TSTP Solution File: SYN365+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN365+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 09:01:49 EDT 2022

% Result   : Theorem 0.22s 0.44s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   36 (   8 unt;   0 def)
%            Number of atoms       :  102 (   0 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  104 (  38   ~;  29   |;  25   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   42 (   0 sgn  26   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(x2116,conjecture,
    ( ( ! [X] :
        ? [Y] :
          ( big_p(X)
         => ( big_r(X,g(h(Y)))
            & big_p(Y) ) )
      & ! [W] :
          ( big_p(W)
         => ( big_p(g(W))
            & big_p(h(W)) ) ) )
   => ! [X] :
        ( big_p(X)
       => ? [Y] :
            ( big_r(X,Y)
            & big_p(Y) ) ) ) ).

fof(subgoal_0,plain,
    ( ( ! [X] :
        ? [Y] :
          ( big_p(X)
         => ( big_r(X,g(h(Y)))
            & big_p(Y) ) )
      & ! [W] :
          ( big_p(W)
         => ( big_p(g(W))
            & big_p(h(W)) ) ) )
   => ! [X] :
        ( big_p(X)
       => ? [Y] :
            ( big_r(X,Y)
            & big_p(Y) ) ) ),
    inference(strip,[],[x2116]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [X] :
          ? [Y] :
            ( big_p(X)
           => ( big_r(X,g(h(Y)))
              & big_p(Y) ) )
        & ! [W] :
            ( big_p(W)
           => ( big_p(g(W))
              & big_p(h(W)) ) ) )
     => ! [X] :
          ( big_p(X)
         => ? [Y] :
              ( big_r(X,Y)
              & big_p(Y) ) ) ),
    inference(negate,[],[subgoal_0]) ).

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

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

fof(normalize_0_2,plain,
    ( big_p(skolemFOFtoCNF_X)
    & ! [Y] :
        ( ~ big_p(Y)
        | ~ big_r(skolemFOFtoCNF_X,Y) ) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Y] :
      ( ~ big_p(Y)
      | ~ big_r(skolemFOFtoCNF_X,Y) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Y] :
      ( ~ big_p(Y)
      | ~ big_r(skolemFOFtoCNF_X,Y) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    big_p(skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_6,plain,
    ! [X] :
      ( ~ big_p(X)
      | ? [Y] :
          ( big_p(Y)
          & big_r(X,g(h(Y))) ) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_7,plain,
    ! [X] :
      ( ~ big_p(X)
      | ? [Y] :
          ( big_p(Y)
          & big_r(X,g(h(Y))) ) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( ( ~ big_p(X)
        | big_p(skolemFOFtoCNF_Y(X)) )
      & ( ~ big_p(X)
        | big_r(X,g(h(skolemFOFtoCNF_Y(X)))) ) ),
    inference(clausify,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X] :
      ( ~ big_p(X)
      | big_r(X,g(h(skolemFOFtoCNF_Y(X)))) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [W] :
      ( ~ big_p(W)
      | ( big_p(g(W))
        & big_p(h(W)) ) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_11,plain,
    ! [W] :
      ( ~ big_p(W)
      | ( big_p(g(W))
        & big_p(h(W)) ) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [W] :
      ( ( ~ big_p(W)
        | big_p(g(W)) )
      & ( ~ big_p(W)
        | big_p(h(W)) ) ),
    inference(clausify,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [W] :
      ( ~ big_p(W)
      | big_p(g(W)) ),
    inference(conjunct,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [X] :
      ( ~ big_p(X)
      | big_p(skolemFOFtoCNF_Y(X)) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_15,plain,
    ! [W] :
      ( ~ big_p(W)
      | big_p(h(W)) ),
    inference(conjunct,[],[normalize_0_12]) ).

cnf(refute_0_0,plain,
    ( ~ big_p(Y)
    | ~ big_r(skolemFOFtoCNF_X,Y) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    ( ~ big_p(g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))))
    | ~ big_r(skolemFOFtoCNF_X,g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))) ),
    inference(subst,[],[refute_0_0:[bind(Y,$fot(g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))))]]) ).

cnf(refute_0_2,plain,
    big_p(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( ~ big_p(X)
    | big_r(X,g(h(skolemFOFtoCNF_Y(X)))) ),
    inference(canonicalize,[],[normalize_0_9]) ).

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

cnf(refute_0_5,plain,
    big_r(skolemFOFtoCNF_X,g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))),
    inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    ~ big_p(g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))),
    inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))) )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
    ( ~ big_p(W)
    | big_p(g(W)) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_8,plain,
    ( ~ big_p(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))
    | big_p(g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))) ),
    inference(subst,[],[refute_0_7:[bind(W,$fot(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))))]]) ).

cnf(refute_0_9,plain,
    ( ~ big_p(X)
    | big_p(skolemFOFtoCNF_Y(X)) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_10,plain,
    ( ~ big_p(skolemFOFtoCNF_X)
    | big_p(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_11,plain,
    big_p(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),
    inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ big_p(W)
    | big_p(h(W)) ),
    inference(canonicalize,[],[normalize_0_15]) ).

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

cnf(refute_0_14,plain,
    big_p(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
    inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) )],[refute_0_11,refute_0_13]) ).

cnf(refute_0_15,plain,
    big_p(g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))),
    inference(resolve,[$cnf( big_p(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) )],[refute_0_14,refute_0_8]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( big_p(g(h(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))) )],[refute_0_15,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SYN365+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Mon Jul 11 17:05:35 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.44  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.44  
% 0.22/0.44  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.45  
%------------------------------------------------------------------------------