%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SWV005-1 : 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 16:19:39 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   11 (   9 unt;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :    2 (   0 sgn   1   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clause_1,plain,
    ~ less_than(n,k),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),
    [] ).

cnf(157021472,plain,
    ~ less_than(n,k),
    inference(rewrite,[status(thm)],[clause_1]),
    [] ).

fof(clause_6,plain,
    less_than(a(k),a(predecessor(l))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),
    [] ).

cnf(157044856,plain,
    less_than(a(k),a(predecessor(l))),
    inference(rewrite,[status(thm)],[clause_6]),
    [] ).

fof(clause_8,plain,
    ! [A] :
      ( less_than(A,l)
      | less_than(n,A)
      | ~ less_than(one,l)
      | ~ less_than(a(A),a(predecessor(l))) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),
    [] ).

fof(clause_5,plain,
    less_than(one,l),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),
    [] ).

cnf(157036832,plain,
    less_than(one,l),
    inference(rewrite,[status(thm)],[clause_5]),
    [] ).

cnf(157059168,plain,
    ( less_than(A,l)
    | less_than(n,A)
    | ~ less_than(a(A),a(predecessor(l))) ),
    inference(rewrite__forward_subsumption_resolution,[status(thm)],[clause_8,157036832]),
    [] ).

fof(clause_2,plain,
    ~ less_than(k,l),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),
    [] ).

cnf(157025384,plain,
    ~ less_than(k,l),
    inference(rewrite,[status(thm)],[clause_2]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[157021472,157044856,157059168,157025384]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(clause_1,plain,(~less_than(n,k)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),[]).
% 
% cnf(157021472,plain,(~less_than(n,k)),inference(rewrite,[status(thm)],[clause_1]),[]).
% 
% fof(clause_6,plain,(less_than(a(k),a(predecessor(l)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),[]).
% 
% cnf(157044856,plain,(less_than(a(k),a(predecessor(l)))),inference(rewrite,[status(thm)],[clause_6]),[]).
% 
% fof(clause_8,plain,(less_than(A,l)|less_than(n,A)|~less_than(one,l)|~less_than(a(A),a(predecessor(l)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),[]).
% 
% fof(clause_5,plain,(less_than(one,l)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),[]).
% 
% cnf(157036832,plain,(less_than(one,l)),inference(rewrite,[status(thm)],[clause_5]),[]).
% 
% cnf(157059168,plain,(less_than(A,l)|less_than(n,A)|~less_than(a(A),a(predecessor(l)))),inference(rewrite__forward_subsumption_resolution,[status(thm)],[clause_8,157036832]),[]).
% 
% fof(clause_2,plain,(~less_than(k,l)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV005-1.tptp',unknown),[]).
% 
% cnf(157025384,plain,(~less_than(k,l)),inference(rewrite,[status(thm)],[clause_2]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[157021472,157044856,157059168,157025384]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------