%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN407+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n014.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 09:02:10 EDT 2022

% Result   : Theorem 0.18s 0.33s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   22 (   7 unt;   0 def)
%            Number of atoms       :   61 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   63 (  24   ~;  20   |;  10   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   19 (   0 sgn  12   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(kalish241,conjecture,
    ( ! [X] :
        ( f(X)
       => ( g(X)
          | h(X) ) )
   => ( ! [Y] :
          ( f(Y)
         => g(Y) )
      | ? [Z] :
          ( f(Z)
          & h(Z) ) ) ) ).

fof(subgoal_0,plain,
    ( ( ! [X] :
          ( f(X)
         => ( g(X)
            | h(X) ) )
      & ~ ! [Y] :
            ( f(Y)
           => g(Y) ) )
   => ? [Z] :
        ( f(Z)
        & h(Z) ) ),
    inference(strip,[],[kalish241]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [X] :
            ( f(X)
           => ( g(X)
              | h(X) ) )
        & ~ ! [Y] :
              ( f(Y)
             => g(Y) ) )
     => ? [Z] :
          ( f(Z)
          & h(Z) ) ),
    inference(negate,[],[subgoal_0]) ).

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

fof(normalize_0_1,plain,
    ! [Z] :
      ( ~ f(Z)
      | ~ h(Z) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Z] :
      ( ~ f(Z)
      | ~ h(Z) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ? [Y] :
      ( ~ g(Y)
      & f(Y) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_4,plain,
    ( ~ g(skolemFOFtoCNF_Y)
    & f(skolemFOFtoCNF_Y) ),
    inference(skolemize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    f(skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X] :
      ( ~ f(X)
      | g(X)
      | h(X) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_7,plain,
    ! [X] :
      ( ~ f(X)
      | g(X)
      | h(X) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ~ g(skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    ( ~ f(Z)
    | ~ h(Z) ),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ f(skolemFOFtoCNF_Y)
    | ~ h(skolemFOFtoCNF_Y) ),
    inference(subst,[],[refute_0_0:[bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_2,plain,
    f(skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( ~ f(X)
    | g(X)
    | h(X) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    ( ~ f(skolemFOFtoCNF_Y)
    | g(skolemFOFtoCNF_Y)
    | h(skolemFOFtoCNF_Y) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_5,plain,
    ( g(skolemFOFtoCNF_Y)
    | h(skolemFOFtoCNF_Y) ),
    inference(resolve,[$cnf( f(skolemFOFtoCNF_Y) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    ~ g(skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_7,plain,
    h(skolemFOFtoCNF_Y),
    inference(resolve,[$cnf( g(skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ~ f(skolemFOFtoCNF_Y),
    inference(resolve,[$cnf( h(skolemFOFtoCNF_Y) )],[refute_0_7,refute_0_1]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( f(skolemFOFtoCNF_Y) )],[refute_0_2,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SYN407+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n014.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 20:00:49 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.33  
% 0.18/0.33  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.34  
%------------------------------------------------------------------------------