TSTP Solution File: SEU236+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU236+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 16:23:40 EDT 2023

% Result   : Theorem 26.05s 26.12s
% Output   : CNFRefutation 26.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :  165
% Syntax   : Number of formulae    :  239 (  28 unt; 147 typ;   0 def)
%            Number of atoms       :  291 (  56 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  316 ( 117   ~; 130   |;  39   &)
%                                         (  10 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  276 ( 132   >; 144   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-2 aty)
%            Number of functors    :  132 ( 132 usr;  15 con; 0-5 aty)
%            Number of variables   :  133 (   2 sgn;  86   !;   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,
    relation_inverse_image: ( $i * $i ) > $i ).

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

tff(decl_45,type,
    succ: $i > $i ).

tff(decl_46,type,
    singleton: $i > $i ).

tff(decl_47,type,
    empty_set: $i ).

tff(decl_48,type,
    set_meet: $i > $i ).

tff(decl_49,type,
    powerset: $i > $i ).

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

tff(decl_51,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_56,type,
    subset_complement: ( $i * $i ) > $i ).

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

tff(decl_58,type,
    relation_inverse: $i > $i ).

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

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

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

tff(decl_62,type,
    function_inverse: $i > $i ).

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

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

tff(decl_65,type,
    subset_difference: ( $i * $i * $i ) > $i ).

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

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

tff(decl_68,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk5_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk17_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_86,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_87,type,
    esk20_1: $i > $i ).

tff(decl_88,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_90,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_91,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_92,type,
    esk25_1: $i > $i ).

tff(decl_93,type,
    esk26_2: ( $i * $i ) > $i ).

tff(decl_94,type,
    esk27_1: $i > $i ).

tff(decl_95,type,
    esk28_2: ( $i * $i ) > $i ).

tff(decl_96,type,
    esk29_2: ( $i * $i ) > $i ).

tff(decl_97,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk32_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_100,type,
    esk33_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_101,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_102,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_103,type,
    esk36_3: ( $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk37_1: $i > $i ).

tff(decl_105,type,
    esk38_1: $i > $i ).

tff(decl_106,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_107,type,
    esk40_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk41_2: ( $i * $i ) > $i ).

tff(decl_109,type,
    esk42_3: ( $i * $i * $i ) > $i ).

tff(decl_110,type,
    esk43_3: ( $i * $i * $i ) > $i ).

tff(decl_111,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_113,type,
    esk46_3: ( $i * $i * $i ) > $i ).

tff(decl_114,type,
    esk47_2: ( $i * $i ) > $i ).

tff(decl_115,type,
    esk48_2: ( $i * $i ) > $i ).

tff(decl_116,type,
    esk49_3: ( $i * $i * $i ) > $i ).

tff(decl_117,type,
    esk50_3: ( $i * $i * $i ) > $i ).

tff(decl_118,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_119,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_120,type,
    esk53_3: ( $i * $i * $i ) > $i ).

tff(decl_121,type,
    esk54_2: ( $i * $i ) > $i ).

tff(decl_122,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_123,type,
    esk56_2: ( $i * $i ) > $i ).

tff(decl_124,type,
    esk57_2: ( $i * $i ) > $i ).

tff(decl_125,type,
    esk58_1: $i > $i ).

tff(decl_126,type,
    esk59_1: $i > $i ).

tff(decl_127,type,
    esk60_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_128,type,
    esk61_3: ( $i * $i * $i ) > $i ).

tff(decl_129,type,
    esk62_3: ( $i * $i * $i ) > $i ).

tff(decl_130,type,
    esk63_3: ( $i * $i * $i ) > $i ).

tff(decl_131,type,
    esk64_3: ( $i * $i * $i ) > $i ).

tff(decl_132,type,
    esk65_1: $i > $i ).

tff(decl_133,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_134,type,
    esk67_0: $i ).

tff(decl_135,type,
    esk68_0: $i ).

tff(decl_136,type,
    esk69_0: $i ).

tff(decl_137,type,
    esk70_1: $i > $i ).

tff(decl_138,type,
    esk71_0: $i ).

tff(decl_139,type,
    esk72_0: $i ).

tff(decl_140,type,
    esk73_0: $i ).

tff(decl_141,type,
    esk74_0: $i ).

tff(decl_142,type,
    esk75_1: $i > $i ).

tff(decl_143,type,
    esk76_0: $i ).

tff(decl_144,type,
    esk77_0: $i ).

tff(decl_145,type,
    esk78_0: $i ).

tff(decl_146,type,
    esk79_0: $i ).

tff(decl_147,type,
    esk80_0: $i ).

tff(decl_148,type,
    esk81_1: $i > $i ).

tff(decl_149,type,
    esk82_3: ( $i * $i * $i ) > $i ).

tff(decl_150,type,
    esk83_3: ( $i * $i * $i ) > $i ).

tff(decl_151,type,
    esk84_2: ( $i * $i ) > $i ).

tff(decl_152,type,
    esk85_1: $i > $i ).

tff(decl_153,type,
    esk86_2: ( $i * $i ) > $i ).

tff(decl_154,type,
    esk87_0: $i ).

tff(decl_155,type,
    esk88_0: $i ).

tff(decl_156,type,
    esk89_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk90_2: ( $i * $i ) > $i ).

tff(decl_158,type,
    esk91_2: ( $i * $i ) > $i ).

tff(decl_159,type,
    esk92_2: ( $i * $i ) > $i ).

tff(decl_160,type,
    esk93_2: ( $i * $i ) > $i ).

tff(decl_161,type,
    esk94_2: ( $i * $i ) > $i ).

tff(decl_162,type,
    esk95_2: ( $i * $i ) > $i ).

tff(decl_163,type,
    esk96_1: $i > $i ).

tff(decl_164,type,
    esk97_1: $i > $i ).

tff(decl_165,type,
    esk98_3: ( $i * $i * $i ) > $i ).

tff(decl_166,type,
    esk99_2: ( $i * $i ) > $i ).

tff(decl_167,type,
    esk100_1: $i > $i ).

tff(decl_168,type,
    esk101_2: ( $i * $i ) > $i ).

fof(t33_ordinal1,conjecture,
    ! [X1] :
      ( ordinal(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ( in(X1,X2)
          <=> ordinal_subset(succ(X1),X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).

fof(d1_ordinal1,axiom,
    ! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(t69_enumset1,lemma,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

fof(fc3_ordinal1,axiom,
    ! [X1] :
      ( ordinal(X1)
     => ( ~ empty(succ(X1))
        & epsilon_transitive(succ(X1))
        & epsilon_connected(succ(X1))
        & ordinal(succ(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).

fof(redefinition_r1_ordinal1,axiom,
    ! [X1,X2] :
      ( ( ordinal(X1)
        & ordinal(X2) )
     => ( ordinal_subset(X1,X2)
      <=> subset(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

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(t10_ordinal1,lemma,
    ! [X1] : in(X1,succ(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).

fof(connectedness_r1_ordinal1,axiom,
    ! [X1,X2] :
      ( ( ordinal(X1)
        & ordinal(X2) )
     => ( ordinal_subset(X1,X2)
        | ordinal_subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).

fof(d8_xboole_0,axiom,
    ! [X1,X2] :
      ( proper_subset(X1,X2)
    <=> ( subset(X1,X2)
        & X1 != X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).

fof(t21_ordinal1,lemma,
    ! [X1] :
      ( epsilon_transitive(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ( proper_subset(X1,X2)
           => in(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).

fof(cc1_ordinal1,axiom,
    ! [X1] :
      ( ordinal(X1)
     => ( epsilon_transitive(X1)
        & epsilon_connected(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).

fof(antisymmetry_r2_hidden,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(l2_zfmisc_1,lemma,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(l1_zfmisc_1,lemma,
    ! [X1] : singleton(X1) != empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).

fof(t32_ordinal1,lemma,
    ! [X1,X2] :
      ( ordinal(X2)
     => ~ ( subset(X1,X2)
          & X1 != empty_set
          & ! [X3] :
              ( ordinal(X3)
             => ~ ( in(X3,X1)
                  & ! [X4] :
                      ( ordinal(X4)
                     => ( in(X4,X1)
                       => ordinal_subset(X3,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).

fof(reflexivity_r1_ordinal1,axiom,
    ! [X1,X2] :
      ( ( ordinal(X1)
        & ordinal(X2) )
     => ordinal_subset(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).

fof(d2_tarski,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(c_0_18,negated_conjecture,
    ~ ! [X1] :
        ( ordinal(X1)
       => ! [X2] :
            ( ordinal(X2)
           => ( in(X1,X2)
            <=> ordinal_subset(succ(X1),X2) ) ) ),
    inference(assume_negation,[status(cth)],[t33_ordinal1]) ).

fof(c_0_19,plain,
    ! [X108] : succ(X108) = set_union2(X108,singleton(X108)),
    inference(variable_rename,[status(thm)],[d1_ordinal1]) ).

fof(c_0_20,lemma,
    ! [X687] : unordered_pair(X687,X687) = singleton(X687),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_21,negated_conjecture,
    ( ordinal(esk87_0)
    & ordinal(esk88_0)
    & ( ~ in(esk87_0,esk88_0)
      | ~ ordinal_subset(succ(esk87_0),esk88_0) )
    & ( in(esk87_0,esk88_0)
      | ordinal_subset(succ(esk87_0),esk88_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).

cnf(c_0_22,plain,
    succ(X1) = set_union2(X1,singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_24,plain,
    ! [X1] :
      ( ordinal(X1)
     => ( ~ empty(succ(X1))
        & epsilon_transitive(succ(X1))
        & epsilon_connected(succ(X1))
        & ordinal(succ(X1)) ) ),
    inference(fof_simplification,[status(thm)],[fc3_ordinal1]) ).

fof(c_0_25,plain,
    ! [X442,X443] :
      ( ( ~ ordinal_subset(X442,X443)
        | subset(X442,X443)
        | ~ ordinal(X442)
        | ~ ordinal(X443) )
      & ( ~ subset(X442,X443)
        | ordinal_subset(X442,X443)
        | ~ ordinal(X442)
        | ~ ordinal(X443) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).

cnf(c_0_26,negated_conjecture,
    ( in(esk87_0,esk88_0)
    | ordinal_subset(succ(esk87_0),esk88_0) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,plain,
    succ(X1) = set_union2(X1,unordered_pair(X1,X1)),
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_28,plain,
    ! [X363] :
      ( ( ~ empty(succ(X363))
        | ~ ordinal(X363) )
      & ( epsilon_transitive(succ(X363))
        | ~ ordinal(X363) )
      & ( epsilon_connected(succ(X363))
        | ~ ordinal(X363) )
      & ( ordinal(succ(X363))
        | ~ ordinal(X363) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).

cnf(c_0_29,plain,
    ( subset(X1,X2)
    | ~ ordinal_subset(X1,X2)
    | ~ ordinal(X1)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    ( in(esk87_0,esk88_0)
    | ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0) ),
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ordinal(esk88_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_32,plain,
    ( ordinal(succ(X1))
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_33,plain,
    ! [X209,X210,X211,X212,X213] :
      ( ( ~ subset(X209,X210)
        | ~ in(X211,X209)
        | in(X211,X210) )
      & ( in(esk41_2(X212,X213),X212)
        | subset(X212,X213) )
      & ( ~ in(esk41_2(X212,X213),X213)
        | subset(X212,X213) ) ),
    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])])])])])]) ).

cnf(c_0_34,negated_conjecture,
    ( subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
    | in(esk87_0,esk88_0)
    | ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

cnf(c_0_35,plain,
    ( ordinal(set_union2(X1,unordered_pair(X1,X1)))
    | ~ ordinal(X1) ),
    inference(rw,[status(thm)],[c_0_32,c_0_27]) ).

cnf(c_0_36,negated_conjecture,
    ordinal(esk87_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_37,lemma,
    ! [X453] : in(X453,succ(X453)),
    inference(variable_rename,[status(thm)],[t10_ordinal1]) ).

cnf(c_0_38,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    ( subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
    | in(esk87_0,esk88_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).

cnf(c_0_40,lemma,
    in(X1,succ(X1)),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    ( ~ in(esk87_0,esk88_0)
    | ~ ordinal_subset(succ(esk87_0),esk88_0) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_42,negated_conjecture,
    ( in(esk87_0,esk88_0)
    | in(X1,esk88_0)
    | ~ in(X1,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_43,lemma,
    in(X1,set_union2(X1,unordered_pair(X1,X1))),
    inference(rw,[status(thm)],[c_0_40,c_0_27]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ in(esk87_0,esk88_0)
    | ~ ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0) ),
    inference(rw,[status(thm)],[c_0_41,c_0_27]) ).

cnf(c_0_45,lemma,
    in(esk87_0,esk88_0),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_46,plain,
    ! [X23,X24] :
      ( ~ ordinal(X23)
      | ~ ordinal(X24)
      | ordinal_subset(X23,X24)
      | ordinal_subset(X24,X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).

cnf(c_0_47,negated_conjecture,
    ~ ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).

cnf(c_0_48,plain,
    ( ordinal_subset(X1,X2)
    | ordinal_subset(X2,X1)
    | ~ ordinal(X1)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_49,negated_conjecture,
    ( ordinal_subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
    | ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_31])]) ).

cnf(c_0_50,negated_conjecture,
    ordinal_subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_35]),c_0_36])]) ).

fof(c_0_51,plain,
    ! [X317,X318] :
      ( ( subset(X317,X318)
        | ~ proper_subset(X317,X318) )
      & ( X317 != X318
        | ~ proper_subset(X317,X318) )
      & ( ~ subset(X317,X318)
        | X317 = X318
        | proper_subset(X317,X318) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).

cnf(c_0_52,negated_conjecture,
    ( subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
    | ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_50]),c_0_31])]) ).

fof(c_0_53,lemma,
    ! [X534,X535] :
      ( ~ epsilon_transitive(X534)
      | ~ ordinal(X535)
      | ~ proper_subset(X534,X535)
      | in(X534,X535) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])]) ).

cnf(c_0_54,plain,
    ( X1 = X2
    | proper_subset(X1,X2)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_55,negated_conjecture,
    subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_35]),c_0_36])]) ).

cnf(c_0_56,lemma,
    ( in(X1,X2)
    | ~ epsilon_transitive(X1)
    | ~ ordinal(X2)
    | ~ proper_subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_57,negated_conjecture,
    ( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
    | proper_subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

fof(c_0_58,plain,
    ! [X12] :
      ( ( epsilon_transitive(X12)
        | ~ ordinal(X12) )
      & ( epsilon_connected(X12)
        | ~ ordinal(X12) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).

fof(c_0_59,plain,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).

fof(c_0_60,lemma,
    ! [X395,X396] :
      ( ( ~ subset(singleton(X395),X396)
        | in(X395,X396) )
      & ( ~ in(X395,X396)
        | subset(singleton(X395),X396) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).

fof(c_0_61,plain,
    ! [X171,X172,X173,X174,X175,X176,X177,X178] :
      ( ( ~ in(X174,X173)
        | in(X174,X171)
        | in(X174,X172)
        | X173 != set_union2(X171,X172) )
      & ( ~ in(X175,X171)
        | in(X175,X173)
        | X173 != set_union2(X171,X172) )
      & ( ~ in(X175,X172)
        | in(X175,X173)
        | X173 != set_union2(X171,X172) )
      & ( ~ in(esk31_3(X176,X177,X178),X176)
        | ~ in(esk31_3(X176,X177,X178),X178)
        | X178 = set_union2(X176,X177) )
      & ( ~ in(esk31_3(X176,X177,X178),X177)
        | ~ in(esk31_3(X176,X177,X178),X178)
        | X178 = set_union2(X176,X177) )
      & ( in(esk31_3(X176,X177,X178),X178)
        | in(esk31_3(X176,X177,X178),X176)
        | in(esk31_3(X176,X177,X178),X177)
        | X178 = set_union2(X176,X177) ) ),
    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)],[d2_xboole_0])])])])])]) ).

cnf(c_0_62,lemma,
    ( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
    | in(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
    | ~ epsilon_transitive(esk88_0)
    | ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_63,plain,
    ( epsilon_transitive(X1)
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

fof(c_0_64,plain,
    ! [X7,X8] :
      ( ~ in(X7,X8)
      | ~ in(X8,X7) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])]) ).

cnf(c_0_65,lemma,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

fof(c_0_66,lemma,
    ! [X388] : singleton(X388) != empty_set,
    inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).

cnf(c_0_67,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X2 != set_union2(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_68,lemma,
    ( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
    | in(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
    | ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_31])]) ).

cnf(c_0_69,plain,
    ( ~ in(X1,X2)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

fof(c_0_70,lemma,
    ! [X566,X567,X569] :
      ( ( ordinal(esk86_2(X566,X567))
        | ~ subset(X566,X567)
        | X566 = empty_set
        | ~ ordinal(X567) )
      & ( in(esk86_2(X566,X567),X566)
        | ~ subset(X566,X567)
        | X566 = empty_set
        | ~ ordinal(X567) )
      & ( ~ ordinal(X569)
        | ~ in(X569,X566)
        | ordinal_subset(esk86_2(X566,X567),X569)
        | ~ subset(X566,X567)
        | X566 = empty_set
        | ~ ordinal(X567) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t32_ordinal1])])])])]) ).

cnf(c_0_71,lemma,
    ( subset(unordered_pair(X1,X1),X2)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_65,c_0_23]) ).

cnf(c_0_72,lemma,
    singleton(X1) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_73,plain,
    ( in(X1,X2)
    | in(X1,X3)
    | ~ in(X1,set_union2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_67]) ).

cnf(c_0_74,lemma,
    ( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
    | in(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_35]),c_0_36])]) ).

cnf(c_0_75,lemma,
    ~ in(esk88_0,esk87_0),
    inference(spm,[status(thm)],[c_0_69,c_0_45]) ).

fof(c_0_76,plain,
    ! [X444,X445] :
      ( ~ ordinal(X444)
      | ~ ordinal(X445)
      | ordinal_subset(X444,X444) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1])]) ).

cnf(c_0_77,lemma,
    ( ordinal(esk86_2(X1,X2))
    | X1 = empty_set
    | ~ subset(X1,X2)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_78,lemma,
    subset(unordered_pair(esk87_0,esk87_0),esk88_0),
    inference(spm,[status(thm)],[c_0_71,c_0_45]) ).

cnf(c_0_79,lemma,
    unordered_pair(X1,X1) != empty_set,
    inference(rw,[status(thm)],[c_0_72,c_0_23]) ).

fof(c_0_80,plain,
    ! [X162,X163,X164,X165,X166,X167,X168,X169] :
      ( ( ~ in(X165,X164)
        | X165 = X162
        | X165 = X163
        | X164 != unordered_pair(X162,X163) )
      & ( X166 != X162
        | in(X166,X164)
        | X164 != unordered_pair(X162,X163) )
      & ( X166 != X163
        | in(X166,X164)
        | X164 != unordered_pair(X162,X163) )
      & ( esk30_3(X167,X168,X169) != X167
        | ~ in(esk30_3(X167,X168,X169),X169)
        | X169 = unordered_pair(X167,X168) )
      & ( esk30_3(X167,X168,X169) != X168
        | ~ in(esk30_3(X167,X168,X169),X169)
        | X169 = unordered_pair(X167,X168) )
      & ( in(esk30_3(X167,X168,X169),X169)
        | esk30_3(X167,X168,X169) = X167
        | esk30_3(X167,X168,X169) = X168
        | X169 = unordered_pair(X167,X168) ) ),
    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)],[d2_tarski])])])])])]) ).

cnf(c_0_81,lemma,
    ( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
    | in(esk88_0,unordered_pair(esk87_0,esk87_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).

cnf(c_0_82,plain,
    ( ordinal_subset(X1,X1)
    | ~ ordinal(X1)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_83,lemma,
    ordinal(esk86_2(unordered_pair(esk87_0,esk87_0),esk88_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_31])]),c_0_79]) ).

cnf(c_0_84,plain,
    ( X1 = X3
    | X1 = X4
    | ~ in(X1,X2)
    | X2 != unordered_pair(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_85,negated_conjecture,
    ( in(esk88_0,unordered_pair(esk87_0,esk87_0))
    | ~ ordinal_subset(esk88_0,esk88_0) ),
    inference(spm,[status(thm)],[c_0_47,c_0_81]) ).

cnf(c_0_86,lemma,
    ( ordinal_subset(X1,X1)
    | ~ ordinal(X1) ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_87,plain,
    ( X1 = X2
    | X1 = X3
    | ~ in(X1,unordered_pair(X3,X2)) ),
    inference(er,[status(thm)],[c_0_84]) ).

cnf(c_0_88,lemma,
    in(esk88_0,unordered_pair(esk87_0,esk87_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_31])]) ).

cnf(c_0_89,lemma,
    esk88_0 = esk87_0,
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_90,lemma,
    in(esk87_0,esk87_0),
    inference(rw,[status(thm)],[c_0_45,c_0_89]) ).

cnf(c_0_91,lemma,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_90]),c_0_90])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU236+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
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Wed Aug 23 20:39:18 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 26.05/26.12  % Version  : CSE_E---1.5
% 26.05/26.12  % Problem  : theBenchmark.p
% 26.05/26.12  % Proof found
% 26.05/26.12  % SZS status Theorem for theBenchmark.p
% 26.05/26.12  % SZS output start Proof
% See solution above
% 26.05/26.13  % Total time : 25.545000 s
% 26.05/26.13  % SZS output end Proof
% 26.05/26.14  % Total time : 25.554000 s
%------------------------------------------------------------------------------