%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SYN014-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 16:37:55 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (   9 unt;   0 def)
%            Number of atoms       :   21 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (   9   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   11 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(transitivity,plain,
    ! [A,B,C] :
      ( ~ equalish(A,B)
      | ~ equalish(B,C)
      | equalish(A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),
    [] ).

cnf(146096848,plain,
    ( ~ equalish(A,B)
    | ~ equalish(B,C)
    | equalish(A,C) ),
    inference(rewrite,[status(thm)],[transitivity]),
    [] ).

fof(c_23,plain,
    equalish(m,k),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),
    [] ).

cnf(146274008,plain,
    equalish(m,k),
    inference(rewrite,[status(thm)],[c_23]),
    [] ).

cnf(206699136,plain,
    ( ~ equalish(k,A)
    | equalish(m,A) ),
    inference(resolution,[status(thm)],[146096848,146274008]),
    [] ).

fof(symmetry,plain,
    ! [A,B] :
      ( ~ equalish(A,B)
      | equalish(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),
    [] ).

cnf(146090176,plain,
    ( ~ equalish(A,B)
    | equalish(B,A) ),
    inference(rewrite,[status(thm)],[symmetry]),
    [] ).

fof(c_20,plain,
    equalish(n,k),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),
    [] ).

cnf(146081072,plain,
    equalish(n,k),
    inference(rewrite,[status(thm)],[c_20]),
    [] ).

cnf(206597896,plain,
    equalish(k,n),
    inference(resolution,[status(thm)],[146090176,146081072]),
    [] ).

cnf(206735672,plain,
    equalish(m,n),
    inference(resolution,[status(thm)],[206699136,206597896]),
    [] ).

fof(c_19,plain,
    ~ equalish(m,n),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),
    [] ).

cnf(146254688,plain,
    ~ equalish(m,n),
    inference(rewrite,[status(thm)],[c_19]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[206735672,146254688]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(transitivity,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),[]).
% 
% cnf(146096848,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),inference(rewrite,[status(thm)],[transitivity]),[]).
% 
% fof(c_23,plain,(equalish(m,k)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),[]).
% 
% cnf(146274008,plain,(equalish(m,k)),inference(rewrite,[status(thm)],[c_23]),[]).
% 
% cnf(206699136,plain,(~equalish(k,A)|equalish(m,A)),inference(resolution,[status(thm)],[146096848,146274008]),[]).
% 
% fof(symmetry,plain,(~equalish(A,B)|equalish(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),[]).
% 
% cnf(146090176,plain,(~equalish(A,B)|equalish(B,A)),inference(rewrite,[status(thm)],[symmetry]),[]).
% 
% fof(c_20,plain,(equalish(n,k)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),[]).
% 
% cnf(146081072,plain,(equalish(n,k)),inference(rewrite,[status(thm)],[c_20]),[]).
% 
% cnf(206597896,plain,(equalish(k,n)),inference(resolution,[status(thm)],[146090176,146081072]),[]).
% 
% cnf(206735672,plain,(equalish(m,n)),inference(resolution,[status(thm)],[206699136,206597896]),[]).
% 
% fof(c_19,plain,(~equalish(m,n)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN014-2.tptp',unknown),[]).
% 
% cnf(146254688,plain,(~equalish(m,n)),inference(rewrite,[status(thm)],[c_19]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[206735672,146254688]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------