%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN922+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 09:12:12 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   25 (  13 unt;   0 def)
%            Number of atoms       :   53 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   37 (   9   ~;   0   |;  17   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   32 (   1 sgn  29   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
    ( ! [X] :
        ( p(X)
        & q(X) )
  <=> ( ! [X] : p(X)
      & ! [X] : q(X) ) ) ).

fof(subgoal_0,plain,
    ( ! [X] :
        ( p(X)
        & q(X) )
   => ! [X] : p(X) ),
    inference(strip,[],[prove_this]) ).

fof(subgoal_1,plain,
    ( ( ! [X] :
          ( p(X)
          & q(X) )
      & ! [X] : p(X) )
   => ! [X] : q(X) ),
    inference(strip,[],[prove_this]) ).

fof(subgoal_2,plain,
    ( ( ! [X] : p(X)
      & ! [X] : q(X) )
   => ! [X] : p(X) ),
    inference(strip,[],[prove_this]) ).

fof(subgoal_3,plain,
    ( ( ! [X] : p(X)
      & ! [X] : q(X) )
   => ! [X] :
        ( p(X)
       => q(X) ) ),
    inference(strip,[],[prove_this]) ).

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

fof(normalize_0_0,plain,
    $false,
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_0]) ).

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

fof(normalize_1_0,plain,
    $false,
    inference(canonicalize,[],[negate_1_0]) ).

cnf(refute_1_0,plain,
    $false,
    inference(canonicalize,[],[normalize_1_0]) ).

fof(negate_2_0,plain,
    ~ ( ( ! [X] : p(X)
        & ! [X] : q(X) )
     => ! [X] : p(X) ),
    inference(negate,[],[subgoal_2]) ).

fof(normalize_2_0,plain,
    $false,
    inference(canonicalize,[],[negate_2_0]) ).

cnf(refute_2_0,plain,
    $false,
    inference(canonicalize,[],[normalize_2_0]) ).

fof(negate_3_0,plain,
    ~ ( ( ! [X] : p(X)
        & ! [X] : q(X) )
     => ! [X] :
          ( p(X)
         => q(X) ) ),
    inference(negate,[],[subgoal_3]) ).

fof(normalize_3_0,plain,
    ( ? [X] :
        ( ~ q(X)
        & p(X) )
    & ! [X] : p(X)
    & ! [X] : q(X) ),
    inference(canonicalize,[],[negate_3_0]) ).

fof(normalize_3_1,plain,
    ? [X] :
      ( ~ q(X)
      & p(X) ),
    inference(conjunct,[],[normalize_3_0]) ).

fof(normalize_3_2,plain,
    ( ~ q(skolemFOFtoCNF_X)
    & p(skolemFOFtoCNF_X) ),
    inference(skolemize,[],[normalize_3_1]) ).

fof(normalize_3_3,plain,
    ~ q(skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_3_2]) ).

fof(normalize_3_4,plain,
    ! [X] : q(X),
    inference(conjunct,[],[normalize_3_0]) ).

fof(normalize_3_5,plain,
    ! [X] : q(X),
    inference(specialize,[],[normalize_3_4]) ).

cnf(refute_3_0,plain,
    ~ q(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_3_3]) ).

cnf(refute_3_1,plain,
    q(X),
    inference(canonicalize,[],[normalize_3_5]) ).

cnf(refute_3_2,plain,
    q(skolemFOFtoCNF_X),
    inference(subst,[],[refute_3_1:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_3_3,plain,
    $false,
    inference(resolve,[$cnf( q(skolemFOFtoCNF_X) )],[refute_3_2,refute_3_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN922+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jul 12 02:09:42 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------