%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU123+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 : n001.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 16:22:33 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   26 (   6 unt;  14 typ;   0 def)
%            Number of atoms       :   25 (   9 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   22 (   9   ~;   6   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  10   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   11 (   1 sgn;   8   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_28,type,
    esk1_1: $i > $i ).

tff(decl_29,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

tff(decl_33,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk7_0: $i ).

tff(decl_35,type,
    esk8_2: ( $i * $i ) > $i ).

fof(t3_xboole_1,conjecture,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

fof(d10_xboole_0,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(t2_xboole_1,lemma,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1] :
        ( subset(X1,empty_set)
       => X1 = empty_set ),
    inference(assume_negation,[status(cth)],[t3_xboole_1]) ).

fof(c_0_4,plain,
    ! [X9,X10] :
      ( ( subset(X9,X10)
        | X9 != X10 )
      & ( subset(X10,X9)
        | X9 != X10 )
      & ( ~ subset(X9,X10)
        | ~ subset(X10,X9)
        | X9 = X10 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).

fof(c_0_5,negated_conjecture,
    ( subset(esk7_0,empty_set)
    & esk7_0 != empty_set ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_6,lemma,
    ! [X41] : subset(empty_set,X41),
    inference(variable_rename,[status(thm)],[t2_xboole_1]) ).

cnf(c_0_7,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    subset(esk7_0,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,lemma,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    esk7_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU123+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 18:10:55 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.009000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.012000 s
%------------------------------------------------------------------------------