TSTP Solution File: SYN920+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN920+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 09:12:12 EDT 2022

% Result   : Theorem 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   42 (   7 unt;   0 def)
%            Number of atoms       :  158 (   0 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  175 (  59   ~;  63   |;  34   &)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   38 (   0 sgn  24   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
    ( ( ( ! [X] :
            ( ( f(X)
              & g(X) )
           => h(X) )
       => ? [X] :
            ( f(X)
            & ~ g(X) ) )
      & ( ! [W] :
            ( f(W)
           => g(W) )
        | ! [Z] :
            ( f(Z)
           => h(Z) ) ) )
   => ( ! [R] :
          ( ( f(R)
            & h(R) )
         => g(R) )
     => ? [V] :
          ( f(V)
          & g(V)
          & ~ h(V) ) ) ) ).

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

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

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

fof(normalize_0_1,plain,
    ( ? [X] :
        ( ~ g(X)
        & f(X) )
    | ? [X] :
        ( ~ h(X)
        & f(X)
        & g(X) ) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( ( ~ g(skolemFOFtoCNF_X)
      | ~ h(skolemFOFtoCNF_X_1) )
    & ( ~ g(skolemFOFtoCNF_X)
      | f(skolemFOFtoCNF_X_1) )
    & ( ~ g(skolemFOFtoCNF_X)
      | g(skolemFOFtoCNF_X_1) )
    & ( ~ h(skolemFOFtoCNF_X_1)
      | f(skolemFOFtoCNF_X) )
    & ( f(skolemFOFtoCNF_X)
      | f(skolemFOFtoCNF_X_1) )
    & ( f(skolemFOFtoCNF_X)
      | g(skolemFOFtoCNF_X_1) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ~ g(skolemFOFtoCNF_X)
    | ~ h(skolemFOFtoCNF_X_1) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [V] :
      ( ~ f(V)
      | ~ g(V)
      | h(V) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_5,plain,
    ! [V] :
      ( ~ f(V)
      | ~ g(V)
      | h(V) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ( ~ g(skolemFOFtoCNF_X)
    | g(skolemFOFtoCNF_X_1) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_7,plain,
    ! [R] :
      ( ~ f(R)
      | ~ h(R)
      | g(R) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_8,plain,
    ! [R] :
      ( ~ f(R)
      | ~ h(R)
      | g(R) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ( ~ h(skolemFOFtoCNF_X_1)
    | f(skolemFOFtoCNF_X) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_10,plain,
    ( f(skolemFOFtoCNF_X)
    | f(skolemFOFtoCNF_X_1) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_11,plain,
    ( f(skolemFOFtoCNF_X)
    | g(skolemFOFtoCNF_X_1) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_12,plain,
    ( ! [W] :
        ( ~ f(W)
        | g(W) )
    | ! [Z] :
        ( ~ f(Z)
        | h(Z) ) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_13,plain,
    ! [W,Z] :
      ( ~ f(W)
      | ~ f(Z)
      | g(W)
      | h(Z) ),
    inference(clausify,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ( ~ g(skolemFOFtoCNF_X)
    | f(skolemFOFtoCNF_X_1) ),
    inference(conjunct,[],[normalize_0_2]) ).

cnf(refute_0_0,plain,
    ( ~ g(skolemFOFtoCNF_X)
    | ~ h(skolemFOFtoCNF_X_1) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ f(V)
    | ~ g(V)
    | h(V) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    ( ~ f(skolemFOFtoCNF_X_1)
    | ~ g(skolemFOFtoCNF_X_1)
    | h(skolemFOFtoCNF_X_1) ),
    inference(subst,[],[refute_0_1:[bind(V,$fot(skolemFOFtoCNF_X_1))]]) ).

cnf(refute_0_3,plain,
    ( ~ g(skolemFOFtoCNF_X)
    | g(skolemFOFtoCNF_X_1) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_4,plain,
    ( ~ f(R)
    | ~ h(R)
    | g(R) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( ~ f(skolemFOFtoCNF_X)
    | ~ h(skolemFOFtoCNF_X)
    | g(skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_0_4:[bind(R,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_6,plain,
    ( ~ h(skolemFOFtoCNF_X_1)
    | f(skolemFOFtoCNF_X) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_7,plain,
    ( f(skolemFOFtoCNF_X)
    | f(skolemFOFtoCNF_X_1) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_8,plain,
    ( f(skolemFOFtoCNF_X)
    | g(skolemFOFtoCNF_X_1) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_9,plain,
    ( ~ f(skolemFOFtoCNF_X_1)
    | f(skolemFOFtoCNF_X)
    | h(skolemFOFtoCNF_X_1) ),
    inference(resolve,[$cnf( g(skolemFOFtoCNF_X_1) )],[refute_0_8,refute_0_2]) ).

cnf(refute_0_10,plain,
    ( f(skolemFOFtoCNF_X)
    | h(skolemFOFtoCNF_X_1) ),
    inference(resolve,[$cnf( f(skolemFOFtoCNF_X_1) )],[refute_0_7,refute_0_9]) ).

cnf(refute_0_11,plain,
    f(skolemFOFtoCNF_X),
    inference(resolve,[$cnf( h(skolemFOFtoCNF_X_1) )],[refute_0_10,refute_0_6]) ).

cnf(refute_0_12,plain,
    ( ~ f(W)
    | ~ f(Z)
    | g(W)
    | h(Z) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_13,plain,
    ( ~ f(skolemFOFtoCNF_X)
    | g(skolemFOFtoCNF_X)
    | h(skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_0_12:[bind(W,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_14,plain,
    ( g(skolemFOFtoCNF_X)
    | h(skolemFOFtoCNF_X) ),
    inference(resolve,[$cnf( f(skolemFOFtoCNF_X) )],[refute_0_11,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ f(skolemFOFtoCNF_X)
    | g(skolemFOFtoCNF_X) ),
    inference(resolve,[$cnf( h(skolemFOFtoCNF_X) )],[refute_0_14,refute_0_5]) ).

cnf(refute_0_16,plain,
    g(skolemFOFtoCNF_X),
    inference(resolve,[$cnf( f(skolemFOFtoCNF_X) )],[refute_0_11,refute_0_15]) ).

cnf(refute_0_17,plain,
    g(skolemFOFtoCNF_X_1),
    inference(resolve,[$cnf( g(skolemFOFtoCNF_X) )],[refute_0_16,refute_0_3]) ).

cnf(refute_0_18,plain,
    ( ~ f(skolemFOFtoCNF_X_1)
    | h(skolemFOFtoCNF_X_1) ),
    inference(resolve,[$cnf( g(skolemFOFtoCNF_X_1) )],[refute_0_17,refute_0_2]) ).

cnf(refute_0_19,plain,
    ( ~ g(skolemFOFtoCNF_X)
    | f(skolemFOFtoCNF_X_1) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_20,plain,
    f(skolemFOFtoCNF_X_1),
    inference(resolve,[$cnf( g(skolemFOFtoCNF_X) )],[refute_0_16,refute_0_19]) ).

cnf(refute_0_21,plain,
    h(skolemFOFtoCNF_X_1),
    inference(resolve,[$cnf( f(skolemFOFtoCNF_X_1) )],[refute_0_20,refute_0_18]) ).

cnf(refute_0_22,plain,
    ~ g(skolemFOFtoCNF_X),
    inference(resolve,[$cnf( h(skolemFOFtoCNF_X_1) )],[refute_0_21,refute_0_0]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( g(skolemFOFtoCNF_X) )],[refute_0_16,refute_0_22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYN920+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 21:41:59 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------