%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN376+1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 : Thu Jul 21 09:01:54 EDT 2022

% Result   : Theorem 0.20s 0.35s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   23 (  10 unt;   0 def)
%            Number of atoms       :   46 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   48 (  25   ~;   8   |;   5   &)
%                                         (   7 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   28 (   3 sgn  16   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(x2127,conjecture,
    ( ? [X] :
      ! [Y] :
        ( big_p(Y)
      <=> big_p(X) )
   => ( ! [X] : big_p(X)
      | ! [X] : ~ big_p(X) ) ) ).

fof(subgoal_0,plain,
    ( ( ? [X] :
        ! [Y] :
          ( big_p(Y)
        <=> big_p(X) )
      & ~ ! [X] : big_p(X) )
   => ! [X] : ~ big_p(X) ),
    inference(strip,[],[x2127]) ).

fof(negate_0_0,plain,
    ~ ( ( ? [X] :
          ! [Y] :
            ( big_p(Y)
          <=> big_p(X) )
        & ~ ! [X] : big_p(X) )
     => ! [X] : ~ big_p(X) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ? [X] : ~ big_p(X)
    & ? [X] : big_p(X)
    & ? [X] :
      ! [Y] :
        ( ~ big_p(X)
      <=> ~ big_p(Y) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ? [X] : ~ big_p(X),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ~ big_p(skolemFOFtoCNF_X),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ? [X] :
    ! [Y] :
      ( ~ big_p(X)
    <=> ~ big_p(Y) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_4,plain,
    ! [Y] :
      ( ~ big_p(Y)
    <=> ~ big_p(skolemFOFtoCNF_X_2) ),
    inference(skolemize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Y] :
      ( ~ big_p(Y)
    <=> ~ big_p(skolemFOFtoCNF_X_2) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [Y] :
      ( ( ~ big_p(Y)
        | big_p(skolemFOFtoCNF_X_2) )
      & ( ~ big_p(skolemFOFtoCNF_X_2)
        | big_p(Y) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [Y] :
      ( ~ big_p(skolemFOFtoCNF_X_2)
      | big_p(Y) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ? [X] : big_p(X),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_9,plain,
    big_p(skolemFOFtoCNF_X_1),
    inference(skolemize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [Y] :
      ( ~ big_p(Y)
      | big_p(skolemFOFtoCNF_X_2) ),
    inference(conjunct,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    ~ big_p(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ big_p(skolemFOFtoCNF_X_2)
    | big_p(Y) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_2,plain,
    big_p(skolemFOFtoCNF_X_1),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_3,plain,
    ( ~ big_p(Y)
    | big_p(skolemFOFtoCNF_X_2) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_4,plain,
    ( ~ big_p(skolemFOFtoCNF_X_1)
    | big_p(skolemFOFtoCNF_X_2) ),
    inference(subst,[],[refute_0_3:[bind(Y,$fot(skolemFOFtoCNF_X_1))]]) ).

cnf(refute_0_5,plain,
    big_p(skolemFOFtoCNF_X_2),
    inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    big_p(Y),
    inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_2) )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
    big_p(skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_6:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem  : SYN376+1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 19:14:28 EDT 2022
% 0.20/0.34  % CPUTime  : 
% 0.20/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35  
% 0.20/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.35  
%------------------------------------------------------------------------------