%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN044+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n022.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 08:58:51 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   37 (  14 unt;   0 def)
%            Number of atoms       :   70 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   56 (  23   ~;  18   |;   7   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of predicates  :    4 (   3 usr;   4 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0 sgn   0   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel10_1,axiom,
    ( q
   => r ) ).

fof(pel10_2,axiom,
    ( r
   => ( p
      & q ) ) ).

fof(pel10_3,axiom,
    ( p
   => ( q
      | r ) ) ).

fof(pel10,conjecture,
    ( p
  <=> q ) ).

fof(subgoal_0,plain,
    ( p
   => q ),
    inference(strip,[],[pel10]) ).

fof(subgoal_1,plain,
    ( q
   => p ),
    inference(strip,[],[pel10]) ).

fof(negate_0_0,plain,
    ~ ( p
     => q ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ p
    | q
    | r ),
    inference(canonicalize,[],[pel10_3]) ).

fof(normalize_0_1,plain,
    ( ~ q
    & p ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_2,plain,
    p,
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ~ q,
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_4,plain,
    ( ~ r
    | ( p
      & q ) ),
    inference(canonicalize,[],[pel10_2]) ).

fof(normalize_0_5,plain,
    ( ( ~ r
      | p )
    & ( ~ r
      | q ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ( ~ r
    | q ),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ~ p
    | q
    | r ),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    p,
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_2,plain,
    ( q
    | r ),
    inference(resolve,[$cnf( p )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ~ q,
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_4,plain,
    r,
    inference(resolve,[$cnf( q )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ r
    | q ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
    ~ r,
    inference(resolve,[$cnf( q )],[refute_0_5,refute_0_3]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( r )],[refute_0_4,refute_0_6]) ).

fof(negate_1_0,plain,
    ~ ( q
     => p ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ( ~ r
    | ( p
      & q ) ),
    inference(canonicalize,[],[pel10_2]) ).

fof(normalize_1_1,plain,
    ( ( ~ r
      | p )
    & ( ~ r
      | q ) ),
    inference(clausify,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ( ~ r
    | p ),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ( ~ q
    | r ),
    inference(canonicalize,[],[pel10_1]) ).

fof(normalize_1_4,plain,
    ( ~ p
    & q ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_5,plain,
    q,
    inference(conjunct,[],[normalize_1_4]) ).

fof(normalize_1_6,plain,
    ~ p,
    inference(conjunct,[],[normalize_1_4]) ).

cnf(refute_1_0,plain,
    ( ~ r
    | p ),
    inference(canonicalize,[],[normalize_1_2]) ).

cnf(refute_1_1,plain,
    ( ~ q
    | r ),
    inference(canonicalize,[],[normalize_1_3]) ).

cnf(refute_1_2,plain,
    q,
    inference(canonicalize,[],[normalize_1_5]) ).

cnf(refute_1_3,plain,
    r,
    inference(resolve,[$cnf( q )],[refute_1_2,refute_1_1]) ).

cnf(refute_1_4,plain,
    p,
    inference(resolve,[$cnf( r )],[refute_1_3,refute_1_0]) ).

cnf(refute_1_5,plain,
    ~ p,
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_6,plain,
    $false,
    inference(resolve,[$cnf( p )],[refute_1_4,refute_1_5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN044+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul 11 23:35:55 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------