%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN967+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 09:12:30 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   22 (   5 unt;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   68 (  23   ~;  18   |;  15   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   30 (   1 sgn  18   !;   7   ?)

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

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

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

fof(normalize_0_0,plain,
    ( ? [A,B] :
      ! [X] :
        ( ( ~ p(A)
          & p(X) )
        | ( ~ p(B)
          & q(X) ) )
    & ! [Y] :
        ( ~ q(Y)
        | p(Y) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ? [A,B] :
    ! [X] :
      ( ( ~ p(A)
        & p(X) )
      | ( ~ p(B)
        & q(X) ) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] :
      ( ( ~ p(skolemFOFtoCNF_A)
        & p(X) )
      | ( ~ p(skolemFOFtoCNF_B)
        & q(X) ) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ( ~ p(skolemFOFtoCNF_A)
        & p(X) )
      | ( ~ p(skolemFOFtoCNF_B)
        & q(X) ) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X] :
      ( ( ~ p(skolemFOFtoCNF_A)
        | ~ p(skolemFOFtoCNF_B) )
      & ( ~ p(skolemFOFtoCNF_A)
        | q(X) )
      & ( ~ p(skolemFOFtoCNF_B)
        | p(X) )
      & ( p(X)
        | q(X) ) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ( ~ p(skolemFOFtoCNF_A)
    | ~ p(skolemFOFtoCNF_B) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [Y] :
      ( ~ q(Y)
      | p(Y) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_7,plain,
    ! [Y] :
      ( ~ q(Y)
      | p(Y) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( p(X)
      | q(X) ),
    inference(conjunct,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    ( ~ p(skolemFOFtoCNF_A)
    | ~ p(skolemFOFtoCNF_B) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_1,plain,
    ( ~ q(Y)
    | p(Y) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_2,plain,
    ( ~ q(X_1)
    | p(X_1) ),
    inference(subst,[],[refute_0_1:[bind(Y,$fot(X_1))]]) ).

cnf(refute_0_3,plain,
    ( p(X)
    | q(X) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_4,plain,
    ( p(X_1)
    | q(X_1) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(X_1))]]) ).

cnf(refute_0_5,plain,
    p(X_1),
    inference(resolve,[$cnf( q(X_1) )],[refute_0_4,refute_0_2]) ).

cnf(refute_0_6,plain,
    p(skolemFOFtoCNF_B),
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_7,plain,
    ~ p(skolemFOFtoCNF_A),
    inference(resolve,[$cnf( p(skolemFOFtoCNF_B) )],[refute_0_6,refute_0_0]) ).

cnf(refute_0_8,plain,
    p(skolemFOFtoCNF_A),
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(skolemFOFtoCNF_A))]]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( p(skolemFOFtoCNF_A) )],[refute_0_8,refute_0_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN967+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n018.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 : Tue Jul 12 09:12:59 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------