%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN360+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 09:01:46 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   20 (  11 unt;   0 def)
%            Number of atoms       :   37 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   28 (  11   ~;   6   |;   5   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   53 (   5 sgn  31   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(x2111,conjecture,
    ( ( ! [X] :
          ( ? [Y] : big_p(X,Y)
         => ! [Y] : big_q(X,Y) )
      & ! [Z] :
        ? [Y] : big_p(Z,Y) )
   => ! [Y,X] : big_q(X,Y) ) ).

fof(subgoal_0,plain,
    ( ( ! [X] :
          ( ? [Y] : big_p(X,Y)
         => ! [Y] : big_q(X,Y) )
      & ! [Z] :
        ? [Y] : big_p(Z,Y) )
   => ! [Y,X] : big_q(X,Y) ),
    inference(strip,[],[x2111]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [X] :
            ( ? [Y] : big_p(X,Y)
           => ! [Y] : big_q(X,Y) )
        & ! [Z] :
          ? [Y] : big_p(Z,Y) )
     => ! [Y,X] : big_q(X,Y) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ? [X,Y] : ~ big_q(X,Y)
    & ! [X] :
        ( ! [Y] : ~ big_p(X,Y)
        | ! [Y] : big_q(X,Y) )
    & ! [Z] :
      ? [Y] : big_p(Z,Y) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ? [X,Y] : ~ big_q(X,Y),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ~ big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Z] :
    ? [Y] : big_p(Z,Y),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_4,plain,
    ! [Z] :
    ? [Y] : big_p(Z,Y),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Z] : big_p(Z,skolemFOFtoCNF_Y_1(Z)),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X] :
      ( ! [Y] : ~ big_p(X,Y)
      | ! [Y] : big_q(X,Y) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_7,plain,
    ! [X] :
      ( ! [Y] : ~ big_p(X,Y)
      | ! [Y] : big_q(X,Y) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X,Y,Y0] :
      ( ~ big_p(X,Y)
      | big_q(X,Y0) ),
    inference(clausify,[],[normalize_0_7]) ).

cnf(refute_0_0,plain,
    ~ big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    big_p(Z,skolemFOFtoCNF_Y_1(Z)),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    big_p(X_1,skolemFOFtoCNF_Y_1(X_1)),
    inference(subst,[],[refute_0_1:[bind(Z,$fot(X_1))]]) ).

cnf(refute_0_3,plain,
    ( ~ big_p(X,Y)
    | big_q(X,Y0) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_4,plain,
    ( ~ big_p(X_1,skolemFOFtoCNF_Y_1(X_1))
    | big_q(X_1,X_3) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1(X_1))),bind(Y0,$fot(X_3))]]) ).

cnf(refute_0_5,plain,
    big_q(X_1,X_3),
    inference(resolve,[$cnf( big_p(X_1,skolemFOFtoCNF_Y_1(X_1)) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(skolemFOFtoCNF_X)),bind(X_3,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_6,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN360+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n010.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 16:24:45 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------