TSTP Solution File: SEU234+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU234+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 : n010.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 16:23:38 EDT 2023

% Result   : Theorem 29.08s 29.17s
% Output   : CNFRefutation 29.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  148
% Syntax   : Number of formulae    :  176 (   6 unt; 143 typ;   0 def)
%            Number of atoms       :  111 (   9 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  125 (  47   ~;  41   |;  24   &)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  271 ( 129   >; 142   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :  129 ( 129 usr;  14 con; 0-5 aty)
%            Number of variables   :   41 (   0 sgn;  28   !;   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,
    identity_relation: $i > $i ).

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

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

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

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

tff(decl_39,type,
    relation_dom: $i > $i ).

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

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

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

tff(decl_43,type,
    unordered_triple: ( $i * $i * $i ) > $i ).

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

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

tff(decl_46,type,
    empty_set: $i ).

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

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

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

tff(decl_50,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_51,type,
    cast_to_subset: $i > $i ).

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

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

tff(decl_54,type,
    relation_rng: $i > $i ).

tff(decl_55,type,
    subset_complement: ( $i * $i ) > $i ).

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

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

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

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

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

tff(decl_61,type,
    function_inverse: $i > $i ).

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

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

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

tff(decl_65,type,
    relation_empty_yielding: $i > $o ).

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

tff(decl_67,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk5_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk17_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_85,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_86,type,
    esk20_1: $i > $i ).

tff(decl_87,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_89,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_90,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_91,type,
    esk25_1: $i > $i ).

tff(decl_92,type,
    esk26_2: ( $i * $i ) > $i ).

tff(decl_93,type,
    esk27_1: $i > $i ).

tff(decl_94,type,
    esk28_2: ( $i * $i ) > $i ).

tff(decl_95,type,
    esk29_2: ( $i * $i ) > $i ).

tff(decl_96,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk32_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk33_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_100,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_101,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_102,type,
    esk36_3: ( $i * $i * $i ) > $i ).

tff(decl_103,type,
    esk37_1: $i > $i ).

tff(decl_104,type,
    esk38_1: $i > $i ).

tff(decl_105,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_106,type,
    esk40_2: ( $i * $i ) > $i ).

tff(decl_107,type,
    esk41_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk42_3: ( $i * $i * $i ) > $i ).

tff(decl_109,type,
    esk43_3: ( $i * $i * $i ) > $i ).

tff(decl_110,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_111,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk46_3: ( $i * $i * $i ) > $i ).

tff(decl_113,type,
    esk47_2: ( $i * $i ) > $i ).

tff(decl_114,type,
    esk48_2: ( $i * $i ) > $i ).

tff(decl_115,type,
    esk49_3: ( $i * $i * $i ) > $i ).

tff(decl_116,type,
    esk50_3: ( $i * $i * $i ) > $i ).

tff(decl_117,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_118,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_119,type,
    esk53_3: ( $i * $i * $i ) > $i ).

tff(decl_120,type,
    esk54_2: ( $i * $i ) > $i ).

tff(decl_121,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_122,type,
    esk56_2: ( $i * $i ) > $i ).

tff(decl_123,type,
    esk57_2: ( $i * $i ) > $i ).

tff(decl_124,type,
    esk58_1: $i > $i ).

tff(decl_125,type,
    esk59_1: $i > $i ).

tff(decl_126,type,
    esk60_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_127,type,
    esk61_3: ( $i * $i * $i ) > $i ).

tff(decl_128,type,
    esk62_3: ( $i * $i * $i ) > $i ).

tff(decl_129,type,
    esk63_3: ( $i * $i * $i ) > $i ).

tff(decl_130,type,
    esk64_3: ( $i * $i * $i ) > $i ).

tff(decl_131,type,
    esk65_1: $i > $i ).

tff(decl_132,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_133,type,
    esk67_0: $i ).

tff(decl_134,type,
    esk68_0: $i ).

tff(decl_135,type,
    esk69_0: $i ).

tff(decl_136,type,
    esk70_1: $i > $i ).

tff(decl_137,type,
    esk71_0: $i ).

tff(decl_138,type,
    esk72_0: $i ).

tff(decl_139,type,
    esk73_0: $i ).

tff(decl_140,type,
    esk74_0: $i ).

tff(decl_141,type,
    esk75_1: $i > $i ).

tff(decl_142,type,
    esk76_0: $i ).

tff(decl_143,type,
    esk77_0: $i ).

tff(decl_144,type,
    esk78_0: $i ).

tff(decl_145,type,
    esk79_0: $i ).

tff(decl_146,type,
    esk80_0: $i ).

tff(decl_147,type,
    esk81_1: $i > $i ).

tff(decl_148,type,
    esk82_3: ( $i * $i * $i ) > $i ).

tff(decl_149,type,
    esk83_3: ( $i * $i * $i ) > $i ).

tff(decl_150,type,
    esk84_2: ( $i * $i ) > $i ).

tff(decl_151,type,
    esk85_0: $i ).

tff(decl_152,type,
    esk86_2: ( $i * $i ) > $i ).

tff(decl_153,type,
    esk87_2: ( $i * $i ) > $i ).

tff(decl_154,type,
    esk88_2: ( $i * $i ) > $i ).

tff(decl_155,type,
    esk89_2: ( $i * $i ) > $i ).

tff(decl_156,type,
    esk90_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk91_2: ( $i * $i ) > $i ).

tff(decl_158,type,
    esk92_2: ( $i * $i ) > $i ).

tff(decl_159,type,
    esk93_1: $i > $i ).

tff(decl_160,type,
    esk94_1: $i > $i ).

tff(decl_161,type,
    esk95_3: ( $i * $i * $i ) > $i ).

tff(decl_162,type,
    esk96_2: ( $i * $i ) > $i ).

tff(decl_163,type,
    esk97_1: $i > $i ).

tff(decl_164,type,
    esk98_2: ( $i * $i ) > $i ).

fof(t31_ordinal1,conjecture,
    ! [X1] :
      ( ! [X2] :
          ( in(X2,X1)
         => ( ordinal(X2)
            & subset(X2,X1) ) )
     => ordinal(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).

fof(d3_ordinal1,axiom,
    ! [X1] :
      ( epsilon_connected(X1)
    <=> ! [X2,X3] :
          ~ ( in(X2,X1)
            & in(X3,X1)
            & ~ in(X2,X3)
            & X2 != X3
            & ~ in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).

fof(d2_ordinal1,axiom,
    ! [X1] :
      ( epsilon_transitive(X1)
    <=> ! [X2] :
          ( in(X2,X1)
         => subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(t24_ordinal1,lemma,
    ! [X1] :
      ( ordinal(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ~ ( ~ in(X1,X2)
              & X1 != X2
              & ~ in(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).

fof(cc2_ordinal1,axiom,
    ! [X1] :
      ( ( epsilon_transitive(X1)
        & epsilon_connected(X1) )
     => ordinal(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
        ( ! [X2] :
            ( in(X2,X1)
           => ( ordinal(X2)
              & subset(X2,X1) ) )
       => ordinal(X1) ),
    inference(assume_negation,[status(cth)],[t31_ordinal1]) ).

fof(c_0_6,plain,
    ! [X1] :
      ( epsilon_connected(X1)
    <=> ! [X2,X3] :
          ~ ( in(X2,X1)
            & in(X3,X1)
            & ~ in(X2,X3)
            & X2 != X3
            & ~ in(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[d3_ordinal1]) ).

fof(c_0_7,negated_conjecture,
    ! [X558] :
      ( ( ordinal(X558)
        | ~ in(X558,esk85_0) )
      & ( subset(X558,esk85_0)
        | ~ in(X558,esk85_0) )
      & ~ ordinal(esk85_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_5])])])])]) ).

fof(c_0_8,plain,
    ! [X146,X147,X148] :
      ( ( ~ epsilon_transitive(X146)
        | ~ in(X147,X146)
        | subset(X147,X146) )
      & ( in(esk27_1(X148),X148)
        | epsilon_transitive(X148) )
      & ( ~ subset(esk27_1(X148),X148)
        | epsilon_transitive(X148) ) ),
    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_ordinal1])])])])])]) ).

fof(c_0_9,lemma,
    ! [X1] :
      ( ordinal(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ~ ( ~ in(X1,X2)
              & X1 != X2
              & ~ in(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).

fof(c_0_10,plain,
    ! [X195,X196,X197,X198] :
      ( ( ~ epsilon_connected(X195)
        | ~ in(X196,X195)
        | ~ in(X197,X195)
        | in(X196,X197)
        | X196 = X197
        | in(X197,X196) )
      & ( in(esk37_1(X198),X198)
        | epsilon_connected(X198) )
      & ( in(esk38_1(X198),X198)
        | epsilon_connected(X198) )
      & ( ~ in(esk37_1(X198),esk38_1(X198))
        | epsilon_connected(X198) )
      & ( esk37_1(X198) != esk38_1(X198)
        | epsilon_connected(X198) )
      & ( ~ in(esk38_1(X198),esk37_1(X198))
        | epsilon_connected(X198) ) ),
    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)],[c_0_6])])])])])]) ).

fof(c_0_11,plain,
    ! [X15] :
      ( ~ epsilon_transitive(X15)
      | ~ epsilon_connected(X15)
      | ordinal(X15) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).

cnf(c_0_12,negated_conjecture,
    ( subset(X1,esk85_0)
    | ~ in(X1,esk85_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( in(esk27_1(X1),X1)
    | epsilon_transitive(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( epsilon_transitive(X1)
    | ~ subset(esk27_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_15,lemma,
    ! [X538,X539] :
      ( ~ ordinal(X538)
      | ~ ordinal(X539)
      | in(X538,X539)
      | X538 = X539
      | in(X539,X538) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_16,negated_conjecture,
    ( ordinal(X1)
    | ~ in(X1,esk85_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,plain,
    ( in(esk37_1(X1),X1)
    | epsilon_connected(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    ( ordinal(X1)
    | ~ epsilon_transitive(X1)
    | ~ epsilon_connected(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    epsilon_transitive(esk85_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    ~ ordinal(esk85_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_21,plain,
    ( in(esk38_1(X1),X1)
    | epsilon_connected(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_22,plain,
    ( epsilon_connected(X1)
    | ~ in(esk38_1(X1),esk37_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_23,lemma,
    ( in(X1,X2)
    | X1 = X2
    | in(X2,X1)
    | ~ ordinal(X1)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,plain,
    ( epsilon_connected(X1)
    | ~ in(esk37_1(X1),esk38_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_25,plain,
    ( epsilon_connected(X1)
    | esk37_1(X1) != esk38_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    ( epsilon_connected(esk85_0)
    | ordinal(esk37_1(esk85_0)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_27,negated_conjecture,
    ~ epsilon_connected(esk85_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_28,negated_conjecture,
    ( epsilon_connected(esk85_0)
    | ordinal(esk38_1(esk85_0)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_29,lemma,
    ( epsilon_connected(X1)
    | ~ ordinal(esk37_1(X1))
    | ~ ordinal(esk38_1(X1)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    ordinal(esk37_1(esk85_0)),
    inference(sr,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ordinal(esk38_1(esk85_0)),
    inference(sr,[status(thm)],[c_0_28,c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU234+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
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 18:15:51 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.60  start to proof: theBenchmark
% 29.08/29.17  % Version  : CSE_E---1.5
% 29.08/29.17  % Problem  : theBenchmark.p
% 29.08/29.17  % Proof found
% 29.08/29.17  % SZS status Theorem for theBenchmark.p
% 29.08/29.17  % SZS output start Proof
% See solution above
% 29.16/29.19  % Total time : 28.512000 s
% 29.16/29.19  % SZS output end Proof
% 29.16/29.19  % Total time : 28.521000 s
%------------------------------------------------------------------------------