TSTP Solution File: SET086+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 14:32:55 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   54 (   6 unt;  40 typ;   0 def)
%            Number of atoms       :   32 (  21 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   32 (  14   ~;  10   |;   8   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  32   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   35 (  35 usr;   8 con; 0-3 aty)
%            Number of variables   :   15 (   0 sgn;   5   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    subclass: ( $i * $i ) > $o ).

tff(decl_23,type,
    member: ( $i * $i ) > $o ).

tff(decl_24,type,
    universal_class: $i ).

tff(decl_25,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_26,type,
    singleton: $i > $i ).

tff(decl_27,type,
    ordered_pair: ( $i * $i ) > $i ).

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

tff(decl_29,type,
    first: $i > $i ).

tff(decl_30,type,
    second: $i > $i ).

tff(decl_31,type,
    element_relation: $i ).

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

tff(decl_33,type,
    complement: $i > $i ).

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

tff(decl_35,type,
    null_class: $i ).

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

tff(decl_37,type,
    rotate: $i > $i ).

tff(decl_38,type,
    flip: $i > $i ).

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

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

tff(decl_41,type,
    successor_relation: $i ).

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

tff(decl_43,type,
    range_of: $i > $i ).

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

tff(decl_45,type,
    inductive: $i > $o ).

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

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

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

tff(decl_49,type,
    identity_relation: $i ).

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

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

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

tff(decl_53,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk2_0: $i ).

tff(decl_55,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk4_1: $i > $i ).

tff(decl_57,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk6_1: $i > $i ).

tff(decl_59,type,
    esk7_0: $i ).

tff(decl_60,type,
    esk8_0: $i ).

tff(decl_61,type,
    esk9_1: $i > $i ).

fof(member_of_substitution,conjecture,
    ! [X1] :
    ? [X3] :
      ( ( member(X3,universal_class)
        & X1 = singleton(X3) )
      | ( ~ ? [X2] :
              ( member(X2,universal_class)
              & X1 = singleton(X2) )
        & X3 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_substitution) ).

fof(singleton_set_defn,axiom,
    ! [X1] : singleton(X1) = unordered_pair(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).

fof(c_0_2,negated_conjecture,
    ~ ! [X1] :
      ? [X3] :
        ( ( member(X3,universal_class)
          & X1 = singleton(X3) )
        | ( ~ ? [X2] :
                ( member(X2,universal_class)
                & X1 = singleton(X2) )
          & X3 = X1 ) ),
    inference(assume_negation,[status(cth)],[member_of_substitution]) ).

fof(c_0_3,negated_conjecture,
    ! [X108] :
      ( ( ~ member(X108,universal_class)
        | esk8_0 != singleton(X108) )
      & ( member(esk9_1(X108),universal_class)
        | X108 != esk8_0 )
      & ( esk8_0 = singleton(esk9_1(X108))
        | X108 != esk8_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).

fof(c_0_4,plain,
    ! [X24] : singleton(X24) = unordered_pair(X24,X24),
    inference(variable_rename,[status(thm)],[singleton_set_defn]) ).

cnf(c_0_5,negated_conjecture,
    ( esk8_0 = singleton(esk9_1(X1))
    | X1 != esk8_0 ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,plain,
    singleton(X1) = unordered_pair(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ( ~ member(X1,universal_class)
    | esk8_0 != singleton(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_8,negated_conjecture,
    ( member(esk9_1(X1),universal_class)
    | X1 != esk8_0 ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_9,negated_conjecture,
    ( esk8_0 = unordered_pair(esk9_1(X1),esk9_1(X1))
    | X1 != esk8_0 ),
    inference(rw,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( esk8_0 != unordered_pair(X1,X1)
    | ~ member(X1,universal_class) ),
    inference(rw,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    member(esk9_1(esk8_0),universal_class),
    inference(er,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    unordered_pair(esk9_1(esk8_0),esk9_1(esk8_0)) = esk8_0,
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n025.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
% 0.20/0.34  % CPULimit   : 300
% 0.20/0.34  % WCLimit    : 300
% 0.20/0.34  % DateTime   : Sat Aug 26 12:09:52 EDT 2023
% 0.20/0.34  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.017000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.021000 s
%------------------------------------------------------------------------------