TSTP Solution File: SYN350+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN350+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 09:01:39 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   29 (   8 unt;   0 def)
%            Number of atoms       :   95 (   0 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  114 (  48   ~;  28   |;  16   &)
%                                         (  16 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   57 (   6 sgn  30   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(church_46_18_2,conjecture,
    ! [X] :
    ? [Y1,Y2] :
    ! [Z] :
      ( ( big_f(X,Z)
      <=> big_f(Z,X) )
     => ( big_f(X,Z)
      <=> ( big_f(Y2,Z)
          & ( big_f(Y1,Z)
           => big_f(Y1,Y2) ) ) ) ) ).

fof(subgoal_0,plain,
    ! [X] :
    ? [Y1,Y2] :
    ! [Z] :
      ( ( big_f(X,Z)
      <=> big_f(Z,X) )
     => ( big_f(X,Z)
      <=> ( big_f(Y2,Z)
          & ( big_f(Y1,Z)
           => big_f(Y1,Y2) ) ) ) ),
    inference(strip,[],[church_46_18_2]) ).

fof(negate_0_0,plain,
    ~ ! [X] :
      ? [Y1,Y2] :
      ! [Z] :
        ( ( big_f(X,Z)
        <=> big_f(Z,X) )
       => ( big_f(X,Z)
        <=> ( big_f(Y2,Z)
            & ( big_f(Y1,Z)
             => big_f(Y1,Y2) ) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X] :
    ! [Y1,Y2] :
    ? [Z] :
      ( ( ~ big_f(X,Z)
      <=> ~ big_f(Z,X) )
      & ( ~ big_f(X,Z)
      <=> ( big_f(Y2,Z)
          & ( ~ big_f(Y1,Z)
            | big_f(Y1,Y2) ) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [Y1,Y2] :
    ? [Z] :
      ( ( ~ big_f(Z,skolemFOFtoCNF_X)
      <=> ~ big_f(skolemFOFtoCNF_X,Z) )
      & ( ~ big_f(skolemFOFtoCNF_X,Z)
      <=> ( big_f(Y2,Z)
          & ( ~ big_f(Y1,Z)
            | big_f(Y1,Y2) ) ) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Y1,Y2] :
    ? [Z] :
      ( ( ~ big_f(Z,skolemFOFtoCNF_X)
      <=> ~ big_f(skolemFOFtoCNF_X,Z) )
      & ( ~ big_f(skolemFOFtoCNF_X,Z)
      <=> ( big_f(Y2,Z)
          & ( ~ big_f(Y1,Z)
            | big_f(Y1,Y2) ) ) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Y1,Y2] :
      ( ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
      <=> ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) )
      & ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
      <=> ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
          & ( ~ big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2))
            | big_f(Y1,Y2) ) ) ) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Y1,Y2] :
      ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
    <=> ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
        & ( ~ big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2))
          | big_f(Y1,Y2) ) ) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Y1,Y2] :
      ( ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
        | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) )
      & ( ~ big_f(Y1,Y2)
        | ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
        | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) )
      & ( ~ big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2))
        | big_f(Y1,Y2)
        | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) )
      & ( ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
        | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
        | big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [Y1,Y2] :
      ( ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
      | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
      | big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [Y1,Y2] :
      ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
      | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_8,plain,
    ! [Y1,Y2] :
      ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
    <=> ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_9,plain,
    ! [Y1,Y2] :
      ( ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
        | big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) )
      & ( ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X)
        | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [Y1,Y2] :
      ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
      | big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [Y1,Y2] :
      ( ~ big_f(Y1,Y2)
      | ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
      | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
    | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
    | big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2)) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_1,plain,
    ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X))
    | big_f(Y1,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_0:[bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_2,plain,
    ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
    | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)),
    inference(subst,[],[refute_0_2:[bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_4,plain,
    big_f(Y1,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) )],[refute_0_3,refute_0_1]) ).

cnf(refute_0_5,plain,
    big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X,skolemFOFtoCNF_X)),
    inference(subst,[],[refute_0_4:[bind(Y1,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_6,plain,
    ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
    | big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_7,plain,
    ( ~ big_f(Y1,Y2)
    | ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
    | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_8,plain,
    ( ~ big_f(Y1,skolemFOFtoCNF_X)
    | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_7:[bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_9,plain,
    ~ big_f(Y1,skolemFOFtoCNF_X),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) )],[refute_0_3,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_9:[bind(Y1,$fot(skolemFOFtoCNF_Z(Y1,Y2)))]]) ).

cnf(refute_0_11,plain,
    ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) )],[refute_0_6,refute_0_10]) ).

cnf(refute_0_12,plain,
    ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X,skolemFOFtoCNF_X)),
    inference(subst,[],[refute_0_11:[bind(Y1,$fot(skolemFOFtoCNF_X)),bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN350+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n007.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 11:26:02 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  
%------------------------------------------------------------------------------