TSTP Solution File: SEU230+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU230+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 : n014.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 16:23:36 EDT 2023

% Result   : Theorem 0.67s 0.80s
% Output   : CNFRefutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  140
% Syntax   : Number of formulae    :  158 (  17 unt; 134 typ;   0 def)
%            Number of atoms       :   58 (  15 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :   56 (  22   ~;  23   |;   8   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  265 ( 123   >; 142   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :  123 ( 123 usr;  11 con; 0-5 aty)
%            Number of variables   :   43 (   5 sgn;  27   !;   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,
    relation: $i > $o ).

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

tff(decl_28,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_29,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_30,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

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

tff(decl_36,type,
    relation_dom: $i > $i ).

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

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

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

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

tff(decl_41,type,
    succ: $i > $i ).

tff(decl_42,type,
    singleton: $i > $i ).

tff(decl_43,type,
    empty_set: $i ).

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

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

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

tff(decl_47,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_52,type,
    subset_complement: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

tff(decl_64,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk5_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk17_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_82,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_83,type,
    esk20_1: $i > $i ).

tff(decl_84,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_86,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_87,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_88,type,
    esk25_1: $i > $i ).

tff(decl_89,type,
    esk26_2: ( $i * $i ) > $i ).

tff(decl_90,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_91,type,
    esk28_2: ( $i * $i ) > $i ).

tff(decl_92,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk31_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk32_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_96,type,
    esk33_3: ( $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk36_2: ( $i * $i ) > $i ).

tff(decl_100,type,
    esk37_2: ( $i * $i ) > $i ).

tff(decl_101,type,
    esk38_2: ( $i * $i ) > $i ).

tff(decl_102,type,
    esk39_3: ( $i * $i * $i ) > $i ).

tff(decl_103,type,
    esk40_3: ( $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk41_2: ( $i * $i ) > $i ).

tff(decl_105,type,
    esk42_2: ( $i * $i ) > $i ).

tff(decl_106,type,
    esk43_3: ( $i * $i * $i ) > $i ).

tff(decl_107,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_109,type,
    esk46_3: ( $i * $i * $i ) > $i ).

tff(decl_110,type,
    esk47_3: ( $i * $i * $i ) > $i ).

tff(decl_111,type,
    esk48_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk49_2: ( $i * $i ) > $i ).

tff(decl_113,type,
    esk50_3: ( $i * $i * $i ) > $i ).

tff(decl_114,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_115,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_116,type,
    esk53_2: ( $i * $i ) > $i ).

tff(decl_117,type,
    esk54_2: ( $i * $i ) > $i ).

tff(decl_118,type,
    esk55_1: $i > $i ).

tff(decl_119,type,
    esk56_1: $i > $i ).

tff(decl_120,type,
    esk57_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_121,type,
    esk58_3: ( $i * $i * $i ) > $i ).

tff(decl_122,type,
    esk59_3: ( $i * $i * $i ) > $i ).

tff(decl_123,type,
    esk60_3: ( $i * $i * $i ) > $i ).

tff(decl_124,type,
    esk61_3: ( $i * $i * $i ) > $i ).

tff(decl_125,type,
    esk62_1: $i > $i ).

tff(decl_126,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_127,type,
    esk64_0: $i ).

tff(decl_128,type,
    esk65_0: $i ).

tff(decl_129,type,
    esk66_1: $i > $i ).

tff(decl_130,type,
    esk67_0: $i ).

tff(decl_131,type,
    esk68_0: $i ).

tff(decl_132,type,
    esk69_0: $i ).

tff(decl_133,type,
    esk70_1: $i > $i ).

tff(decl_134,type,
    esk71_0: $i ).

tff(decl_135,type,
    esk72_0: $i ).

tff(decl_136,type,
    esk73_0: $i ).

tff(decl_137,type,
    esk74_0: $i ).

tff(decl_138,type,
    esk75_0: $i ).

tff(decl_139,type,
    esk76_1: $i > $i ).

tff(decl_140,type,
    esk77_3: ( $i * $i * $i ) > $i ).

tff(decl_141,type,
    esk78_3: ( $i * $i * $i ) > $i ).

tff(decl_142,type,
    esk79_2: ( $i * $i ) > $i ).

tff(decl_143,type,
    esk80_2: ( $i * $i ) > $i ).

tff(decl_144,type,
    esk81_2: ( $i * $i ) > $i ).

tff(decl_145,type,
    esk82_2: ( $i * $i ) > $i ).

tff(decl_146,type,
    esk83_2: ( $i * $i ) > $i ).

tff(decl_147,type,
    esk84_2: ( $i * $i ) > $i ).

tff(decl_148,type,
    esk85_2: ( $i * $i ) > $i ).

tff(decl_149,type,
    esk86_2: ( $i * $i ) > $i ).

tff(decl_150,type,
    esk87_1: $i > $i ).

tff(decl_151,type,
    esk88_1: $i > $i ).

tff(decl_152,type,
    esk89_3: ( $i * $i * $i ) > $i ).

tff(decl_153,type,
    esk90_2: ( $i * $i ) > $i ).

tff(decl_154,type,
    esk91_1: $i > $i ).

tff(decl_155,type,
    esk92_2: ( $i * $i ) > $i ).

fof(t10_ordinal1,conjecture,
    ! [X1] : in(X1,succ(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_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(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(t38_zfmisc_1,lemma,
    ! [X1,X2,X3] :
      ( subset(unordered_pair(X1,X2),X3)
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] : in(X1,succ(X1)),
    inference(assume_negation,[status(cth)],[t10_ordinal1]) ).

fof(c_0_7,plain,
    ! [X103] : succ(X103) = set_union2(X103,singleton(X103)),
    inference(variable_rename,[status(thm)],[d1_ordinal1]) ).

fof(c_0_8,lemma,
    ! [X647] : unordered_pair(X647,X647) = singleton(X647),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_9,negated_conjecture,
    ~ in(esk75_0,succ(esk75_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_10,plain,
    succ(X1) = set_union2(X1,singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X162,X163,X164,X165,X166,X167,X168,X169] :
      ( ( ~ in(X165,X164)
        | in(X165,X162)
        | in(X165,X163)
        | X164 != set_union2(X162,X163) )
      & ( ~ in(X166,X162)
        | in(X166,X164)
        | X164 != set_union2(X162,X163) )
      & ( ~ in(X166,X163)
        | in(X166,X164)
        | X164 != set_union2(X162,X163) )
      & ( ~ in(esk30_3(X167,X168,X169),X167)
        | ~ in(esk30_3(X167,X168,X169),X169)
        | X169 = set_union2(X167,X168) )
      & ( ~ in(esk30_3(X167,X168,X169),X168)
        | ~ in(esk30_3(X167,X168,X169),X169)
        | X169 = set_union2(X167,X168) )
      & ( in(esk30_3(X167,X168,X169),X169)
        | in(esk30_3(X167,X168,X169),X167)
        | in(esk30_3(X167,X168,X169),X168)
        | X169 = set_union2(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_xboole_0])])])])])]) ).

fof(c_0_13,lemma,
    ! [X552,X553,X554] :
      ( ( in(X552,X554)
        | ~ subset(unordered_pair(X552,X553),X554) )
      & ( in(X553,X554)
        | ~ subset(unordered_pair(X552,X553),X554) )
      & ( ~ in(X552,X554)
        | ~ in(X553,X554)
        | subset(unordered_pair(X552,X553),X554) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).

fof(c_0_14,plain,
    ! [X420] : subset(X420,X420),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

cnf(c_0_15,negated_conjecture,
    ~ in(esk75_0,succ(esk75_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    succ(X1) = set_union2(X1,unordered_pair(X1,X1)),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_17,plain,
    ( in(X1,X3)
    | ~ in(X1,X2)
    | X3 != set_union2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,lemma,
    ( in(X1,X2)
    | ~ subset(unordered_pair(X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    ~ in(esk75_0,set_union2(esk75_0,unordered_pair(esk75_0,esk75_0))),
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_22,lemma,
    in(X1,unordered_pair(X2,X1)),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU230+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
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Thu Aug 24 01:04:04 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.54  start to proof: theBenchmark
% 0.67/0.80  % Version  : CSE_E---1.5
% 0.67/0.80  % Problem  : theBenchmark.p
% 0.67/0.80  % Proof found
% 0.67/0.80  % SZS status Theorem for theBenchmark.p
% 0.67/0.80  % SZS output start Proof
% See solution above
% 0.67/0.81  % Total time : 0.246000 s
% 0.67/0.81  % SZS output end Proof
% 0.67/0.81  % Total time : 0.255000 s
%------------------------------------------------------------------------------