%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU123+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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  : 600s
% DateTime : Tue Jul 19 12:38:31 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   24 (  11 unt;   0 def)
%            Number of atoms       :   48 (  18 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   46 (  22   ~;  13   |;   5   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   20 (   1 sgn  16   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
    ! [A,B] :
      ( A = B
    <=> ( subset(A,B)
        & subset(B,A) ) ) ).

fof(t2_xboole_1,axiom,
    ! [A] : subset(empty_set,A) ).

fof(t3_xboole_1,conjecture,
    ! [A] :
      ( subset(A,empty_set)
     => A = empty_set ) ).

fof(subgoal_0,plain,
    ! [A] :
      ( subset(A,empty_set)
     => A = empty_set ),
    inference(strip,[],[t3_xboole_1]) ).

fof(negate_0_0,plain,
    ~ ! [A] :
        ( subset(A,empty_set)
       => A = empty_set ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A] :
      ( A != empty_set
      & subset(A,empty_set) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( skolemFOFtoCNF_A_2 != empty_set
    & subset(skolemFOFtoCNF_A_2,empty_set) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    subset(skolemFOFtoCNF_A_2,empty_set),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( A != B
    <=> ( ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(canonicalize,[],[d10_xboole_0]) ).

fof(normalize_0_4,plain,
    ! [A,B] :
      ( A != B
    <=> ( ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A,B] :
      ( ( A != B
        | subset(A,B) )
      & ( A != B
        | subset(B,A) )
      & ( ~ subset(A,B)
        | ~ subset(B,A)
        | A = B ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | ~ subset(B,A)
      | A = B ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [A] : subset(empty_set,A),
    inference(canonicalize,[],[t2_xboole_1]) ).

fof(normalize_0_8,plain,
    ! [A] : subset(empty_set,A),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    skolemFOFtoCNF_A_2 != empty_set,
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    subset(skolemFOFtoCNF_A_2,empty_set),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ subset(A,B)
    | ~ subset(B,A)
    | A = B ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ( ~ subset(empty_set,skolemFOFtoCNF_A_2)
    | ~ subset(skolemFOFtoCNF_A_2,empty_set)
    | skolemFOFtoCNF_A_2 = empty_set ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(empty_set))]]) ).

cnf(refute_0_3,plain,
    ( ~ subset(empty_set,skolemFOFtoCNF_A_2)
    | skolemFOFtoCNF_A_2 = empty_set ),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    subset(empty_set,A),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    subset(empty_set,skolemFOFtoCNF_A_2),
    inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_6,plain,
    skolemFOFtoCNF_A_2 = empty_set,
    inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_A_2) )],[refute_0_5,refute_0_3]) ).

cnf(refute_0_7,plain,
    skolemFOFtoCNF_A_2 != empty_set,
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_6,refute_0_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU123+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 20 05:37:14 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------