TSTP Solution File: SET095+4 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 14:32:59 EDT 2023

% Result   : Theorem 0.19s 0.56s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   33 (   6 unt;  17 typ;   0 def)
%            Number of atoms       :   34 (   5 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   29 (  11   ~;   9   |;   4   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  14   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn;  16   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    equal_set: ( $i * $i ) > $o ).

tff(decl_25,type,
    power_set: $i > $i ).

tff(decl_26,type,
    intersection: ( $i * $i ) > $i ).

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

tff(decl_28,type,
    empty_set: $i ).

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

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

tff(decl_31,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_32,type,
    sum: $i > $i ).

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

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk4_0: $i ).

tff(decl_38,type,
    esk5_0: $i ).

fof(thI44,conjecture,
    ! [X1,X3] :
      ( member(X3,X1)
     => subset(singleton(X3),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI44) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).

fof(singleton,axiom,
    ! [X3,X1] :
      ( member(X3,singleton(X1))
    <=> X3 = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X3] :
        ( member(X3,X1)
       => subset(singleton(X3),X1) ),
    inference(assume_negation,[status(cth)],[thI44]) ).

fof(c_0_4,negated_conjecture,
    ( member(esk5_0,esk4_0)
    & ~ subset(singleton(esk5_0),esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_5,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( ~ subset(X6,X7)
        | ~ member(X8,X6)
        | member(X8,X7) )
      & ( member(esk1_2(X9,X10),X9)
        | subset(X9,X10) )
      & ( ~ member(esk1_2(X9,X10),X10)
        | subset(X9,X10) ) ),
    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)],[subset])])])])])]) ).

fof(c_0_6,plain,
    ! [X26,X27] :
      ( ( ~ member(X26,singleton(X27))
        | X26 = X27 )
      & ( X26 != X27
        | member(X26,singleton(X27)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).

cnf(c_0_7,negated_conjecture,
    ~ subset(singleton(esk5_0),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    member(esk1_2(singleton(esk5_0),esk4_0),singleton(esk5_0)),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ~ member(esk1_2(singleton(esk5_0),esk4_0),esk4_0),
    inference(spm,[status(thm)],[c_0_7,c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    esk1_2(singleton(esk5_0),esk4_0) = esk5_0,
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    member(esk5_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat Aug 26 14:35:39 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.56  % Version  : CSE_E---1.5
% 0.19/0.56  % Problem  : theBenchmark.p
% 0.19/0.56  % Proof found
% 0.19/0.56  % SZS status Theorem for theBenchmark.p
% 0.19/0.56  % SZS output start Proof
% See solution above
% 0.19/0.57  % Total time : 0.007000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.010000 s
%------------------------------------------------------------------------------