TSTP Solution File: SYN327+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN327+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 09:01:20 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   19 (   7 unt;   0 def)
%            Number of atoms       :   74 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   90 (  35   ~;  16   |;  27   &)
%                                         (   0 <=>;  12  =>;   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    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   33 (   1 sgn  17   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(church_46_12_2,conjecture,
    ! [X] :
    ? [Y] :
    ! [Z] :
      ( big_f(Y,X)
     => ( ( big_f(X,Z)
         => big_f(X,Y) )
        & ( big_f(X,Y)
         => ( ~ big_f(X,Z)
           => ( big_f(Y,X)
              & big_f(Z,Y) ) ) ) ) ) ).

fof(subgoal_0,plain,
    ! [X] :
    ? [Y] :
    ! [Z] :
      ( big_f(Y,X)
     => ( ( big_f(X,Z)
         => big_f(X,Y) )
        & ( big_f(X,Y)
         => ( ~ big_f(X,Z)
           => ( big_f(Y,X)
              & big_f(Z,Y) ) ) ) ) ),
    inference(strip,[],[church_46_12_2]) ).

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

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

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

fof(normalize_0_2,plain,
    ! [Y] : big_f(Y,skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_0_1]) ).

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

fof(normalize_0_4,plain,
    ! [Y] :
      ( ( ~ big_f(skolemFOFtoCNF_X,Y)
        & ? [Z] : big_f(skolemFOFtoCNF_X,Z) )
      | ? [Z] :
          ( ~ big_f(skolemFOFtoCNF_X,Z)
          & big_f(skolemFOFtoCNF_X,Y)
          & ( ~ big_f(Y,skolemFOFtoCNF_X)
            | ~ big_f(Z,Y) ) ) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_5,plain,
    ! [Y] :
      ( ( ~ big_f(skolemFOFtoCNF_X,Y)
        & ? [Z] : big_f(skolemFOFtoCNF_X,Z) )
      | ? [Z] :
          ( ~ big_f(Z,Y)
          & ~ big_f(skolemFOFtoCNF_X,Z)
          & big_f(skolemFOFtoCNF_X,Y) ) ),
    inference(simplify,[],[normalize_0_4,normalize_0_3]) ).

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

fof(normalize_0_7,plain,
    ! [Y] :
      ( ( ~ big_f(skolemFOFtoCNF_X,Y)
        | ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z_1(Y)) )
      & ( ~ big_f(skolemFOFtoCNF_X,Y)
        | ~ big_f(skolemFOFtoCNF_Z_1(Y),Y) )
      & ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z_1(Y))
        | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )
      & ( ~ big_f(skolemFOFtoCNF_Z_1(Y),Y)
        | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )
      & ( big_f(skolemFOFtoCNF_X,Y)
        | big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [Y] :
      ( ~ big_f(skolemFOFtoCNF_X,Y)
      | ~ big_f(skolemFOFtoCNF_Z_1(Y),Y) ),
    inference(conjunct,[],[normalize_0_7]) ).

cnf(refute_0_0,plain,
    big_f(Y,skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X),skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X)))]]) ).

cnf(refute_0_2,plain,
    ( ~ big_f(skolemFOFtoCNF_X,Y)
    | ~ big_f(skolemFOFtoCNF_Z_1(Y),Y) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_3,plain,
    ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
    | ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X),skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_0_2:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_4,plain,
    ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X),skolemFOFtoCNF_X) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_5,refute_0_4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SYN327+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jul 12 04:43:10 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------