%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 09:05:01 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   25 (   7 unt;   0 def)
%            Number of atoms       :   63 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   62 (  24   ~;  17   |;  12   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   49 (   5 sgn  35   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(lx1,conjecture,
    ( ( r(a,b)
      & ! [X] :
          ( ? [Y] : r(X,Y)
         => q(X,X) )
      & ! [U,V] :
          ( q(U,V)
         => ! [Z] : r(Z,V) ) )
   => ? [W] :
        ( r(b,W)
        & q(W,a) ) ) ).

fof(subgoal_0,plain,
    ( ( r(a,b)
      & ! [X] :
          ( ? [Y] : r(X,Y)
         => q(X,X) )
      & ! [U,V] :
          ( q(U,V)
         => ! [Z] : r(Z,V) ) )
   => ? [W] :
        ( r(b,W)
        & q(W,a) ) ),
    inference(strip,[],[lx1]) ).

fof(negate_0_0,plain,
    ~ ( ( r(a,b)
        & ! [X] :
            ( ? [Y] : r(X,Y)
           => q(X,X) )
        & ! [U,V] :
            ( q(U,V)
           => ! [Z] : r(Z,V) ) )
     => ? [W] :
          ( r(b,W)
          & q(W,a) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( r(a,b)
    & ! [W] :
        ( ~ q(W,a)
        | ~ r(b,W) )
    & ! [X] :
        ( q(X,X)
        | ! [Y] : ~ r(X,Y) )
    & ! [U,V] :
        ( ~ q(U,V)
        | ! [Z] : r(Z,V) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [W] :
      ( ~ q(W,a)
      | ~ r(b,W) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [W] :
      ( ~ q(W,a)
      | ~ r(b,W) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    r(a,b),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_4,plain,
    ! [X] :
      ( q(X,X)
      | ! [Y] : ~ r(X,Y) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_5,plain,
    ! [X] :
      ( q(X,X)
      | ! [Y] : ~ r(X,Y) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] :
      ( ~ r(X,Y)
      | q(X,X) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [U,V] :
      ( ~ q(U,V)
      | ! [Z] : r(Z,V) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_8,plain,
    ! [U,V] :
      ( ~ q(U,V)
      | ! [Z] : r(Z,V) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [U,V,Z] :
      ( ~ q(U,V)
      | r(Z,V) ),
    inference(clausify,[],[normalize_0_8]) ).

cnf(refute_0_0,plain,
    ( ~ q(W,a)
    | ~ r(b,W) ),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ q(a,a)
    | ~ r(b,a) ),
    inference(subst,[],[refute_0_0:[bind(W,$fot(a))]]) ).

cnf(refute_0_2,plain,
    r(a,b),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ( ~ r(X,Y)
    | q(X,X) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_4,plain,
    ( ~ r(a,b)
    | q(a,a) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_5,plain,
    q(a,a),
    inference(resolve,[$cnf( r(a,b) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ q(U,V)
    | r(Z,V) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_7,plain,
    ( ~ q(a,a)
    | r(X_5,a) ),
    inference(subst,[],[refute_0_6:[bind(U,$fot(a)),bind(V,$fot(a)),bind(Z,$fot(X_5))]]) ).

cnf(refute_0_8,plain,
    r(X_5,a),
    inference(resolve,[$cnf( q(a,a) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    r(b,a),
    inference(subst,[],[refute_0_8:[bind(X_5,$fot(b))]]) ).

cnf(refute_0_10,plain,
    ~ q(a,a),
    inference(resolve,[$cnf( r(b,a) )],[refute_0_9,refute_0_1]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( q(a,a) )],[refute_0_5,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % 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 : Mon Jul 11 20:36:18 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------