk113_1: $i > $i ).

tff(decl_201,type,
    esk114_2: ( $i * $i ) > $i ).

tff(decl_202,type,
    esk115_1: $i > $i ).

tff(decl_203,type,
    esk116_2: ( $i * $i ) > $i ).

tff(decl_204,type,
    esk117_2: ( $i * $i ) > $i ).

tff(decl_205,type,
    esk118_2: ( $i * $i ) > $i ).

tff(decl_206,type,
    esk119_1: $i > $i ).

tff(decl_207,type,
    esk120_1: $i > $i ).

tff(decl_208,type,
    esk121_2: ( $i * $i ) > $i ).

tff(decl_209,type,
    esk122_2: ( $i * $i ) > $i ).

tff(decl_210,type,
    esk123_2: ( $i * $i ) > $i ).

tff(decl_211,type,
    esk124_2: ( $i * $i ) > $i ).

tff(decl_212,type,
    esk125_2: ( $i * $i ) > $i ).

tff(decl_213,type,
    esk126_1: $i > $i ).

tff(decl_214,type,
    esk127_1: $i > $i ).

tff(decl_215,type,
    esk128_3: ( $i * $i * $i ) > $i ).

tff(decl_216,type,
    esk129_2: ( $i * $i ) > $i ).

tff(decl_217,type,
    esk130_1: $i > $i ).

tff(decl_218,type,
    esk131_2: ( $i * $i ) > $i ).

fof(t22_relset_1,conjecture,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X2,X1)
     => ( ! [X4] :
            ~ ( in(X4,X2)
              & ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
      <=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(t69_enumset1,lemma,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(t12_relset_1,lemma,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => ( subset(relation_dom(X3),X1)
        & subset(relation_rng(X3),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).

fof(d10_xboole_0,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(d4_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

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

fof(redefinition_k4_relset_1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2(X3,X1,X2)
     => relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).

fof(redefinition_m2_relset_1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
    <=> relation_of2(X3,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

fof(cc1_relset_1,axiom,
    ! [X1,X2,X3] :
      ( element(X3,powerset(cartesian_product2(X1,X2)))
     => relation(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

fof(dt_m2_relset_1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => element(X3,powerset(cartesian_product2(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

fof(t20_relat_1,lemma,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_dom(X3))
          & in(X2,relation_rng(X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation_of2_as_subset(X3,X2,X1)
       => ( ! [X4] :
              ~ ( in(X4,X2)
                & ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
        <=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t22_relset_1])]) ).

fof(c_0_14,plain,
    ! [X323,X324] : ordered_pair(X323,X324) = unordered_pair(unordered_pair(X323,X324),singleton(X323)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_15,lemma,
    ! [X868] : unordered_pair(X868,X868) = singleton(X868),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_16,lemma,
    ! [X594,X595,X596] :
      ( ( subset(relation_dom(X596),X594)
        | ~ relation_of2_as_subset(X596,X594,X595) )
      & ( subset(relation_rng(X596),X595)
        | ~ relation_of2_as_subset(X596,X594,X595) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])]) ).

fof(c_0_17,negated_conjecture,
    ! [X688,X689] :
      ( relation_of2_as_subset(esk111_0,esk110_0,esk109_0)
      & ( in(esk112_0,esk110_0)
        | relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 )
      & ( ~ in(ordered_pair(esk112_0,X688),esk111_0)
        | relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 )
      & ( ~ in(X689,esk110_0)
        | in(ordered_pair(X689,esk113_1(X689)),esk111_0)
        | relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).

cnf(c_0_18,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_20,plain,
    ! [X36,X37] :
      ( ( subset(X36,X37)
        | X36 != X37 )
      & ( subset(X37,X36)
        | X36 != X37 )
      & ( ~ subset(X36,X37)
        | ~ subset(X37,X36)
        | X36 = X37 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).

cnf(c_0_21,lemma,
    ( subset(relation_dom(X1),X2)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    relation_of2_as_subset(esk111_0,esk110_0,esk109_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_23,plain,
    ! [X262,X263,X264,X266,X267,X268,X270] :
      ( ( ~ in(X264,X263)
        | in(ordered_pair(X264,esk49_3(X262,X263,X264)),X262)
        | X263 != relation_dom(X262)
        | ~ relation(X262) )
      & ( ~ in(ordered_pair(X266,X267),X262)
        | in(X266,X263)
        | X263 != relation_dom(X262)
        | ~ relation(X262) )
      & ( ~ in(esk50_2(X262,X268),X268)
        | ~ in(ordered_pair(esk50_2(X262,X268),X270),X262)
        | X268 = relation_dom(X262)
        | ~ relation(X262) )
      & ( in(esk50_2(X262,X268),X268)
        | in(ordered_pair(esk50_2(X262,X268),esk51_2(X262,X268)),X262)
        | X268 = relation_dom(X262)
        | ~ relation(X262) ) ),
    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)],[d4_relat_1])])])])])]) ).

cnf(c_0_24,negated_conjecture,
    ( in(ordered_pair(X1,esk113_1(X1)),esk111_0)
    | relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
    | ~ in(X1,esk110_0) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_26,plain,
    ! [X20,X21] : unordered_pair(X20,X21) = unordered_pair(X21,X20),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_27,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,negated_conjecture,
    subset(relation_dom(esk111_0),esk110_0),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_29,plain,
    ! [X236,X237,X238,X239,X240] :
      ( ( ~ subset(X236,X237)
        | ~ in(X238,X236)
        | in(X238,X237) )
      & ( in(esk45_2(X239,X240),X239)
        | subset(X239,X240) )
      & ( ~ in(esk45_2(X239,X240),X240)
        | subset(X239,X240) ) ),
    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_30,plain,
    ! [X547,X548,X549] :
      ( ~ relation_of2(X549,X547,X548)
      | relation_dom_as_subset(X547,X548,X549) = relation_dom(X549) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).

fof(c_0_31,plain,
    ! [X557,X558,X559] :
      ( ( ~ relation_of2_as_subset(X559,X557,X558)
        | relation_of2(X559,X557,X558) )
      & ( ~ relation_of2(X559,X557,X558)
        | relation_of2_as_subset(X559,X557,X558) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).

cnf(c_0_32,negated_conjecture,
    ( ~ in(ordered_pair(esk112_0,X1),esk111_0)
    | relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_33,plain,
    ( in(ordered_pair(X1,esk49_3(X3,X2,X1)),X3)
    | ~ in(X1,X2)
    | X2 != relation_dom(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_34,plain,
    ! [X14,X15,X16] :
      ( ~ element(X16,powerset(cartesian_product2(X14,X15)))
      | relation(X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).

fof(c_0_35,plain,
    ! [X419,X420,X421] :
      ( ~ relation_of2_as_subset(X421,X419,X420)
      | element(X421,powerset(cartesian_product2(X419,X420))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).

fof(c_0_36,lemma,
    ! [X667,X668,X669] :
      ( ( in(X667,relation_dom(X669))
        | ~ in(ordered_pair(X667,X668),X669)
        | ~ relation(X669) )
      & ( in(X668,relation_rng(X669))
        | ~ in(ordered_pair(X667,X668),X669)
        | ~ relation(X669) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).

cnf(c_0_37,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
    | in(unordered_pair(unordered_pair(X1,esk113_1(X1)),unordered_pair(X1,X1)),esk111_0)
    | ~ in(X1,esk110_0) ),
    inference(rw,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_38,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_39,negated_conjecture,
    ( relation_dom(esk111_0) = esk110_0
    | ~ subset(esk110_0,relation_dom(esk111_0)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_40,plain,
    ( in(esk45_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_41,plain,
    ( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
    | ~ relation_of2(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_42,plain,
    ( relation_of2(X1,X2,X3)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_43,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
    | ~ in(unordered_pair(unordered_pair(esk112_0,X1),unordered_pair(esk112_0,esk112_0)),esk111_0) ),
    inference(rw,[status(thm)],[c_0_32,c_0_25]) ).

cnf(c_0_44,plain,
    ( in(unordered_pair(unordered_pair(X1,esk49_3(X3,X2,X1)),unordered_pair(X1,X1)),X3)
    | X2 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_33,c_0_25]) ).

cnf(c_0_45,plain,
    ( relation(X1)
    | ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_46,plain,
    ( element(X1,powerset(cartesian_product2(X2,X3)))
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_47,lemma,
    ( in(X1,relation_dom(X2))
    | ~ in(ordered_pair(X1,X3),X2)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_48,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
    | in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk113_1(X1))),esk111_0)
    | ~ in(X1,esk110_0) ),
    inference(rw,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_49,negated_conjecture,
    ( relation_dom(esk111_0) = esk110_0
    | in(esk45_2(esk110_0,relation_dom(esk111_0)),esk110_0) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_50,plain,
    ( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
    | ~ relation_of2_as_subset(X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_51,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
    | ~ in(unordered_pair(unordered_pair(esk112_0,esk112_0),unordered_pair(esk112_0,X1)),esk111_0) ),
    inference(spm,[status(thm)],[c_0_43,c_0_38]) ).

cnf(c_0_52,plain,
    ( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk49_3(X2,relation_dom(X2),X1))),X2)
    | ~ relation(X2)
    | ~ in(X1,relation_dom(X2)) ),
    inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_38])]) ).

cnf(c_0_53,plain,
    ( relation(X1)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_54,lemma,
    ( in(X1,relation_dom(X2))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
    inference(rw,[status(thm)],[c_0_47,c_0_25]) ).

cnf(c_0_55,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
    | relation_dom(esk111_0) = esk110_0
    | in(unordered_pair(unordered_pair(esk45_2(esk110_0,relation_dom(esk111_0)),esk45_2(esk110_0,relation_dom(esk111_0))),unordered_pair(esk45_2(esk110_0,relation_dom(esk111_0)),esk113_1(esk45_2(esk110_0,relation_dom(esk111_0))))),esk111_0) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_56,negated_conjecture,
    relation_dom(esk111_0) = relation_dom_as_subset(esk110_0,esk109_0,esk111_0),
    inference(spm,[status(thm)],[c_0_50,c_0_22]) ).

cnf(c_0_57,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
    | ~ relation(esk111_0)
    | ~ in(esk112_0,relation_dom(esk111_0)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    relation(esk111_0),
    inference(spm,[status(thm)],[c_0_53,c_0_22]) ).

cnf(c_0_59,lemma,
    ( in(X1,relation_dom(X2))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_54,c_0_38]) ).

cnf(c_0_60,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
    | in(unordered_pair(unordered_pair(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)),esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0))),unordered_pair(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)),esk113_1(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0))))),esk111_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56])]) ).

cnf(c_0_61,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
    | ~ in(esk112_0,relation_dom(esk111_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).

cnf(c_0_62,plain,
    ( subset(X1,X2)
    | ~ in(esk45_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_63,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
    | in(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)),relation_dom_as_subset(esk110_0,esk109_0,esk111_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_56]),c_0_58])]) ).

cnf(c_0_64,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
    | ~ subset(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_56]),c_0_56]) ).

cnf(c_0_65,negated_conjecture,
    ( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
    | ~ in(esk112_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)) ),
    inference(rw,[status(thm)],[c_0_61,c_0_56]) ).

cnf(c_0_66,negated_conjecture,
    relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).

cnf(c_0_67,negated_conjecture,
    ( in(esk112_0,esk110_0)
    | relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_68,negated_conjecture,
    ~ in(esk112_0,esk110_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66])]) ).

cnf(c_0_69,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_66])]),c_0_68]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU265+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/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   : Wed Aug 23 13:14:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 73.09/73.30  % Version  : CSE_E---1.5
% 73.09/73.30  % Problem  : theBenchmark.p
% 73.09/73.30  % Proof found
% 73.09/73.30  % SZS status Theorem for theBenchmark.p
% 73.09/73.30  % SZS output start Proof
% See solution above
% 73.09/73.31  % Total time : 72.728000 s
% 73.09/73.31  % SZS output end Proof
% 73.09/73.31  % Total time : 72.738000 s
%------------------------------------------------------------------------------