%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n010.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 08:58:58 EDT 2022

% Result   : Theorem 0.15s 0.37s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   24 (   4 unt;   0 def)
%            Number of atoms       :   46 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   40 (  18   ~;  14   |;   1   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   2 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   14 (   2 sgn   5   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel21_1,axiom,
    ? [X] :
      ( p
     => big_f(X) ) ).

fof(pel21_2,axiom,
    ? [X] :
      ( big_f(X)
     => p ) ).

fof(pel21,conjecture,
    ? [X] :
      ( p
    <=> big_f(X) ) ).

fof(subgoal_0,plain,
    ? [X] :
      ( p
    <=> big_f(X) ),
    inference(strip,[],[pel21]) ).

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

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

fof(normalize_0_1,plain,
    ! [X] :
      ( ~ big_f(X)
    <=> p ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] :
      ( ( ~ big_f(X)
        | ~ p )
      & ( big_f(X)
        | p ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ~ big_f(X)
      | ~ p ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( ~ p
    | ? [X] : big_f(X) ),
    inference(canonicalize,[],[pel21_1]) ).

fof(normalize_0_5,plain,
    ( ~ p
    | big_f(skolemFOFtoCNF_X) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ( p
    | ? [X] : ~ big_f(X) ),
    inference(canonicalize,[],[pel21_2]) ).

fof(normalize_0_7,plain,
    ( ~ big_f(skolemFOFtoCNF_X_1)
    | p ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( big_f(X)
      | p ),
    inference(conjunct,[],[normalize_0_2]) ).

cnf(refute_0_0,plain,
    ( ~ big_f(X)
    | ~ p ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ big_f(skolemFOFtoCNF_X)
    | ~ p ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_2,plain,
    ( ~ p
    | big_f(skolemFOFtoCNF_X) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( ~ big_f(skolemFOFtoCNF_X_1)
    | p ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    ( big_f(X)
    | p ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( big_f(skolemFOFtoCNF_X_1)
    | p ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X_1))]]) ).

cnf(refute_0_6,plain,
    p,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X_1) )],[refute_0_5,refute_0_3]) ).

cnf(refute_0_7,plain,
    big_f(skolemFOFtoCNF_X),
    inference(resolve,[$cnf( p )],[refute_0_6,refute_0_2]) ).

cnf(refute_0_8,plain,
    ~ p,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_1]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( p )],[refute_0_6,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.15  % Command  : metis --show proof --show saturation %s
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Tue Jul 12 03:02:30 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37  
% 0.15/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.37  
%------------------------------------------------------------------------------