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Metis---2.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET876+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Tue Jul 19 03:38:03 EDT 2022

% Result   : Theorem 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   27 (   8 unt;   0 def)
%            Number of atoms       :   62 (  31 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   66 (  31   ~;  20   |;   5   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   0 sgn  25   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
    ! [A,B] :
      ( B = singleton(A)
    <=> ! [C] :
          ( in(C,B)
        <=> C = A ) ) ).

fof(l28_zfmisc_1,axiom,
    ! [A,B] :
      ( ~ in(A,B)
     => disjoint(singleton(A),B) ) ).

fof(t17_zfmisc_1,conjecture,
    ! [A,B] :
      ( A != B
     => disjoint(singleton(A),singleton(B)) ) ).

fof(subgoal_0,plain,
    ! [A,B] :
      ( A != B
     => disjoint(singleton(A),singleton(B)) ),
    inference(strip,[],[t17_zfmisc_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B] :
        ( A != B
       => disjoint(singleton(A),singleton(B)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B] :
      ( B != singleton(A)
    <=> ? [C] :
          ( C != A
        <=> in(C,B) ) ),
    inference(canonicalize,[],[d1_tarski]) ).

fof(normalize_0_1,plain,
    ! [A,B] :
      ( B != singleton(A)
    <=> ? [C] :
          ( C != A
        <=> in(C,B) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B,C] :
      ( ( B != singleton(A)
        | C != A
        | in(C,B) )
      & ( B != singleton(A)
        | ~ in(C,B)
        | C = A )
      & ( skolemFOFtoCNF_C(A,B) != A
        | ~ in(skolemFOFtoCNF_C(A,B),B)
        | B = singleton(A) )
      & ( B = singleton(A)
        | skolemFOFtoCNF_C(A,B) = A
        | in(skolemFOFtoCNF_C(A,B),B) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B,C] :
      ( B != singleton(A)
      | ~ in(C,B)
      | C = A ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [A,B] :
      ( A != B
      & ~ disjoint(singleton(A),singleton(B)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B
    & ~ disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ~ disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [A,B] :
      ( disjoint(singleton(A),B)
      | in(A,B) ),
    inference(canonicalize,[],[l28_zfmisc_1]) ).

fof(normalize_0_8,plain,
    ! [A,B] :
      ( disjoint(singleton(A),B)
      | in(A,B) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( B != singleton(A)
    | ~ in(C,B)
    | C = A ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( singleton(A) != singleton(A)
    | ~ in(C,singleton(A))
    | C = A ),
    inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A)))]]) ).

cnf(refute_0_2,plain,
    singleton(A) = singleton(A),
    introduced(tautology,[refl,[$fot(singleton(A))]]) ).

cnf(refute_0_3,plain,
    ( ~ in(C,singleton(A))
    | C = A ),
    inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_2,refute_0_1]) ).

cnf(refute_0_4,plain,
    ( ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
    | skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B ),
    inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_5,plain,
    ~ disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
    ( disjoint(singleton(A),B)
    | in(A,B) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_7,plain,
    ( disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))
    | in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
    inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_8,plain,
    in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) )],[refute_0_7,refute_0_5]) ).

cnf(refute_0_9,plain,
    skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
    inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_8,refute_0_4]) ).

cnf(refute_0_10,plain,
    skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_9,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET876+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 08:41:32 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------