TSTP Solution File: SYN333+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 09:01:25 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   25 (  10 unt;   0 def)
%            Number of atoms       :   82 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   99 (  42   ~;  31   |;  20   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   61 (   7 sgn  25   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(church_46_14_5,conjecture,
    ? [X,Y] :
    ! [Z] :
      ( big_f(X,Y)
     => ( big_f(Y,Z)
        & big_f(Z,Z)
        & ( ( big_f(X,Y)
            & big_g(X,Y) )
         => ( big_g(X,Z)
            & big_g(Z,Z) ) ) ) ) ).

fof(subgoal_0,plain,
    ? [X,Y] :
    ! [Z] :
      ( big_f(X,Y)
     => ( big_f(Y,Z)
        & big_f(Z,Z)
        & ( ( big_f(X,Y)
            & big_g(X,Y) )
         => ( big_g(X,Z)
            & big_g(Z,Z) ) ) ) ),
    inference(strip,[],[church_46_14_5]) ).

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

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

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

fof(normalize_0_2,plain,
    ! [X,Y] : big_f(X,Y),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_3,plain,
    ! [X,Y] : big_f(X,Y),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Y] :
      ( ( ( ? [Z] : ~ big_g(Z,Z)
          | ! [X] :
            ? [Z] : ~ big_g(X,Z) )
        & ! [X] : big_g(X,Y) )
      | ? [Z] : ~ big_f(Y,Z)
      | ? [Z] : ~ big_f(Z,Z) ),
    inference(simplify,[],[normalize_0_1,normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Y] :
      ( ( ( ? [Z] : ~ big_g(Z,Z)
          | ! [X] :
            ? [Z] : ~ big_g(X,Z) )
        & ! [X] : big_g(X,Y) )
      | ? [Z] : ~ big_f(Y,Z)
      | ? [Z] : ~ big_f(Z,Z) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] :
      ( ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
        | ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
        | big_g(X,Y) )
      & ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
        | ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
        | ~ big_g(X,skolemFOFtoCNF_Z_1(X))
        | ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
      | ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
      | ~ big_g(X,skolemFOFtoCNF_Z_1(X))
      | ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X,Y] :
      ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
      | ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
      | big_g(X,Y) ),
    inference(conjunct,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
    | ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
    | ~ big_g(X,skolemFOFtoCNF_Z_1(X))
    | ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_1,plain,
    big_f(X,Y),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    big_f(Y,skolemFOFtoCNF_Z_2(Y)),
    inference(subst,[],[refute_0_1:[bind(X,$fot(Y)),bind(Y,$fot(skolemFOFtoCNF_Z_2(Y)))]]) ).

cnf(refute_0_3,plain,
    ( ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
    | ~ big_g(X,skolemFOFtoCNF_Z_1(X))
    | ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
    inference(resolve,[$cnf( big_f(Y,skolemFOFtoCNF_Z_2(Y)) )],[refute_0_2,refute_0_0]) ).

cnf(refute_0_4,plain,
    big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Z_3)),bind(Y,$fot(skolemFOFtoCNF_Z_3))]]) ).

cnf(refute_0_5,plain,
    ( ~ big_g(X,skolemFOFtoCNF_Z_1(X))
    | ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3) )],[refute_0_4,refute_0_3]) ).

cnf(refute_0_6,plain,
    ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
    | ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
    | big_g(X,Y) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_7,plain,
    ( ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
    | big_g(X,Y) ),
    inference(resolve,[$cnf( big_f(Y,skolemFOFtoCNF_Z_2(Y)) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    big_g(X,Y),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3) )],[refute_0_4,refute_0_7]) ).

cnf(refute_0_9,plain,
    big_g(X,skolemFOFtoCNF_Z_1(X)),
    inference(subst,[],[refute_0_8:[bind(Y,$fot(skolemFOFtoCNF_Z_1(X)))]]) ).

cnf(refute_0_10,plain,
    ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
    inference(resolve,[$cnf( big_g(X,skolemFOFtoCNF_Z_1(X)) )],[refute_0_9,refute_0_5]) ).

cnf(refute_0_11,plain,
    big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
    inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_11,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul 11 18:25:23 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------