TSTP Solution File: SYN321+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN321+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 09:01:15 EDT 2022

% Result   : Theorem 0.12s 0.32s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   29 (   7 unt;   0 def)
%            Number of atoms       :   69 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   64 (  24   ~;  19   |;   3   &)
%                                         (   6 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 1-1 aty)
%            Number of variables   :   81 (  17 sgn  44   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(church_46_3_2,conjecture,
    ? [X,Y] :
      ( ( ? [Z] : big_f(X,Z)
       => ! [Z] : big_g(X,Z) )
     => ( ! [Z] :
            ( big_g(Z,Z)
           => big_f(Z,Y) )
       => ( big_f(X,Y)
        <=> ! [Z] : big_g(X,Z) ) ) ) ).

fof(subgoal_0,plain,
    ? [X,Y] :
      ( ( ? [Z] : big_f(X,Z)
       => ! [Z] : big_g(X,Z) )
     => ( ! [Z] :
            ( big_g(Z,Z)
           => big_f(Z,Y) )
       => ( big_f(X,Y)
        <=> ! [Z] : big_g(X,Z) ) ) ),
    inference(strip,[],[church_46_3_2]) ).

fof(negate_0_0,plain,
    ~ ? [X,Y] :
        ( ( ? [Z] : big_f(X,Z)
         => ! [Z] : big_g(X,Z) )
       => ( ! [Z] :
              ( big_g(Z,Z)
             => big_f(Z,Y) )
         => ( big_f(X,Y)
          <=> ! [Z] : big_g(X,Z) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ! [X] :
        ( ! [Z] : ~ big_f(X,Z)
        | ! [Z] : big_g(X,Z) )
    & ! [X,Y] :
        ( ~ big_f(X,Y)
      <=> ! [Z] : big_g(X,Z) )
    & ! [Y,Z] :
        ( ~ big_g(Z,Z)
        | big_f(Z,Y) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [X,Y] :
      ( ~ big_f(X,Y)
    <=> ! [Z] : big_g(X,Z) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X,Y] :
      ( ~ big_f(X,Y)
    <=> ! [Z] : big_g(X,Z) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y,Z] :
      ( ( ~ big_f(X,Y)
        | ~ big_g(X,skolemFOFtoCNF_Z(X)) )
      & ( big_f(X,Y)
        | big_g(X,Z) ) ),
    inference(clausify,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ big_f(X,Y)
      | ~ big_g(X,skolemFOFtoCNF_Z(X)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Y,Z] :
      ( ~ big_g(Z,Z)
      | big_f(Z,Y) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_6,plain,
    ! [Y,Z] :
      ( ~ big_g(Z,Z)
      | big_f(Z,Y) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y,Z] :
      ( big_f(X,Y)
      | big_g(X,Z) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( ! [Z] : ~ big_f(X,Z)
      | ! [Z] : big_g(X,Z) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_9,plain,
    ! [X] :
      ( ! [Z] : ~ big_f(X,Z)
      | ! [Z] : big_g(X,Z) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X,Z,Z0] :
      ( ~ big_f(X,Z)
      | big_g(X,Z0) ),
    inference(clausify,[],[normalize_0_9]) ).

cnf(refute_0_0,plain,
    ( ~ big_f(X,Y)
    | ~ big_g(X,skolemFOFtoCNF_Z(X)) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    ( ~ big_f(X_8,X_7)
    | ~ big_g(X_8,skolemFOFtoCNF_Z(X_8)) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(X_8)),bind(Y,$fot(X_7))]]) ).

cnf(refute_0_2,plain,
    ( ~ big_g(Z,Z)
    | big_f(Z,Y) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( ~ big_g(X_6,X_6)
    | big_f(X_6,Y) ),
    inference(subst,[],[refute_0_2:[bind(Z,$fot(X_6))]]) ).

cnf(refute_0_4,plain,
    ( big_f(X,Y)
    | big_g(X,Z) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_5,plain,
    ( big_f(X_6,X_5)
    | big_g(X_6,X_6) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_6)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_6,plain,
    ( big_f(X_6,Y)
    | big_f(X_6,X_5) ),
    inference(resolve,[$cnf( big_g(X_6,X_6) )],[refute_0_5,refute_0_3]) ).

cnf(refute_0_7,plain,
    big_f(X_8,X_7),
    inference(subst,[],[refute_0_6:[bind(Y,$fot(X_7)),bind(X_5,$fot(X_7)),bind(X_6,$fot(X_8))]]) ).

cnf(refute_0_8,plain,
    ~ big_g(X_8,skolemFOFtoCNF_Z(X_8)),
    inference(resolve,[$cnf( big_f(X_8,X_7) )],[refute_0_7,refute_0_1]) ).

cnf(refute_0_9,plain,
    ~ big_g(X_10,skolemFOFtoCNF_Z(X_10)),
    inference(subst,[],[refute_0_8:[bind(X_8,$fot(X_10))]]) ).

cnf(refute_0_10,plain,
    ( ~ big_f(X,Z)
    | big_g(X,Z0) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_11,plain,
    big_f(X,Z),
    inference(subst,[],[refute_0_6:[bind(Y,$fot(Z)),bind(X_5,$fot(Z)),bind(X_6,$fot(X))]]) ).

cnf(refute_0_12,plain,
    big_g(X,Z0),
    inference(resolve,[$cnf( big_f(X,Z) )],[refute_0_11,refute_0_10]) ).

cnf(refute_0_13,plain,
    big_g(X_10,skolemFOFtoCNF_Z(X_10)),
    inference(subst,[],[refute_0_12:[bind(X,$fot(X_10)),bind(Z0,$fot(skolemFOFtoCNF_Z(X_10)))]]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( big_g(X_10,skolemFOFtoCNF_Z(X_10)) )],[refute_0_13,refute_0_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYN321+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.31  % Computer : n023.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 600
% 0.12/0.31  % DateTime : Tue Jul 12 02:51:39 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.12/0.32  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.32  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32  
% 0.12/0.32  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.33  
%------------------------------------------------------------------------------