TSTP Solution File: SYN059+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN059+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n022.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 08:59:06 EDT 2022

% Result   : Theorem 0.14s 0.35s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   77 (  33 unt;   0 def)
%            Number of atoms       :  218 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  215 (  74   ~;  48   |;  59   &)
%                                         (   1 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-1 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :   91 (   5 sgn  63   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel29_1,axiom,
    ? [X] : big_f(X) ).

fof(pel29_2,axiom,
    ? [Y] : big_g(Y) ).

fof(pel29,conjecture,
    ( ( ! [X] :
          ( big_f(X)
         => big_h(X) )
      & ! [U] :
          ( big_g(U)
         => big_j(U) ) )
  <=> ! [W,Y] :
        ( ( big_f(W)
          & big_g(Y) )
       => ( big_h(W)
          & big_j(Y) ) ) ) ).

fof(subgoal_0,plain,
    ( ( ! [X] :
          ( big_f(X)
         => big_h(X) )
      & ! [U] :
          ( big_g(U)
         => big_j(U) ) )
   => ! [W,Y] :
        ( ( big_f(W)
          & big_g(Y) )
       => big_h(W) ) ),
    inference(strip,[],[pel29]) ).

fof(subgoal_1,plain,
    ( ( ! [X] :
          ( big_f(X)
         => big_h(X) )
      & ! [U] :
          ( big_g(U)
         => big_j(U) ) )
   => ! [W,Y] :
        ( ( big_f(W)
          & big_g(Y)
          & big_h(W) )
       => big_j(Y) ) ),
    inference(strip,[],[pel29]) ).

fof(subgoal_2,plain,
    ( ! [W,Y] :
        ( ( big_f(W)
          & big_g(Y) )
       => ( big_h(W)
          & big_j(Y) ) )
   => ! [X] :
        ( big_f(X)
       => big_h(X) ) ),
    inference(strip,[],[pel29]) ).

fof(subgoal_3,plain,
    ( ( ! [W,Y] :
          ( ( big_f(W)
            & big_g(Y) )
         => ( big_h(W)
            & big_j(Y) ) )
      & ! [X] :
          ( big_f(X)
         => big_h(X) ) )
   => ! [U] :
        ( big_g(U)
       => big_j(U) ) ),
    inference(strip,[],[pel29]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [X] :
            ( big_f(X)
           => big_h(X) )
        & ! [U] :
            ( big_g(U)
           => big_j(U) ) )
     => ! [W,Y] :
          ( ( big_f(W)
            & big_g(Y) )
         => big_h(W) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ? [W] :
        ( ~ big_h(W)
        & big_f(W)
        & ? [Y] : big_g(Y) )
    & ! [U] :
        ( ~ big_g(U)
        | big_j(U) )
    & ! [X] :
        ( ~ big_f(X)
        | big_h(X) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ? [W] :
      ( ~ big_h(W)
      & big_f(W)
      & ? [Y] : big_g(Y) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( ~ big_h(skolemFOFtoCNF_W)
    & big_f(skolemFOFtoCNF_W)
    & ? [Y] : big_g(Y) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    big_f(skolemFOFtoCNF_W),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X] :
      ( ~ big_f(X)
      | big_h(X) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_5,plain,
    ! [X] :
      ( ~ big_f(X)
      | big_h(X) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ~ big_h(skolemFOFtoCNF_W),
    inference(conjunct,[],[normalize_0_2]) ).

cnf(refute_0_0,plain,
    big_f(skolemFOFtoCNF_W),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ big_f(X)
    | big_h(X) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    ( ~ big_f(skolemFOFtoCNF_W)
    | big_h(skolemFOFtoCNF_W) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_W))]]) ).

cnf(refute_0_3,plain,
    big_h(skolemFOFtoCNF_W),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ~ big_h(skolemFOFtoCNF_W),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( big_h(skolemFOFtoCNF_W) )],[refute_0_3,refute_0_4]) ).

fof(negate_1_0,plain,
    ~ ( ( ! [X] :
            ( big_f(X)
           => big_h(X) )
        & ! [U] :
            ( big_g(U)
           => big_j(U) ) )
     => ! [W,Y] :
          ( ( big_f(W)
            & big_g(Y)
            & big_h(W) )
         => big_j(Y) ) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ( ? [W,Y] :
        ( ~ big_j(Y)
        & big_f(W)
        & big_g(Y)
        & big_h(W) )
    & ! [U] :
        ( ~ big_g(U)
        | big_j(U) )
    & ! [X] :
        ( ~ big_f(X)
        | big_h(X) ) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ? [W,Y] :
      ( ~ big_j(Y)
      & big_f(W)
      & big_g(Y)
      & big_h(W) ),
    inference(conjunct,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ( ~ big_j(skolemFOFtoCNF_Y_2)
    & big_f(skolemFOFtoCNF_W_1)
    & big_g(skolemFOFtoCNF_Y_2)
    & big_h(skolemFOFtoCNF_W_1) ),
    inference(skolemize,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    big_g(skolemFOFtoCNF_Y_2),
    inference(conjunct,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ! [U] :
      ( ~ big_g(U)
      | big_j(U) ),
    inference(conjunct,[],[normalize_1_0]) ).

fof(normalize_1_5,plain,
    ! [U] :
      ( ~ big_g(U)
      | big_j(U) ),
    inference(specialize,[],[normalize_1_4]) ).

fof(normalize_1_6,plain,
    ~ big_j(skolemFOFtoCNF_Y_2),
    inference(conjunct,[],[normalize_1_2]) ).

cnf(refute_1_0,plain,
    big_g(skolemFOFtoCNF_Y_2),
    inference(canonicalize,[],[normalize_1_3]) ).

cnf(refute_1_1,plain,
    ( ~ big_g(U)
    | big_j(U) ),
    inference(canonicalize,[],[normalize_1_5]) ).

cnf(refute_1_2,plain,
    ( ~ big_g(skolemFOFtoCNF_Y_2)
    | big_j(skolemFOFtoCNF_Y_2) ),
    inference(subst,[],[refute_1_1:[bind(U,$fot(skolemFOFtoCNF_Y_2))]]) ).

cnf(refute_1_3,plain,
    big_j(skolemFOFtoCNF_Y_2),
    inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Y_2) )],[refute_1_0,refute_1_2]) ).

cnf(refute_1_4,plain,
    ~ big_j(skolemFOFtoCNF_Y_2),
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_5,plain,
    $false,
    inference(resolve,[$cnf( big_j(skolemFOFtoCNF_Y_2) )],[refute_1_3,refute_1_4]) ).

fof(negate_2_0,plain,
    ~ ( ! [W,Y] :
          ( ( big_f(W)
            & big_g(Y) )
         => ( big_h(W)
            & big_j(Y) ) )
     => ! [X] :
          ( big_f(X)
         => big_h(X) ) ),
    inference(negate,[],[subgoal_2]) ).

fof(normalize_2_0,plain,
    ( ? [X] :
        ( ~ big_h(X)
        & big_f(X) )
    & ! [W,Y] :
        ( ~ big_f(W)
        | ~ big_g(Y)
        | ( big_h(W)
          & big_j(Y) ) ) ),
    inference(canonicalize,[],[negate_2_0]) ).

fof(normalize_2_1,plain,
    ? [X] :
      ( ~ big_h(X)
      & big_f(X) ),
    inference(conjunct,[],[normalize_2_0]) ).

fof(normalize_2_2,plain,
    ( ~ big_h(skolemFOFtoCNF_X_1)
    & big_f(skolemFOFtoCNF_X_1) ),
    inference(skolemize,[],[normalize_2_1]) ).

fof(normalize_2_3,plain,
    big_f(skolemFOFtoCNF_X_1),
    inference(conjunct,[],[normalize_2_2]) ).

fof(normalize_2_4,plain,
    ? [Y] : big_g(Y),
    inference(canonicalize,[],[pel29_2]) ).

fof(normalize_2_5,plain,
    big_g(skolemFOFtoCNF_Y),
    inference(skolemize,[],[normalize_2_4]) ).

fof(normalize_2_6,plain,
    ! [W,Y] :
      ( ~ big_f(W)
      | ~ big_g(Y)
      | ( big_h(W)
        & big_j(Y) ) ),
    inference(conjunct,[],[normalize_2_0]) ).

fof(normalize_2_7,plain,
    ! [W,Y] :
      ( ~ big_f(W)
      | ~ big_g(Y)
      | ( big_h(W)
        & big_j(Y) ) ),
    inference(specialize,[],[normalize_2_6]) ).

fof(normalize_2_8,plain,
    ! [W,Y] :
      ( ( ~ big_f(W)
        | ~ big_g(Y)
        | big_h(W) )
      & ( ~ big_f(W)
        | ~ big_g(Y)
        | big_j(Y) ) ),
    inference(clausify,[],[normalize_2_7]) ).

fof(normalize_2_9,plain,
    ! [W,Y] :
      ( ~ big_f(W)
      | ~ big_g(Y)
      | big_h(W) ),
    inference(conjunct,[],[normalize_2_8]) ).

fof(normalize_2_10,plain,
    ~ big_h(skolemFOFtoCNF_X_1),
    inference(conjunct,[],[normalize_2_2]) ).

cnf(refute_2_0,plain,
    big_f(skolemFOFtoCNF_X_1),
    inference(canonicalize,[],[normalize_2_3]) ).

cnf(refute_2_1,plain,
    big_g(skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_2_5]) ).

cnf(refute_2_2,plain,
    ( ~ big_f(W)
    | ~ big_g(Y)
    | big_h(W) ),
    inference(canonicalize,[],[normalize_2_9]) ).

cnf(refute_2_3,plain,
    ( ~ big_f(X_2)
    | ~ big_g(skolemFOFtoCNF_Y)
    | big_h(X_2) ),
    inference(subst,[],[refute_2_2:[bind(W,$fot(X_2)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_2_4,plain,
    ( ~ big_f(X_2)
    | big_h(X_2) ),
    inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Y) )],[refute_2_1,refute_2_3]) ).

cnf(refute_2_5,plain,
    ( ~ big_f(skolemFOFtoCNF_X_1)
    | big_h(skolemFOFtoCNF_X_1) ),
    inference(subst,[],[refute_2_4:[bind(X_2,$fot(skolemFOFtoCNF_X_1))]]) ).

cnf(refute_2_6,plain,
    big_h(skolemFOFtoCNF_X_1),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X_1) )],[refute_2_0,refute_2_5]) ).

cnf(refute_2_7,plain,
    ~ big_h(skolemFOFtoCNF_X_1),
    inference(canonicalize,[],[normalize_2_10]) ).

cnf(refute_2_8,plain,
    $false,
    inference(resolve,[$cnf( big_h(skolemFOFtoCNF_X_1) )],[refute_2_6,refute_2_7]) ).

fof(negate_3_0,plain,
    ~ ( ( ! [W,Y] :
            ( ( big_f(W)
              & big_g(Y) )
           => ( big_h(W)
              & big_j(Y) ) )
        & ! [X] :
            ( big_f(X)
           => big_h(X) ) )
     => ! [U] :
          ( big_g(U)
         => big_j(U) ) ),
    inference(negate,[],[subgoal_3]) ).

fof(normalize_3_0,plain,
    ? [X] : big_f(X),
    inference(canonicalize,[],[pel29_1]) ).

fof(normalize_3_1,plain,
    big_f(skolemFOFtoCNF_X),
    inference(skolemize,[],[normalize_3_0]) ).

fof(normalize_3_2,plain,
    ( ? [U] :
        ( ~ big_j(U)
        & big_g(U) )
    & ! [X] :
        ( ~ big_f(X)
        | big_h(X) )
    & ! [W,Y] :
        ( ~ big_f(W)
        | ~ big_g(Y)
        | ( big_h(W)
          & big_j(Y) ) ) ),
    inference(canonicalize,[],[negate_3_0]) ).

fof(normalize_3_3,plain,
    ? [U] :
      ( ~ big_j(U)
      & big_g(U) ),
    inference(conjunct,[],[normalize_3_2]) ).

fof(normalize_3_4,plain,
    ( ~ big_j(skolemFOFtoCNF_U)
    & big_g(skolemFOFtoCNF_U) ),
    inference(skolemize,[],[normalize_3_3]) ).

fof(normalize_3_5,plain,
    big_g(skolemFOFtoCNF_U),
    inference(conjunct,[],[normalize_3_4]) ).

fof(normalize_3_6,plain,
    ! [W,Y] :
      ( ~ big_f(W)
      | ~ big_g(Y)
      | ( big_h(W)
        & big_j(Y) ) ),
    inference(conjunct,[],[normalize_3_2]) ).

fof(normalize_3_7,plain,
    ! [W,Y] :
      ( ~ big_f(W)
      | ~ big_g(Y)
      | ( big_h(W)
        & big_j(Y) ) ),
    inference(specialize,[],[normalize_3_6]) ).

fof(normalize_3_8,plain,
    ! [W,Y] :
      ( ( ~ big_f(W)
        | ~ big_g(Y)
        | big_h(W) )
      & ( ~ big_f(W)
        | ~ big_g(Y)
        | big_j(Y) ) ),
    inference(clausify,[],[normalize_3_7]) ).

fof(normalize_3_9,plain,
    ! [W,Y] :
      ( ~ big_f(W)
      | ~ big_g(Y)
      | big_j(Y) ),
    inference(conjunct,[],[normalize_3_8]) ).

fof(normalize_3_10,plain,
    ~ big_j(skolemFOFtoCNF_U),
    inference(conjunct,[],[normalize_3_4]) ).

cnf(refute_3_0,plain,
    big_f(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_3_1]) ).

cnf(refute_3_1,plain,
    big_g(skolemFOFtoCNF_U),
    inference(canonicalize,[],[normalize_3_5]) ).

cnf(refute_3_2,plain,
    ( ~ big_f(W)
    | ~ big_g(Y)
    | big_j(Y) ),
    inference(canonicalize,[],[normalize_3_9]) ).

cnf(refute_3_3,plain,
    ( ~ big_f(X_6)
    | ~ big_g(skolemFOFtoCNF_U)
    | big_j(skolemFOFtoCNF_U) ),
    inference(subst,[],[refute_3_2:[bind(W,$fot(X_6)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_3_4,plain,
    ( ~ big_f(X_6)
    | big_j(skolemFOFtoCNF_U) ),
    inference(resolve,[$cnf( big_g(skolemFOFtoCNF_U) )],[refute_3_1,refute_3_3]) ).

cnf(refute_3_5,plain,
    ~ big_j(skolemFOFtoCNF_U),
    inference(canonicalize,[],[normalize_3_10]) ).

cnf(refute_3_6,plain,
    ~ big_f(X_6),
    inference(resolve,[$cnf( big_j(skolemFOFtoCNF_U) )],[refute_3_4,refute_3_5]) ).

cnf(refute_3_7,plain,
    ~ big_f(skolemFOFtoCNF_X),
    inference(subst,[],[refute_3_6:[bind(X_6,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_3_8,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_3_0,refute_3_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN059+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n022.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 : Tue Jul 12 00:29:40 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  
% 0.14/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36  
%------------------------------------------------------------------------------