TSTP Solution File: SEU244+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU244+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 : n032.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 16:23:45 EDT 2023

% Result   : Theorem 0.76s 0.88s
% Output   : CNFRefutation 0.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  190
% Syntax   : Number of formulae    :  247 (   7 unt; 182 typ;   0 def)
%            Number of atoms       :  247 (   0 equ)
%            Maximal formula atoms :   22 (   3 avg)
%            Number of connectives :  321 ( 139   ~; 139   |;  25   &)
%                                         (   9 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  331 ( 168   >; 163   *;   0   +;   0  <<)
%            Number of predicates  :   29 (  28 usr;   1 prp; 0-2 aty)
%            Number of functors    :  154 ( 154 usr;  14 con; 0-5 aty)
%            Number of variables   :   48 (   0 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_inverse: $i > $i ).

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

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

tff(decl_76,type,
    function_inverse: $i > $i ).

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

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

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

tff(decl_80,type,
    relation_empty_yielding: $i > $o ).

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

tff(decl_82,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_83,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_84,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk5_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_96,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk17_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_100,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_101,type,
    esk20_1: $i > $i ).

tff(decl_102,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_103,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_105,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_106,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_107,type,
    esk26_1: $i > $i ).

tff(decl_108,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_109,type,
    esk28_1: $i > $i ).

tff(decl_110,type,
    esk29_2: ( $i * $i ) > $i ).

tff(decl_111,type,
    esk30_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_113,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_114,type,
    esk33_1: $i > $i ).

tff(decl_115,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_116,type,
    esk35_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_117,type,
    esk36_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_118,type,
    esk37_3: ( $i * $i * $i ) > $i ).

tff(decl_119,type,
    esk38_3: ( $i * $i * $i ) > $i ).

tff(decl_120,type,
    esk39_3: ( $i * $i * $i ) > $i ).

tff(decl_121,type,
    esk40_1: $i > $i ).

tff(decl_122,type,
    esk41_1: $i > $i ).

tff(decl_123,type,
    esk42_2: ( $i * $i ) > $i ).

tff(decl_124,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_125,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_126,type,
    esk45_3: ( $i * $i * $i ) > $i ).

tff(decl_127,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_128,type,
    esk47_3: ( $i * $i * $i ) > $i ).

tff(decl_129,type,
    esk48_3: ( $i * $i * $i ) > $i ).

tff(decl_130,type,
    esk49_2: ( $i * $i ) > $i ).

tff(decl_131,type,
    esk50_2: ( $i * $i ) > $i ).

tff(decl_132,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_133,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_134,type,
    esk53_3: ( $i * $i * $i ) > $i ).

tff(decl_135,type,
    esk54_2: ( $i * $i ) > $i ).

tff(decl_136,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_137,type,
    esk56_3: ( $i * $i * $i ) > $i ).

tff(decl_138,type,
    esk57_3: ( $i * $i * $i ) > $i ).

tff(decl_139,type,
    esk58_2: ( $i * $i ) > $i ).

tff(decl_140,type,
    esk59_2: ( $i * $i ) > $i ).

tff(decl_141,type,
    esk60_3: ( $i * $i * $i ) > $i ).

tff(decl_142,type,
    esk61_2: ( $i * $i ) > $i ).

tff(decl_143,type,
    esk62_2: ( $i * $i ) > $i ).

tff(decl_144,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_145,type,
    esk64_2: ( $i * $i ) > $i ).

tff(decl_146,type,
    esk65_2: ( $i * $i ) > $i ).

tff(decl_147,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_148,type,
    esk67_1: $i > $i ).

tff(decl_149,type,
    esk68_1: $i > $i ).

tff(decl_150,type,
    esk69_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_151,type,
    esk70_3: ( $i * $i * $i ) > $i ).

tff(decl_152,type,
    esk71_3: ( $i * $i * $i ) > $i ).

tff(decl_153,type,
    esk72_3: ( $i * $i * $i ) > $i ).

tff(decl_154,type,
    esk73_2: ( $i * $i ) > $i ).

tff(decl_155,type,
    esk74_2: ( $i * $i ) > $i ).

tff(decl_156,type,
    esk75_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk76_3: ( $i * $i * $i ) > $i ).

tff(decl_158,type,
    esk77_1: $i > $i ).

tff(decl_159,type,
    esk78_1: $i > $i ).

tff(decl_160,type,
    esk79_1: $i > $i ).

tff(decl_161,type,
    esk80_1: $i > $i ).

tff(decl_162,type,
    esk81_1: $i > $i ).

tff(decl_163,type,
    esk82_1: $i > $i ).

tff(decl_164,type,
    esk83_1: $i > $i ).

tff(decl_165,type,
    esk84_1: $i > $i ).

tff(decl_166,type,
    esk85_1: $i > $i ).

tff(decl_167,type,
    esk86_2: ( $i * $i ) > $i ).

tff(decl_168,type,
    esk87_0: $i ).

tff(decl_169,type,
    esk88_0: $i ).

tff(decl_170,type,
    esk89_0: $i ).

tff(decl_171,type,
    esk90_1: $i > $i ).

tff(decl_172,type,
    esk91_0: $i ).

tff(decl_173,type,
    esk92_0: $i ).

tff(decl_174,type,
    esk93_0: $i ).

tff(decl_175,type,
    esk94_0: $i ).

tff(decl_176,type,
    esk95_1: $i > $i ).

tff(decl_177,type,
    esk96_0: $i ).

tff(decl_178,type,
    esk97_0: $i ).

tff(decl_179,type,
    esk98_0: $i ).

tff(decl_180,type,
    esk99_0: $i ).

tff(decl_181,type,
    esk100_0: $i ).

tff(decl_182,type,
    esk101_1: $i > $i ).

tff(decl_183,type,
    esk102_3: ( $i * $i * $i ) > $i ).

tff(decl_184,type,
    esk103_3: ( $i * $i * $i ) > $i ).

tff(decl_185,type,
    esk104_2: ( $i * $i ) > $i ).

tff(decl_186,type,
    esk105_1: $i > $i ).

tff(decl_187,type,
    esk106_2: ( $i * $i ) > $i ).

tff(decl_188,type,
    esk107_2: ( $i * $i ) > $i ).

tff(decl_189,type,
    esk108_2: ( $i * $i ) > $i ).

tff(decl_190,type,
    esk109_1: $i > $i ).

tff(decl_191,type,
    esk110_1: $i > $i ).

tff(decl_192,type,
    esk111_2: ( $i * $i ) > $i ).

tff(decl_193,type,
    esk112_2: ( $i * $i ) > $i ).

tff(decl_194,type,
    esk113_2: ( $i * $i ) > $i ).

tff(decl_195,type,
    esk114_2: ( $i * $i ) > $i ).

tff(decl_196,type,
    esk115_2: ( $i * $i ) > $i ).

tff(decl_197,type,
    esk116_1: $i > $i ).

tff(decl_198,type,
    esk117_1: $i > $i ).

tff(decl_199,type,
    esk118_3: ( $i * $i * $i ) > $i ).

tff(decl_200,type,
    esk119_2: ( $i * $i ) > $i ).

tff(decl_201,type,
    esk120_0: $i ).

tff(decl_202,type,
    esk121_1: $i > $i ).

tff(decl_203,type,
    esk122_2: ( $i * $i ) > $i ).

fof(t8_wellord1,conjecture,
    ! [X1] :
      ( relation(X1)
     => ( well_orders(X1,relation_field(X1))
      <=> well_ordering(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).

fof(d5_wellord1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( well_orders(X1,X2)
        <=> ( is_reflexive_in(X1,X2)
            & is_transitive_in(X1,X2)
            & is_antisymmetric_in(X1,X2)
            & is_connected_in(X1,X2)
            & is_well_founded_in(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).

fof(d9_relat_2,axiom,
    ! [X1] :
      ( relation(X1)
     => ( reflexive(X1)
      <=> is_reflexive_in(X1,relation_field(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).

fof(t5_wellord1,lemma,
    ! [X1] :
      ( relation(X1)
     => ( well_founded_relation(X1)
      <=> is_well_founded_in(X1,relation_field(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).

fof(d14_relat_2,axiom,
    ! [X1] :
      ( relation(X1)
     => ( connected(X1)
      <=> is_connected_in(X1,relation_field(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).

fof(d4_wellord1,axiom,
    ! [X1] :
      ( relation(X1)
     => ( well_ordering(X1)
      <=> ( reflexive(X1)
          & transitive(X1)
          & antisymmetric(X1)
          & connected(X1)
          & well_founded_relation(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).

fof(d12_relat_2,axiom,
    ! [X1] :
      ( relation(X1)
     => ( antisymmetric(X1)
      <=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).

fof(d16_relat_2,axiom,
    ! [X1] :
      ( relation(X1)
     => ( transitive(X1)
      <=> is_transitive_in(X1,relation_field(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( well_orders(X1,relation_field(X1))
        <=> well_ordering(X1) ) ),
    inference(assume_negation,[status(cth)],[t8_wellord1]) ).

fof(c_0_9,plain,
    ! [X311,X312] :
      ( ( is_reflexive_in(X311,X312)
        | ~ well_orders(X311,X312)
        | ~ relation(X311) )
      & ( is_transitive_in(X311,X312)
        | ~ well_orders(X311,X312)
        | ~ relation(X311) )
      & ( is_antisymmetric_in(X311,X312)
        | ~ well_orders(X311,X312)
        | ~ relation(X311) )
      & ( is_connected_in(X311,X312)
        | ~ well_orders(X311,X312)
        | ~ relation(X311) )
      & ( is_well_founded_in(X311,X312)
        | ~ well_orders(X311,X312)
        | ~ relation(X311) )
      & ( ~ is_reflexive_in(X311,X312)
        | ~ is_transitive_in(X311,X312)
        | ~ is_antisymmetric_in(X311,X312)
        | ~ is_connected_in(X311,X312)
        | ~ is_well_founded_in(X311,X312)
        | well_orders(X311,X312)
        | ~ relation(X311) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_wellord1])])])]) ).

fof(c_0_10,negated_conjecture,
    ( relation(esk120_0)
    & ( ~ well_orders(esk120_0,relation_field(esk120_0))
      | ~ well_ordering(esk120_0) )
    & ( well_orders(esk120_0,relation_field(esk120_0))
      | well_ordering(esk120_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_11,plain,
    ! [X367] :
      ( ( ~ reflexive(X367)
        | is_reflexive_in(X367,relation_field(X367))
        | ~ relation(X367) )
      & ( ~ is_reflexive_in(X367,relation_field(X367))
        | reflexive(X367)
        | ~ relation(X367) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).

fof(c_0_12,lemma,
    ! [X747] :
      ( ( ~ well_founded_relation(X747)
        | is_well_founded_in(X747,relation_field(X747))
        | ~ relation(X747) )
      & ( ~ is_well_founded_in(X747,relation_field(X747))
        | well_founded_relation(X747)
        | ~ relation(X747) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_wellord1])])]) ).

cnf(c_0_13,plain,
    ( is_well_founded_in(X1,X2)
    | ~ well_orders(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    ( well_orders(esk120_0,relation_field(esk120_0))
    | well_ordering(esk120_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    relation(esk120_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,plain,
    ! [X98] :
      ( ( ~ connected(X98)
        | is_connected_in(X98,relation_field(X98))
        | ~ relation(X98) )
      & ( ~ is_connected_in(X98,relation_field(X98))
        | connected(X98)
        | ~ relation(X98) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d14_relat_2])])]) ).

cnf(c_0_17,plain,
    ( is_connected_in(X1,X2)
    | ~ well_orders(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,plain,
    ( reflexive(X1)
    | ~ is_reflexive_in(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    ( is_reflexive_in(X1,X2)
    | ~ well_orders(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_20,plain,
    ! [X277] :
      ( ( reflexive(X277)
        | ~ well_ordering(X277)
        | ~ relation(X277) )
      & ( transitive(X277)
        | ~ well_ordering(X277)
        | ~ relation(X277) )
      & ( antisymmetric(X277)
        | ~ well_ordering(X277)
        | ~ relation(X277) )
      & ( connected(X277)
        | ~ well_ordering(X277)
        | ~ relation(X277) )
      & ( well_founded_relation(X277)
        | ~ well_ordering(X277)
        | ~ relation(X277) )
      & ( ~ reflexive(X277)
        | ~ transitive(X277)
        | ~ antisymmetric(X277)
        | ~ connected(X277)
        | ~ well_founded_relation(X277)
        | well_ordering(X277)
        | ~ relation(X277) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).

cnf(c_0_21,lemma,
    ( well_founded_relation(X1)
    | ~ is_well_founded_in(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,negated_conjecture,
    ( well_ordering(esk120_0)
    | is_well_founded_in(esk120_0,relation_field(esk120_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_23,plain,
    ( connected(X1)
    | ~ is_connected_in(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    ( well_ordering(esk120_0)
    | is_connected_in(esk120_0,relation_field(esk120_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15])]) ).

fof(c_0_25,plain,
    ! [X65] :
      ( ( ~ antisymmetric(X65)
        | is_antisymmetric_in(X65,relation_field(X65))
        | ~ relation(X65) )
      & ( ~ is_antisymmetric_in(X65,relation_field(X65))
        | antisymmetric(X65)
        | ~ relation(X65) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])]) ).

cnf(c_0_26,plain,
    ( is_antisymmetric_in(X1,X2)
    | ~ well_orders(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_27,plain,
    ! [X99] :
      ( ( ~ transitive(X99)
        | is_transitive_in(X99,relation_field(X99))
        | ~ relation(X99) )
      & ( ~ is_transitive_in(X99,relation_field(X99))
        | transitive(X99)
        | ~ relation(X99) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_relat_2])])]) ).

cnf(c_0_28,plain,
    ( is_transitive_in(X1,X2)
    | ~ well_orders(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_29,plain,
    ( reflexive(X1)
    | ~ well_orders(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_30,plain,
    ( well_founded_relation(X1)
    | ~ well_ordering(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_31,lemma,
    ( well_ordering(esk120_0)
    | well_founded_relation(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15])]) ).

cnf(c_0_32,plain,
    ( connected(X1)
    | ~ well_ordering(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_33,negated_conjecture,
    ( well_ordering(esk120_0)
    | connected(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15])]) ).

cnf(c_0_34,plain,
    ( antisymmetric(X1)
    | ~ is_antisymmetric_in(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_35,negated_conjecture,
    ( well_ordering(esk120_0)
    | is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_15])]) ).

cnf(c_0_36,plain,
    ( transitive(X1)
    | ~ is_transitive_in(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,negated_conjecture,
    ( well_ordering(esk120_0)
    | is_transitive_in(esk120_0,relation_field(esk120_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_14]),c_0_15])]) ).

cnf(c_0_38,plain,
    ( well_ordering(X1)
    | ~ reflexive(X1)
    | ~ transitive(X1)
    | ~ antisymmetric(X1)
    | ~ connected(X1)
    | ~ well_founded_relation(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_39,negated_conjecture,
    ( reflexive(esk120_0)
    | well_ordering(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_15])]) ).

cnf(c_0_40,lemma,
    well_founded_relation(esk120_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_15])]) ).

cnf(c_0_41,negated_conjecture,
    connected(esk120_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_15])]) ).

cnf(c_0_42,negated_conjecture,
    ( well_ordering(esk120_0)
    | antisymmetric(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_15])]) ).

cnf(c_0_43,negated_conjecture,
    ( well_ordering(esk120_0)
    | transitive(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_15])]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ well_orders(esk120_0,relation_field(esk120_0))
    | ~ well_ordering(esk120_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_45,negated_conjecture,
    well_ordering(esk120_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]),c_0_15])]),c_0_42]),c_0_43]) ).

cnf(c_0_46,plain,
    ( well_orders(X1,X2)
    | ~ is_reflexive_in(X1,X2)
    | ~ is_transitive_in(X1,X2)
    | ~ is_antisymmetric_in(X1,X2)
    | ~ is_connected_in(X1,X2)
    | ~ is_well_founded_in(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_47,plain,
    ( is_reflexive_in(X1,relation_field(X1))
    | ~ reflexive(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_48,negated_conjecture,
    ~ well_orders(esk120_0,relation_field(esk120_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).

cnf(c_0_49,plain,
    ( well_orders(X1,relation_field(X1))
    | ~ reflexive(X1)
    | ~ is_well_founded_in(X1,relation_field(X1))
    | ~ is_transitive_in(X1,relation_field(X1))
    | ~ is_connected_in(X1,relation_field(X1))
    | ~ is_antisymmetric_in(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_50,negated_conjecture,
    ( ~ reflexive(esk120_0)
    | ~ is_well_founded_in(esk120_0,relation_field(esk120_0))
    | ~ is_transitive_in(esk120_0,relation_field(esk120_0))
    | ~ is_connected_in(esk120_0,relation_field(esk120_0))
    | ~ is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_15])]) ).

cnf(c_0_51,lemma,
    ( is_well_founded_in(X1,relation_field(X1))
    | ~ well_founded_relation(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_52,lemma,
    ( ~ reflexive(esk120_0)
    | ~ is_transitive_in(esk120_0,relation_field(esk120_0))
    | ~ is_connected_in(esk120_0,relation_field(esk120_0))
    | ~ is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_40]),c_0_15])]) ).

cnf(c_0_53,plain,
    ( is_connected_in(X1,relation_field(X1))
    | ~ connected(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_54,lemma,
    ( ~ reflexive(esk120_0)
    | ~ is_transitive_in(esk120_0,relation_field(esk120_0))
    | ~ is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_41]),c_0_15])]) ).

cnf(c_0_55,plain,
    ( is_antisymmetric_in(X1,relation_field(X1))
    | ~ antisymmetric(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_56,lemma,
    ( ~ reflexive(esk120_0)
    | ~ is_transitive_in(esk120_0,relation_field(esk120_0))
    | ~ antisymmetric(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_15])]) ).

cnf(c_0_57,plain,
    ( is_transitive_in(X1,relation_field(X1))
    | ~ transitive(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_58,lemma,
    ( ~ reflexive(esk120_0)
    | ~ transitive(esk120_0)
    | ~ antisymmetric(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_15])]) ).

cnf(c_0_59,plain,
    ( reflexive(X1)
    | ~ well_ordering(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_60,lemma,
    ( ~ transitive(esk120_0)
    | ~ antisymmetric(esk120_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_45]),c_0_15])]) ).

cnf(c_0_61,plain,
    ( transitive(X1)
    | ~ well_ordering(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_62,lemma,
    ~ antisymmetric(esk120_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_45]),c_0_15])]) ).

cnf(c_0_63,plain,
    ( antisymmetric(X1)
    | ~ well_ordering(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_64,lemma,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_45]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU244+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Wed Aug 23 20:03:56 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.16/0.54  start to proof: theBenchmark
% 0.76/0.88  % Version  : CSE_E---1.5
% 0.76/0.88  % Problem  : theBenchmark.p
% 0.76/0.88  % Proof found
% 0.76/0.88  % SZS status Theorem for theBenchmark.p
% 0.76/0.88  % SZS output start Proof
% See solution above
% 0.76/0.89  % Total time : 0.319000 s
% 0.76/0.89  % SZS output end Proof
% 0.76/0.89  % Total time : 0.327000 s
%------------------------------------------------------------------------------