%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET926+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 14:36:18 EDT 2023

% Result   : Theorem 0.16s 0.57s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   23 (   4 unt;   9 typ;   0 def)
%            Number of atoms       :   28 (  17 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   26 (  12   ~;   8   |;   3   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   2 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   :   18 (   0 sgn;  14   !;   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(t69_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = empty_set
      | set_difference(singleton(X1),X2) = singleton(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).

fof(l34_zfmisc_1,axiom,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = singleton(X1)
    <=> ~ in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).

fof(l36_zfmisc_1,axiom,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = empty_set
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(singleton(X1),X2) = empty_set
        | set_difference(singleton(X1),X2) = singleton(X1) ),
    inference(assume_negation,[status(cth)],[t69_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = singleton(X1)
    <=> ~ in(X1,X2) ),
    inference(fof_simplification,[status(thm)],[l34_zfmisc_1]) ).

fof(c_0_5,negated_conjecture,
    ( set_difference(singleton(esk3_0),esk4_0) != empty_set
    & set_difference(singleton(esk3_0),esk4_0) != singleton(esk3_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_6,plain,
    ! [X5,X6] :
      ( ( set_difference(singleton(X5),X6) != singleton(X5)
        | ~ in(X5,X6) )
      & ( in(X5,X6)
        | set_difference(singleton(X5),X6) = singleton(X5) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

fof(c_0_7,plain,
    ! [X7,X8] :
      ( ( set_difference(singleton(X7),X8) != empty_set
        | in(X7,X8) )
      & ( ~ in(X7,X8)
        | set_difference(singleton(X7),X8) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l36_zfmisc_1])]) ).

cnf(c_0_8,negated_conjecture,
    set_difference(singleton(esk3_0),esk4_0) != singleton(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( in(X1,X2)
    | set_difference(singleton(X1),X2) = singleton(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    set_difference(singleton(esk3_0),esk4_0) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ( set_difference(singleton(X1),X2) = empty_set
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(spm,[status(thm)],[c_0_8,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
% 0.09/0.11  % Problem    : SET926+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n031.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sat Aug 26 12:10:23 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.16/0.55  start to proof: theBenchmark
% 0.16/0.57  % Version  : CSE_E---1.5
% 0.16/0.57  % Problem  : theBenchmark.p
% 0.16/0.57  % Proof found
% 0.16/0.57  % SZS status Theorem for theBenchmark.p
% 0.16/0.57  % SZS output start Proof
% See solution above
% 0.16/0.57  % Total time : 0.006000 s
% 0.16/0.57  % SZS output end Proof
% 0.16/0.57  % Total time : 0.008000 s
%------------------------------------------------------------------------------