%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU144+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n007.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 16:22:44 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   29 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :   63 (  16 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   66 (  25   ~;  29   |;   6   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (   0 sgn;  21   !;   0   ?;   0   :)

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

tff(decl_23,type,
    singleton: $i > $i ).

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

tff(decl_25,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_26,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk3_0: $i ).

tff(decl_28,type,
    esk4_0: $i ).

fof(l2_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(singleton(X1),X2)
      <=> in(X1,X2) ),
    inference(assume_negation,[status(cth)],[l2_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ( ~ subset(X13,X14)
        | ~ in(X15,X13)
        | in(X15,X14) )
      & ( in(esk2_2(X16,X17),X16)
        | subset(X16,X17) )
      & ( ~ in(esk2_2(X16,X17),X17)
        | subset(X16,X17) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ( ( ~ subset(singleton(esk3_0),esk4_0)
      | ~ in(esk3_0,esk4_0) )
    & ( subset(singleton(esk3_0),esk4_0)
      | in(esk3_0,esk4_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_6,plain,
    ! [X6,X7,X8,X9,X10,X11] :
      ( ( ~ in(X8,X7)
        | X8 = X6
        | X7 != singleton(X6) )
      & ( X9 != X6
        | in(X9,X7)
        | X7 != singleton(X6) )
      & ( ~ in(esk1_2(X10,X11),X11)
        | esk1_2(X10,X11) != X10
        | X11 = singleton(X10) )
      & ( in(esk1_2(X10,X11),X11)
        | esk1_2(X10,X11) = X10
        | X11 = singleton(X10) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).

cnf(c_0_7,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    ( subset(singleton(esk3_0),esk4_0)
    | in(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    ( in(esk3_0,esk4_0)
    | in(X1,esk4_0)
    | ~ in(X1,singleton(esk3_0)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).

cnf(c_0_13,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( in(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_15,negated_conjecture,
    ( ~ subset(singleton(esk3_0),esk4_0)
    | ~ in(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,plain,
    ( subset(X1,X2)
    | ~ in(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_18,plain,
    ( esk2_2(singleton(X1),X2) = X1
    | subset(singleton(X1),X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    ~ subset(singleton(esk3_0),esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).

cnf(c_0_20,plain,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU144+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.36  % Computer : n007.cluster.edu
% 0.17/0.36  % Model    : x86_64 x86_64
% 0.17/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36  % Memory   : 8042.1875MB
% 0.17/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36  % CPULimit   : 300
% 0.17/0.36  % WCLimit    : 300
% 0.17/0.36  % DateTime   : Wed Aug 23 14:43:54 EDT 2023
% 0.17/0.36  % CPUTime  : 
% 0.21/0.59  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 : 0.008000 s
%------------------------------------------------------------------------------