TSTP Solution File: SEU223+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU223+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 : n006.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 16:23:30 EDT 2023

% Result   : Theorem 0.74s 0.92s
% Output   : CNFRefutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  128
% Syntax   : Number of formulae    :  142 (   5 unt; 124 typ;   0 def)
%            Number of atoms       :   82 (  19 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  106 (  42   ~;  40   |;  14   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  235 ( 112   >; 123   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :  113 ( 113 usr;  12 con; 0-5 aty)
%            Number of variables   :   33 (   3 sgn;  22   !;   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_rng_restriction: ( $i * $i ) > $i ).

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

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

tff(decl_38,type,
    empty_set: $i ).

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

tff(decl_40,type,
    singleton: $i > $i ).

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

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

tff(decl_43,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(decl_60,type,
    relation_empty_yielding: $i > $o ).

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

tff(decl_62,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk7_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_75,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_76,type,
    esk15_1: $i > $i ).

tff(decl_77,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_79,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_80,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_81,type,
    esk20_1: $i > $i ).

tff(decl_82,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_83,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_84,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_85,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk27_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk31_2: ( $i * $i ) > $i ).

tff(decl_93,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_94,type,
    esk33_2: ( $i * $i ) > $i ).

tff(decl_95,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_96,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk36_2: ( $i * $i ) > $i ).

tff(decl_98,type,
    esk37_2: ( $i * $i ) > $i ).

tff(decl_99,type,
    esk38_3: ( $i * $i * $i ) > $i ).

tff(decl_100,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_101,type,
    esk40_2: ( $i * $i ) > $i ).

tff(decl_102,type,
    esk41_3: ( $i * $i * $i ) > $i ).

tff(decl_103,type,
    esk42_3: ( $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_105,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_106,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_107,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk47_1: $i > $i ).

tff(decl_109,type,
    esk48_1: $i > $i ).

tff(decl_110,type,
    esk49_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_111,type,
    esk50_3: ( $i * $i * $i ) > $i ).

tff(decl_112,type,
    esk51_3: ( $i * $i * $i ) > $i ).

tff(decl_113,type,
    esk52_3: ( $i * $i * $i ) > $i ).

tff(decl_114,type,
    esk53_3: ( $i * $i * $i ) > $i ).

tff(decl_115,type,
    esk54_1: $i > $i ).

tff(decl_116,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_117,type,
    esk56_0: $i ).

tff(decl_118,type,
    esk57_0: $i ).

tff(decl_119,type,
    esk58_1: $i > $i ).

tff(decl_120,type,
    esk59_0: $i ).

tff(decl_121,type,
    esk60_0: $i ).

tff(decl_122,type,
    esk61_0: $i ).

tff(decl_123,type,
    esk62_1: $i > $i ).

tff(decl_124,type,
    esk63_0: $i ).

tff(decl_125,type,
    esk64_0: $i ).

tff(decl_126,type,
    esk65_0: $i ).

tff(decl_127,type,
    esk66_1: $i > $i ).

tff(decl_128,type,
    esk67_3: ( $i * $i * $i ) > $i ).

tff(decl_129,type,
    esk68_3: ( $i * $i * $i ) > $i ).

tff(decl_130,type,
    esk69_2: ( $i * $i ) > $i ).

tff(decl_131,type,
    esk70_2: ( $i * $i ) > $i ).

tff(decl_132,type,
    esk71_2: ( $i * $i ) > $i ).

tff(decl_133,type,
    esk72_2: ( $i * $i ) > $i ).

tff(decl_134,type,
    esk73_2: ( $i * $i ) > $i ).

tff(decl_135,type,
    esk74_2: ( $i * $i ) > $i ).

tff(decl_136,type,
    esk75_2: ( $i * $i ) > $i ).

tff(decl_137,type,
    esk76_2: ( $i * $i ) > $i ).

tff(decl_138,type,
    esk77_1: $i > $i ).

tff(decl_139,type,
    esk78_1: $i > $i ).

tff(decl_140,type,
    esk79_3: ( $i * $i * $i ) > $i ).

tff(decl_141,type,
    esk80_0: $i ).

tff(decl_142,type,
    esk81_0: $i ).

tff(decl_143,type,
    esk82_0: $i ).

tff(decl_144,type,
    esk83_1: $i > $i ).

tff(decl_145,type,
    esk84_2: ( $i * $i ) > $i ).

fof(t70_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
       => apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).

fof(t68_funct_1,lemma,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( X2 = relation_dom_restriction(X3,X1)
          <=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
              & ! [X4] :
                  ( in(X4,relation_dom(X2))
                 => apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).

fof(fc4_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(relation_dom_restriction(X1,X2))
        & function(relation_dom_restriction(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(dt_k7_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X1)
     => relation(relation_dom_restriction(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
         => apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
    inference(assume_negation,[status(cth)],[t70_funct_1]) ).

fof(c_0_5,lemma,
    ! [X585,X586,X587,X588] :
      ( ( relation_dom(X586) = set_intersection2(relation_dom(X587),X585)
        | X586 != relation_dom_restriction(X587,X585)
        | ~ relation(X587)
        | ~ function(X587)
        | ~ relation(X586)
        | ~ function(X586) )
      & ( ~ in(X588,relation_dom(X586))
        | apply(X586,X588) = apply(X587,X588)
        | X586 != relation_dom_restriction(X587,X585)
        | ~ relation(X587)
        | ~ function(X587)
        | ~ relation(X586)
        | ~ function(X586) )
      & ( in(esk79_3(X585,X586,X587),relation_dom(X586))
        | relation_dom(X586) != set_intersection2(relation_dom(X587),X585)
        | X586 = relation_dom_restriction(X587,X585)
        | ~ relation(X587)
        | ~ function(X587)
        | ~ relation(X586)
        | ~ function(X586) )
      & ( apply(X586,esk79_3(X585,X586,X587)) != apply(X587,esk79_3(X585,X586,X587))
        | relation_dom(X586) != set_intersection2(relation_dom(X587),X585)
        | X586 = relation_dom_restriction(X587,X585)
        | ~ relation(X587)
        | ~ function(X587)
        | ~ relation(X586)
        | ~ function(X586) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).

fof(c_0_6,plain,
    ! [X308,X309] :
      ( ( relation(relation_dom_restriction(X308,X309))
        | ~ relation(X308)
        | ~ function(X308) )
      & ( function(relation_dom_restriction(X308,X309))
        | ~ relation(X308)
        | ~ function(X308) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).

fof(c_0_7,plain,
    ! [X277,X278] :
      ( ~ relation(X277)
      | relation(relation_dom_restriction(X277,X278)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).

fof(c_0_8,negated_conjecture,
    ( relation(esk82_0)
    & function(esk82_0)
    & in(esk81_0,relation_dom(relation_dom_restriction(esk82_0,esk80_0)))
    & apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_9,lemma,
    ( apply(X2,X1) = apply(X3,X1)
    | ~ in(X1,relation_dom(X2))
    | X2 != relation_dom_restriction(X3,X4)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( function(relation_dom_restriction(X1,X2))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( relation(relation_dom_restriction(X1,X2))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,lemma,
    ( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,relation_dom(relation_dom_restriction(X1,X2))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]),c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    relation(esk82_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    function(esk82_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    in(esk81_0,relation_dom(relation_dom_restriction(esk82_0,esk80_0))),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.35  % Computer : n006.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit   : 300
% 0.12/0.35  % WCLimit    : 300
% 0.12/0.35  % DateTime   : Wed Aug 23 15:15:23 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.17/0.58  start to proof: theBenchmark
% 0.74/0.92  % Version  : CSE_E---1.5
% 0.74/0.92  % Problem  : theBenchmark.p
% 0.74/0.92  % Proof found
% 0.74/0.92  % SZS status Theorem for theBenchmark.p
% 0.74/0.92  % SZS output start Proof
% See solution above
% 0.74/0.92  % Total time : 0.320000 s
% 0.74/0.92  % SZS output end Proof
% 0.74/0.92  % Total time : 0.325000 s
%------------------------------------------------------------------------------