%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : HWV010-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art08.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 13:17:48 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   20 (   7 unt;   0 def)
%            Number of atoms       :   33 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   25 (  12   ~;  13   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   13 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_25,plain,
    ! [A] :
      ( $equal(n0,int_level(A))
      | ~ p_empty(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),
    [] ).

cnf(167279416,plain,
    ( $equal(n0,int_level(A))
    | ~ p_empty(A) ),
    inference(rewrite,[status(thm)],[axiom_25]),
    [] ).

fof(axiom_21,plain,
    ! [A] : $equal(int_level(A),level(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),
    [] ).

cnf(167246712,plain,
    $equal(int_level(A),level(A)),
    inference(rewrite,[status(thm)],[axiom_21]),
    [] ).

cnf(179452776,plain,
    ( ~ p_empty(A)
    | $equal(n0,level(A)) ),
    inference(paramodulation,[status(thm)],[167279416,167246712,theory(equality)]),
    [] ).

fof(quest_2,plain,
    ( p_empty(t_139)
    | $equal(level(t_139),n0) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),
    [] ).

cnf(167861168,plain,
    ( p_empty(t_139)
    | $equal(level(t_139),n0) ),
    inference(rewrite,[status(thm)],[quest_2]),
    [] ).

cnf(180157776,plain,
    $equal(n0,level(t_139)),
    inference(resolution,[status(thm)],[179452776,167861168]),
    [] ).

fof(axiom_15,plain,
    ! [A] :
      ( $equal(n0,A)
      | gt(A,n0) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),
    [] ).

cnf(167205496,plain,
    ( $equal(n0,A)
    | gt(A,n0) ),
    inference(rewrite,[status(thm)],[axiom_15]),
    [] ).

cnf(180426464,plain,
    ( $equal(level(t_139),A)
    | gt(A,n0) ),
    inference(paramodulation,[status(thm)],[180157776,167205496,theory(equality)]),
    [] ).

fof(axiom_17,plain,
    ! [A] : ~ gt(A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),
    [] ).

cnf(167220120,plain,
    ~ gt(A,A),
    inference(rewrite,[status(thm)],[axiom_17]),
    [] ).

cnf(181228896,plain,
    $equal(level(t_139),n0),
    inference(resolution,[status(thm)],[180426464,167220120]),
    [] ).

fof(quest_1,plain,
    ( ~ p_empty(t_139)
    | ~ $equal(level(t_139),n0) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),
    [] ).

cnf(167850136,plain,
    ( ~ p_empty(t_139)
    | ~ $equal(level(t_139),n0) ),
    inference(rewrite,[status(thm)],[quest_1]),
    [] ).

fof(axiom_24,plain,
    ! [A] :
      ( ~ $equal(n0,int_level(A))
      | p_empty(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),
    [] ).

cnf(167268936,plain,
    ( ~ $equal(n0,int_level(A))
    | p_empty(A) ),
    inference(rewrite,[status(thm)],[axiom_24]),
    [] ).

cnf(179201104,plain,
    ( ~ $equal(n0,level(A))
    | p_empty(A) ),
    inference(paramodulation,[status(thm)],[167268936,167246712,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[181228896,167850136,179201104]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(axiom_25,plain,($equal(n0,int_level(A))|~p_empty(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),[]).
% 
% cnf(167279416,plain,($equal(n0,int_level(A))|~p_empty(A)),inference(rewrite,[status(thm)],[axiom_25]),[]).
% 
% fof(axiom_21,plain,($equal(int_level(A),level(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),[]).
% 
% cnf(167246712,plain,($equal(int_level(A),level(A))),inference(rewrite,[status(thm)],[axiom_21]),[]).
% 
% cnf(179452776,plain,(~p_empty(A)|$equal(n0,level(A))),inference(paramodulation,[status(thm)],[167279416,167246712,theory(equality)]),[]).
% 
% fof(quest_2,plain,(p_empty(t_139)|$equal(level(t_139),n0)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),[]).
% 
% cnf(167861168,plain,(p_empty(t_139)|$equal(level(t_139),n0)),inference(rewrite,[status(thm)],[quest_2]),[]).
% 
% cnf(180157776,plain,($equal(n0,level(t_139))),inference(resolution,[status(thm)],[179452776,167861168]),[]).
% 
% fof(axiom_15,plain,($equal(n0,A)|gt(A,n0)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),[]).
% 
% cnf(167205496,plain,($equal(n0,A)|gt(A,n0)),inference(rewrite,[status(thm)],[axiom_15]),[]).
% 
% cnf(180426464,plain,($equal(level(t_139),A)|gt(A,n0)),inference(paramodulation,[status(thm)],[180157776,167205496,theory(equality)]),[]).
% 
% fof(axiom_17,plain,(~gt(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),[]).
% 
% cnf(167220120,plain,(~gt(A,A)),inference(rewrite,[status(thm)],[axiom_17]),[]).
% 
% cnf(181228896,plain,($equal(level(t_139),n0)),inference(resolution,[status(thm)],[180426464,167220120]),[]).
% 
% fof(quest_1,plain,(~p_empty(t_139)|~$equal(level(t_139),n0)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),[]).
% 
% cnf(167850136,plain,(~p_empty(t_139)|~$equal(level(t_139),n0)),inference(rewrite,[status(thm)],[quest_1]),[]).
% 
% fof(axiom_24,plain,(~$equal(n0,int_level(A))|p_empty(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HWV/HWV010-1.tptp',unknown),[]).
% 
% cnf(167268936,plain,(~$equal(n0,int_level(A))|p_empty(A)),inference(rewrite,[status(thm)],[axiom_24]),[]).
% 
% cnf(179201104,plain,(~$equal(n0,level(A))|p_empty(A)),inference(paramodulation,[status(thm)],[167268936,167246712,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[181228896,167850136,179201104]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------