%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET583+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/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 14:34:37 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   15 (   4 unt;   5 typ;   0 def)
%            Number of atoms       :   26 (   9 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   25 (   9   ~;   6   |;   7   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   10 (   0 sgn;   8   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_25,type,
    esk2_0: $i ).

tff(decl_26,type,
    esk3_0: $i ).

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

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

fof(c_0_2,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( subset(X1,X2)
          & subset(X2,X1) )
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[prove_extensionality]) ).

fof(c_0_3,plain,
    ! [X4,X5] :
      ( ( subset(X4,X5)
        | X4 != X5 )
      & ( subset(X5,X4)
        | X4 != X5 )
      & ( ~ subset(X4,X5)
        | ~ subset(X5,X4)
        | X4 = X5 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).

fof(c_0_4,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    & subset(esk3_0,esk2_0)
    & esk2_0 != esk3_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

cnf(c_0_5,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    subset(esk3_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    subset(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    esk2_0 != esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_9,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7])]),c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET583+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.33  % Computer : n025.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Sat Aug 26 08:33:22 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.005000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.008000 s
%------------------------------------------------------------------------------