TSTP Solution File: SYN068+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN068+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 08:59:15 EDT 2022

% Result   : Theorem 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   31 (   7 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   76 (  34   ~;  22   |;  18   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   28 (   0 sgn  13   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel44_1,axiom,
    ! [X] :
      ( big_f(X)
     => ( ? [Y] :
            ( big_g(Y)
            & big_h(X,Y) )
        & ? [Y1] :
            ( big_g(Y1)
            & ~ big_h(X,Y1) ) ) ) ).

fof(pel44_2,axiom,
    ? [X] :
      ( big_j(X)
      & ! [Y] :
          ( big_g(Y)
         => big_h(X,Y) ) ) ).

fof(pel44,conjecture,
    ? [X] :
      ( big_j(X)
      & ~ big_f(X) ) ).

fof(subgoal_0,plain,
    ? [X] :
      ( big_j(X)
      & ~ big_f(X) ),
    inference(strip,[],[pel44]) ).

fof(negate_0_0,plain,
    ~ ? [X] :
        ( big_j(X)
        & ~ big_f(X) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X] :
      ( big_j(X)
      & ! [Y] :
          ( ~ big_g(Y)
          | big_h(X,Y) ) ),
    inference(canonicalize,[],[pel44_2]) ).

fof(normalize_0_1,plain,
    ( big_j(skolemFOFtoCNF_X)
    & ! [Y] :
        ( ~ big_g(Y)
        | big_h(skolemFOFtoCNF_X,Y) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Y] :
      ( ~ big_g(Y)
      | big_h(skolemFOFtoCNF_X,Y) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Y] :
      ( ~ big_g(Y)
      | big_h(skolemFOFtoCNF_X,Y) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    big_j(skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_5,plain,
    ! [X] :
      ( ~ big_j(X)
      | big_f(X) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_6,plain,
    ! [X] :
      ( ~ big_j(X)
      | big_f(X) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X] :
      ( ~ big_f(X)
      | ( ? [Y] :
            ( big_g(Y)
            & big_h(X,Y) )
        & ? [Y1] :
            ( ~ big_h(X,Y1)
            & big_g(Y1) ) ) ),
    inference(canonicalize,[],[pel44_1]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( ~ big_f(X)
      | ( ? [Y] :
            ( big_g(Y)
            & big_h(X,Y) )
        & ? [Y1] :
            ( ~ big_h(X,Y1)
            & big_g(Y1) ) ) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X] :
      ( ( ~ big_f(X)
        | ~ big_h(X,skolemFOFtoCNF_Y1(X)) )
      & ( ~ big_f(X)
        | big_g(skolemFOFtoCNF_Y(X)) )
      & ( ~ big_f(X)
        | big_g(skolemFOFtoCNF_Y1(X)) )
      & ( ~ big_f(X)
        | big_h(X,skolemFOFtoCNF_Y(X)) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X] :
      ( ~ big_f(X)
      | big_g(skolemFOFtoCNF_Y1(X)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X] :
      ( ~ big_f(X)
      | ~ big_h(X,skolemFOFtoCNF_Y1(X)) ),
    inference(conjunct,[],[normalize_0_9]) ).

cnf(refute_0_0,plain,
    ( ~ big_g(Y)
    | big_h(skolemFOFtoCNF_X,Y) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ big_g(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X))
    | big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)))]]) ).

cnf(refute_0_2,plain,
    big_j(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    ( ~ big_j(X)
    | big_f(X) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_4,plain,
    ( ~ big_j(skolemFOFtoCNF_X)
    | big_f(skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_5,plain,
    big_f(skolemFOFtoCNF_X),
    inference(resolve,[$cnf( big_j(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ big_f(X)
    | big_g(skolemFOFtoCNF_Y1(X)) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_7,plain,
    ( ~ big_f(skolemFOFtoCNF_X)
    | big_g(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_8,plain,
    big_g(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)),
    inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)) )],[refute_0_8,refute_0_1]) ).

cnf(refute_0_10,plain,
    ( ~ big_f(X)
    | ~ big_h(X,skolemFOFtoCNF_Y1(X)) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_11,plain,
    ( ~ big_f(skolemFOFtoCNF_X)
    | ~ big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_12,plain,
    ~ big_f(skolemFOFtoCNF_X),
    inference(resolve,[$cnf( big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X)) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_5,refute_0_12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN068+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n011.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jul 12 00:26:42 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------