%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET062+3 : 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 : n021.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 14:32:37 EDT 2023

% Result   : Theorem 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   20 (  10 unt;   7 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   19 (  10   ~;   5   |;   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  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   17 (   2 sgn;  13   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk2_1: $i > $i ).

tff(decl_28,type,
    esk3_0: $i ).

fof(empty_set_defn,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

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

fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(c_0_3,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[empty_set_defn]) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] : subset(empty_set,X1),
    inference(assume_negation,[status(cth)],[prove_empty_set_subset]) ).

fof(c_0_5,plain,
    ! [X4] : ~ member(X4,empty_set),
    inference(variable_rename,[status(thm)],[c_0_3]) ).

fof(c_0_6,plain,
    ! [X5,X6,X7,X8,X9] :
      ( ( ~ subset(X5,X6)
        | ~ member(X7,X5)
        | member(X7,X6) )
      & ( member(esk1_2(X8,X9),X8)
        | subset(X8,X9) )
      & ( ~ member(esk1_2(X8,X9),X9)
        | subset(X8,X9) ) ),
    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_defn])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ~ subset(empty_set,esk3_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_8,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ~ subset(empty_set,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SET062+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 12:13:42 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.19/0.61  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.005000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.007000 s
%------------------------------------------------------------------------------