%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET923+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 : 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 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   23 (   5 unt;   9 typ;   0 def)
%            Number of atoms       :   35 (  24 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   39 (  18   ~;  10   |;   9   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 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   :   16 (   0 sgn;  12   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    empty_set: $i ).

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

tff(decl_24,type,
    singleton: $i > $i ).

tff(decl_25,type,
    subset: ( $i * $i ) > $o ).

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(t66_zfmisc_1,conjecture,
    ! [X1,X2] :
      ~ ( set_difference(X1,singleton(X2)) = empty_set
        & X1 != empty_set
        & X1 != singleton(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).

fof(t37_xboole_1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(l4_zfmisc_1,axiom,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ~ ( set_difference(X1,singleton(X2)) = empty_set
          & X1 != empty_set
          & X1 != singleton(X2) ),
    inference(assume_negation,[status(cth)],[t66_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X8,X9] :
      ( ( set_difference(X8,X9) != empty_set
        | subset(X8,X9) )
      & ( ~ subset(X8,X9)
        | set_difference(X8,X9) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).

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

fof(c_0_6,plain,
    ! [X3,X4] :
      ( ( ~ subset(X3,singleton(X4))
        | X3 = empty_set
        | X3 = singleton(X4) )
      & ( X3 != empty_set
        | subset(X3,singleton(X4)) )
      & ( X3 != singleton(X4)
        | subset(X3,singleton(X4)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).

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

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

cnf(c_0_9,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | ~ subset(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    subset(esk3_0,singleton(esk4_0)),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    esk3_0 != singleton(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    esk3_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET923+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n004.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   : Sat Aug 26 16:14:38 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.006000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.007000 s
%------------------------------------------------------------------------------