%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 08:58:59 EDT 2022

% Result   : Theorem 0.16s 0.37s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   27 (  18 unt;   0 def)
%            Number of atoms       :   50 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   43 (  20   ~;   0   |;   8   &)
%                                         (  10 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   2 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   27 (   4 sgn  21   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel22,conjecture,
    ( ! [X] :
        ( p
      <=> big_f(X) )
   => ( p
    <=> ! [X1] : big_f(X1) ) ) ).

fof(subgoal_0,plain,
    ( ( ! [X] :
          ( p
        <=> big_f(X) )
      & p )
   => ! [X1] : big_f(X1) ),
    inference(strip,[],[pel22]) ).

fof(subgoal_1,plain,
    ( ( ! [X] :
          ( p
        <=> big_f(X) )
      & ! [X1] : big_f(X1) )
   => p ),
    inference(strip,[],[pel22]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [X] :
            ( p
          <=> big_f(X) )
        & p )
     => ! [X1] : big_f(X1) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( p
    & ? [X1] : ~ big_f(X1)
    & ! [X] :
        ( ~ big_f(X)
      <=> ~ p ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ? [X1] : ~ big_f(X1),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ~ big_f(skolemFOFtoCNF_X1),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ~ big_f(X)
    <=> ~ p ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_4,plain,
    p,
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_5,plain,
    ! [X] : big_f(X),
    inference(simplify,[],[normalize_0_3,normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X] : big_f(X),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ~ big_f(skolemFOFtoCNF_X1),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    big_f(X),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    big_f(skolemFOFtoCNF_X1),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_3,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X1) )],[refute_0_2,refute_0_0]) ).

fof(negate_1_0,plain,
    ~ ( ( ! [X] :
            ( p
          <=> big_f(X) )
        & ! [X1] : big_f(X1) )
     => p ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ( ~ p
    & ! [X] :
        ( ~ big_f(X)
      <=> ~ p )
    & ! [X1] : big_f(X1) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ! [X1] : big_f(X1),
    inference(conjunct,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ! [X1] : big_f(X1),
    inference(specialize,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [X] :
      ( ~ big_f(X)
    <=> ~ p ),
    inference(conjunct,[],[normalize_1_0]) ).

fof(normalize_1_4,plain,
    ~ p,
    inference(conjunct,[],[normalize_1_0]) ).

fof(normalize_1_5,plain,
    ! [X] : ~ big_f(X),
    inference(simplify,[],[normalize_1_3,normalize_1_4]) ).

fof(normalize_1_6,plain,
    ! [X] : ~ big_f(X),
    inference(specialize,[],[normalize_1_5]) ).

cnf(refute_1_0,plain,
    big_f(X1),
    inference(canonicalize,[],[normalize_1_2]) ).

cnf(refute_1_1,plain,
    ~ big_f(X),
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_2,plain,
    ~ big_f(X1),
    inference(subst,[],[refute_1_1:[bind(X,$fot(X1))]]) ).

cnf(refute_1_3,plain,
    $false,
    inference(resolve,[$cnf( big_f(X1) )],[refute_1_0,refute_1_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.15  % Command  : metis --show proof --show saturation %s
% 0.16/0.36  % Computer : n008.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 600
% 0.16/0.36  % DateTime : Mon Jul 11 15:36:08 EDT 2022
% 0.16/0.37  % CPUTime  : 
% 0.16/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.16/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.37  
% 0.16/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.16/0.37  
%------------------------------------------------------------------------------