%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET687+4 : TPTP v8.1.2. Released v2.2.0.
% 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 14:35:13 EDT 2023

% Result   : Theorem 0.16s 0.58s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   26 (   6 unt;  16 typ;   0 def)
%            Number of atoms       :   20 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   18 (   8   ~;   6   |;   2   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  14   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn;  10   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    union: ( $i * $i ) > $i ).

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

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

tff(decl_30,type,
    singleton: $i > $i ).

tff(decl_31,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_32,type,
    sum: $i > $i ).

tff(decl_33,type,
    product: $i > $i ).

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk4_0: $i ).

fof(thI01,conjecture,
    ! [X1] : subset(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI01) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

fof(c_0_2,negated_conjecture,
    ~ ! [X1] : subset(X1,X1),
    inference(assume_negation,[status(cth)],[thI01]) ).

fof(c_0_3,negated_conjecture,
    ~ subset(esk4_0,esk4_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

fof(c_0_4,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( ~ subset(X6,X7)
        | ~ member(X8,X6)
        | member(X8,X7) )
      & ( member(esk1_2(X9,X10),X9)
        | subset(X9,X10) )
      & ( ~ member(esk1_2(X9,X10),X10)
        | subset(X9,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)],[subset])])])])])]) ).

cnf(c_0_5,negated_conjecture,
    ~ subset(esk4_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    ~ member(esk1_2(esk4_0,esk4_0),esk4_0),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SET687+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.32  % Computer : n031.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Sat Aug 26 12:48:08 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.16/0.55  start to proof: theBenchmark
% 0.16/0.58  % Version  : CSE_E---1.5
% 0.16/0.58  % Problem  : theBenchmark.p
% 0.16/0.58  % Proof found
% 0.16/0.58  % SZS status Theorem for theBenchmark.p
% 0.16/0.58  % SZS output start Proof
% See solution above
% 0.16/0.58  % Total time : 0.008000 s
% 0.16/0.58  % SZS output end Proof
% 0.16/0.58  % Total time : 0.010000 s
%------------------------------------------------------------------------------