%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GEO055-3 : 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 11:54:09 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    :   12 (  10 unt;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   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   :   26 (   2 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(d2,plain,
    ! [A,B,C,D] :
      ( ~ equidistant(A,B,C,D)
      | equidistant(C,D,A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO055-3.tptp',unknown),
    [] ).

cnf(169563160,plain,
    ( ~ equidistant(A,B,C,D)
    | equidistant(C,D,A,B) ),
    inference(rewrite,[status(thm)],[d2]),
    [] ).

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/GEO055-3.tptp',unknown),
    [] ).

cnf(169350888,plain,
    equidistant(A,extension(B,A,C,D),C,D),
    inference(rewrite,[status(thm)],[segment_construction2]),
    [] ).

cnf(178904528,plain,
    equidistant(B,C,A,extension(D,A,B,C)),
    inference(resolution,[status(thm)],[169563160,169350888]),
    [] ).

fof(reflection,plain,
    ! [A,B] : $equal(extension(A,B,A,B),reflection(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO055-3.tptp',unknown),
    [] ).

cnf(169550256,plain,
    $equal(extension(A,B,A,B),reflection(A,B)),
    inference(rewrite,[status(thm)],[reflection]),
    [] ).

cnf(178940920,plain,
    equidistant(B,A,A,reflection(B,A)),
    inference(paramodulation,[status(thm)],[178904528,169550256,theory(equality)]),
    [] ).

fof(prove_equidistance,plain,
    ~ equidistant(v,reflection(u,v),u,v),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO055-3.tptp',unknown),
    [] ).

cnf(169625992,plain,
    ~ equidistant(v,reflection(u,v),u,v),
    inference(rewrite,[status(thm)],[prove_equidistance]),
    [] ).

cnf(178560104,plain,
    ~ equidistant(u,v,v,reflection(u,v)),
    inference(resolution,[status(thm)],[169563160,169625992]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[178940920,178560104]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d2,plain,(~equidistant(A,B,C,D)|equidistant(C,D,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO055-3.tptp',unknown),[]).
% 
% cnf(169563160,plain,(~equidistant(A,B,C,D)|equidistant(C,D,A,B)),inference(rewrite,[status(thm)],[d2]),[]).
% 
% fof(segment_construction2,plain,(equidistant(A,extension(B,A,C,D),C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO055-3.tptp',unknown),[]).
% 
% cnf(169350888,plain,(equidistant(A,extension(B,A,C,D),C,D)),inference(rewrite,[status(thm)],[segment_construction2]),[]).
% 
% cnf(178904528,plain,(equidistant(B,C,A,extension(D,A,B,C))),inference(resolution,[status(thm)],[169563160,169350888]),[]).
% 
% fof(reflection,plain,($equal(extension(A,B,A,B),reflection(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO055-3.tptp',unknown),[]).
% 
% cnf(169550256,plain,($equal(extension(A,B,A,B),reflection(A,B))),inference(rewrite,[status(thm)],[reflection]),[]).
% 
% cnf(178940920,plain,(equidistant(B,A,A,reflection(B,A))),inference(paramodulation,[status(thm)],[178904528,169550256,theory(equality)]),[]).
% 
% fof(prove_equidistance,plain,(~equidistant(v,reflection(u,v),u,v)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO055-3.tptp',unknown),[]).
% 
% cnf(169625992,plain,(~equidistant(v,reflection(u,v),u,v)),inference(rewrite,[status(thm)],[prove_equidistance]),[]).
% 
% cnf(178560104,plain,(~equidistant(u,v,v,reflection(u,v))),inference(resolution,[status(thm)],[169563160,169625992]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[178940920,178560104]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------