%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SWV003-1 : 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 16:19:37 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   11 (   8 unt;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   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   :    7 (   0 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clause_3,plain,
    ~ less_than(k,i),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),
    [] ).

cnf(168939416,plain,
    ~ less_than(k,i),
    inference(rewrite,[status(thm)],[clause_3]),
    [] ).

fof(transitivity_of_less_than,plain,
    ! [A,B,C] :
      ( less_than(A,B)
      | ~ less_than(A,C)
      | ~ less_than(C,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),
    [] ).

cnf(168892344,plain,
    ( less_than(A,B)
    | ~ less_than(A,C)
    | ~ less_than(C,B) ),
    inference(rewrite,[status(thm)],[transitivity_of_less_than]),
    [] ).

fof(clause_9,plain,
    less_than(j,i),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),
    [] ).

cnf(168982920,plain,
    less_than(j,i),
    inference(rewrite,[status(thm)],[clause_9]),
    [] ).

cnf(197910992,plain,
    ( less_than(A,i)
    | ~ less_than(A,j) ),
    inference(resolution,[status(thm)],[168892344,168982920]),
    [] ).

fof(clause_2,plain,
    less_than(k,j),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),
    [] ).

cnf(168935552,plain,
    less_than(k,j),
    inference(rewrite,[status(thm)],[clause_2]),
    [] ).

cnf(197915288,plain,
    less_than(k,i),
    inference(resolution,[status(thm)],[197910992,168935552]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[168939416,197915288]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(clause_3,plain,(~less_than(k,i)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),[]).
% 
% cnf(168939416,plain,(~less_than(k,i)),inference(rewrite,[status(thm)],[clause_3]),[]).
% 
% fof(transitivity_of_less_than,plain,(less_than(A,B)|~less_than(A,C)|~less_than(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),[]).
% 
% cnf(168892344,plain,(less_than(A,B)|~less_than(A,C)|~less_than(C,B)),inference(rewrite,[status(thm)],[transitivity_of_less_than]),[]).
% 
% fof(clause_9,plain,(less_than(j,i)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),[]).
% 
% cnf(168982920,plain,(less_than(j,i)),inference(rewrite,[status(thm)],[clause_9]),[]).
% 
% cnf(197910992,plain,(less_than(A,i)|~less_than(A,j)),inference(resolution,[status(thm)],[168892344,168982920]),[]).
% 
% fof(clause_2,plain,(less_than(k,j)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV003-1.tptp',unknown),[]).
% 
% cnf(168935552,plain,(less_than(k,j)),inference(rewrite,[status(thm)],[clause_2]),[]).
% 
% cnf(197915288,plain,(less_than(k,i)),inference(resolution,[status(thm)],[197910992,168935552]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[168939416,197915288]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------