TSTP Solution File: SYN331+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN331+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 09:01:23 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   22 (   7 unt;   0 def)
%            Number of atoms       :   75 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   76 (  23   ~;  18   |;  16   &)
%                                         (   7 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   47 (   5 sgn  19   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(church_46_14_3,conjecture,
    ? [X,Y] :
    ! [Z] :
      ( big_f(X,Z)
     => ( big_f(Y,Z)
       => ( ( big_f(X,Y)
          <=> big_f(Z,Z) )
         => ( ( big_f(Y,X)
              | big_f(Z,Z) )
           => ( big_f(Z,X)
              | big_f(Z,Y) ) ) ) ) ) ).

fof(subgoal_0,plain,
    ? [X,Y] :
    ! [Z] :
      ( big_f(X,Z)
     => ( big_f(Y,Z)
       => ( ( big_f(X,Y)
          <=> big_f(Z,Z) )
         => ( ( big_f(Y,X)
              | big_f(Z,Z) )
           => ( big_f(Z,X)
              | big_f(Z,Y) ) ) ) ) ),
    inference(strip,[],[church_46_14_3]) ).

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

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

fof(normalize_0_1,plain,
    ! [X,Y] :
    ? [Z] :
      ( ~ big_f(Z,X)
      & ~ big_f(Z,Y)
      & big_f(X,Z)
      & big_f(Y,Z)
      & ( big_f(Y,X)
        | big_f(Z,Z) )
      & ( ~ big_f(X,Y)
      <=> ~ big_f(Z,Z) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X,Y] :
      ( ~ big_f(skolemFOFtoCNF_Z(X,Y),X)
      & ~ big_f(skolemFOFtoCNF_Z(X,Y),Y)
      & big_f(X,skolemFOFtoCNF_Z(X,Y))
      & big_f(Y,skolemFOFtoCNF_Z(X,Y))
      & ( big_f(Y,X)
        | big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )
      & ( ~ big_f(X,Y)
      <=> ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ) ),
    inference(skolemize,[],[normalize_0_1]) ).

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

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ big_f(X,Y)
    <=> ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( ( ~ big_f(X,Y)
        | big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )
      & ( ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
        | big_f(X,Y) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] :
      ( ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
      | big_f(X,Y) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( big_f(Y,X)
      | big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ),
    inference(conjunct,[],[normalize_0_2]) ).

cnf(refute_0_0,plain,
    ~ big_f(skolemFOFtoCNF_Z(X,Y),Y),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ~ big_f(skolemFOFtoCNF_Z(X,X_20),X_20),
    inference(subst,[],[refute_0_0:[bind(Y,$fot(X_20))]]) ).

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

cnf(refute_0_3,plain,
    ( big_f(Y,X)
    | big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    ( big_f(X_17,X_16)
    | big_f(skolemFOFtoCNF_Z(X_16,X_17),skolemFOFtoCNF_Z(X_16,X_17)) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).

cnf(refute_0_5,plain,
    ( ~ big_f(skolemFOFtoCNF_Z(X_16,X_17),skolemFOFtoCNF_Z(X_16,X_17))
    | big_f(X_16,X_17) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).

cnf(refute_0_6,plain,
    ( big_f(X_16,X_17)
    | big_f(X_17,X_16) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X_16,X_17),skolemFOFtoCNF_Z(X_16,X_17)) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)),
    inference(subst,[],[refute_0_6:[bind(X_16,$fot(skolemFOFtoCNF_Z(X,Y))),bind(X_17,$fot(skolemFOFtoCNF_Z(X,Y)))]]) ).

cnf(refute_0_8,plain,
    big_f(X,Y),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )],[refute_0_7,refute_0_2]) ).

cnf(refute_0_9,plain,
    big_f(skolemFOFtoCNF_Z(X,X_20),X_20),
    inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Z(X,X_20))),bind(Y,$fot(X_20))]]) ).

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X,X_20),X_20) )],[refute_0_9,refute_0_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN331+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 : Mon Jul 11 19:19:34 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------