%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GEO056-2 : 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 @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:54:11 EDT 2009

% Result   : Unsatisfiable 0.3s
% Output   : Refutation 0.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (  12 unt;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-4 aty)
%            Number of variables   :   22 (   2 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_v_equals_reflection,plain,
    ~ $equal(reflection(u,v),v),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),
    [] ).

cnf(156920216,plain,
    ~ $equal(reflection(u,v),v),
    inference(rewrite,[status(thm)],[prove_v_equals_reflection]),
    [] ).

fof(u_equals_v,plain,
    $equal(v,u),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),
    [] ).

cnf(156911304,plain,
    $equal(v,u),
    inference(rewrite,[status(thm)],[u_equals_v]),
    [] ).

cnf(172155560,plain,
    ~ $equal(reflection(v,v),v),
    inference(paramodulation,[status(thm)],[156920216,156911304,theory(equality)]),
    [] ).

fof(identity_for_equidistance,plain,
    ! [A,B,C] :
      ( ~ equidistant(A,B,C,C)
      | $equal(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),
    [] ).

cnf(156690472,plain,
    ( ~ equidistant(A,B,C,C)
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[identity_for_equidistance]),
    [] ).

fof(segment_construction2,plain,
    ! [A,B,C,D] : equidistant(A,extension(B,A,C,D),C,D),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),
    [] ).

cnf(156703848,plain,
    equidistant(A,extension(B,A,C,D),C,D),
    inference(rewrite,[status(thm)],[segment_construction2]),
    [] ).

cnf(166615192,plain,
    $equal(extension(C,A,B,B),A),
    inference(resolution,[status(thm)],[156690472,156703848]),
    [] ).

fof(reflection,plain,
    ! [A,B] : $equal(extension(A,B,A,B),reflection(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),
    [] ).

cnf(156907336,plain,
    $equal(extension(A,B,A,B),reflection(A,B)),
    inference(rewrite,[status(thm)],[reflection]),
    [] ).

cnf(172268856,plain,
    $equal(reflection(A,A),A),
    inference(paramodulation,[status(thm)],[166615192,156907336,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[172155560,172268856]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_v_equals_reflection,plain,(~$equal(reflection(u,v),v)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),[]).
% 
% cnf(156920216,plain,(~$equal(reflection(u,v),v)),inference(rewrite,[status(thm)],[prove_v_equals_reflection]),[]).
% 
% fof(u_equals_v,plain,($equal(v,u)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),[]).
% 
% cnf(156911304,plain,($equal(v,u)),inference(rewrite,[status(thm)],[u_equals_v]),[]).
% 
% cnf(172155560,plain,(~$equal(reflection(v,v),v)),inference(paramodulation,[status(thm)],[156920216,156911304,theory(equality)]),[]).
% 
% fof(identity_for_equidistance,plain,(~equidistant(A,B,C,C)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),[]).
% 
% cnf(156690472,plain,(~equidistant(A,B,C,C)|$equal(B,A)),inference(rewrite,[status(thm)],[identity_for_equidistance]),[]).
% 
% fof(segment_construction2,plain,(equidistant(A,extension(B,A,C,D),C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),[]).
% 
% cnf(156703848,plain,(equidistant(A,extension(B,A,C,D),C,D)),inference(rewrite,[status(thm)],[segment_construction2]),[]).
% 
% cnf(166615192,plain,($equal(extension(C,A,B,B),A)),inference(resolution,[status(thm)],[156690472,156703848]),[]).
% 
% fof(reflection,plain,($equal(extension(A,B,A,B),reflection(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO056-2.tptp',unknown),[]).
% 
% cnf(156907336,plain,($equal(extension(A,B,A,B),reflection(A,B))),inference(rewrite,[status(thm)],[reflection]),[]).
% 
% cnf(172268856,plain,($equal(reflection(A,A),A)),inference(paramodulation,[status(thm)],[166615192,156907336,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[172155560,172268856]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------