%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN382+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n006.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 09:01:57 EDT 2022

% Result   : Theorem 0.20s 0.35s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   21 (  11 unt;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   33 (  15   ~;  11   |;   4   &)
%                                         (   0 <=>;   3  =>;   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   :   43 (   5 sgn  25   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(x2134,conjecture,
    ( ! [Z] :
      ? [X] :
        ( ! [Y] : big_p(X,Y)
        | big_q(X,Z) )
   => ! [Y] :
      ? [X] :
        ( big_p(X,Y)
        | big_q(X,Y) ) ) ).

fof(subgoal_0,plain,
    ( ! [Z] :
      ? [X] :
        ( ! [Y] : big_p(X,Y)
        | big_q(X,Z) )
   => ! [Y] :
      ? [X] :
        ( big_p(X,Y)
        | big_q(X,Y) ) ),
    inference(strip,[],[x2134]) ).

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

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

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

fof(normalize_0_2,plain,
    ( ! [X] : ~ big_p(X,skolemFOFtoCNF_Y)
    & ! [X] : ~ big_q(X,skolemFOFtoCNF_Y) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X] : ~ big_p(X,skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X] : ~ big_p(X,skolemFOFtoCNF_Y),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X] : ~ big_q(X,skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_6,plain,
    ! [X] : ~ big_q(X,skolemFOFtoCNF_Y),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ( ? [X] :
      ! [Y] : big_p(X,Y)
    | ! [Z] :
      ? [X] : big_q(X,Z) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_8,plain,
    ! [Y,Z] :
      ( big_p(skolemFOFtoCNF_X,Y)
      | big_q(skolemFOFtoCNF_X_1(Z),Z) ),
    inference(clausify,[],[normalize_0_7]) ).

cnf(refute_0_0,plain,
    ~ big_p(X,skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    ~ big_p(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_2,plain,
    ~ big_q(X,skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ~ big_q(skolemFOFtoCNF_X_1(skolemFOFtoCNF_Y),skolemFOFtoCNF_Y),
    inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X_1(skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_4,plain,
    ( big_p(skolemFOFtoCNF_X,Y)
    | big_q(skolemFOFtoCNF_X_1(Z),Z) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( big_p(skolemFOFtoCNF_X,X_2)
    | big_q(skolemFOFtoCNF_X_1(skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) ),
    inference(subst,[],[refute_0_4:[bind(Y,$fot(X_2)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_6,plain,
    big_p(skolemFOFtoCNF_X,X_2),
    inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X_1(skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_3]) ).

cnf(refute_0_7,plain,
    big_p(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(subst,[],[refute_0_6:[bind(X_2,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_7,refute_0_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYN382+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 17:23:05 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.35  
% 0.20/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.35  
%------------------------------------------------------------------------------