%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 14:36:17 EDT 2023

% Result   : Theorem 0.16s 0.56s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   21 (   3 unt;   9 typ;   0 def)
%            Number of atoms       :   25 (  12 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   23 (  10   ~;   8   |;   2   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   12 (   0 sgn;   8   !;   0   ?;   0   :)

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

tff(decl_23,type,
    empty_set: $i ).

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

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

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

tff(decl_27,type,
    esk1_0: $i ).

tff(decl_28,type,
    esk2_0: $i ).

tff(decl_29,type,
    esk3_0: $i ).

tff(decl_30,type,
    esk4_0: $i ).

fof(t68_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = empty_set
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).

fof(l36_zfmisc_1,axiom,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = empty_set
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).

fof(c_0_2,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(singleton(X1),X2) = empty_set
      <=> in(X1,X2) ),
    inference(assume_negation,[status(cth)],[t68_zfmisc_1]) ).

fof(c_0_3,plain,
    ! [X9,X10] :
      ( ( set_difference(singleton(X9),X10) != empty_set
        | in(X9,X10) )
      & ( ~ in(X9,X10)
        | set_difference(singleton(X9),X10) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l36_zfmisc_1])]) ).

fof(c_0_4,negated_conjecture,
    ( ( set_difference(singleton(esk3_0),esk4_0) != empty_set
      | ~ in(esk3_0,esk4_0) )
    & ( set_difference(singleton(esk3_0),esk4_0) = empty_set
      | in(esk3_0,esk4_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

cnf(c_0_5,plain,
    ( in(X1,X2)
    | set_difference(singleton(X1),X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    ( set_difference(singleton(esk3_0),esk4_0) = empty_set
    | in(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ( set_difference(singleton(esk3_0),esk4_0) != empty_set
    | ~ in(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    set_difference(singleton(esk3_0),esk4_0) != empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]) ).

cnf(c_0_10,plain,
    ( set_difference(singleton(X1),X2) = empty_set
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31  % Computer : n004.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Sat Aug 26 15:14:52 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.16/0.54  start to proof: theBenchmark
% 0.16/0.56  % Version  : CSE_E---1.5
% 0.16/0.56  % Problem  : theBenchmark.p
% 0.16/0.56  % Proof found
% 0.16/0.56  % SZS status Theorem for theBenchmark.p
% 0.16/0.56  % SZS output start Proof
% See solution above
% 0.16/0.56  % Total time : 0.005000 s
% 0.16/0.56  % SZS output end Proof
% 0.16/0.56  % Total time : 0.006000 s
%------------------------------------------------------------------------------