%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GEO022-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:52:54 EDT 2009

% Result   : Unsatisfiable 0.4s
% Output   : Refutation 0.4s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (   9 unt;   0 def)
%            Number of atoms       :   21 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   17 (  10   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   22 (   0 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/GEO022-3.tptp',unknown),
    [] ).

cnf(147980664,plain,
    ( ~ equidistant(A,B,C,D)
    | equidistant(C,D,A,B) ),
    inference(rewrite,[status(thm)],[d2]),
    [] ).

fof(u_to_v_equals_w_to_x,plain,
    equidistant(u,v,w,x),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),
    [] ).

cnf(148006368,plain,
    equidistant(u,v,w,x),
    inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),
    [] ).

cnf(156690360,plain,
    equidistant(w,x,u,v),
    inference(resolution,[status(thm)],[147980664,148006368]),
    [] ).

fof(transitivity_for_equidistance,plain,
    ! [A,B,C,D,E,F] :
      ( ~ equidistant(A,B,C,D)
      | ~ equidistant(A,B,E,F)
      | equidistant(C,D,E,F) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),
    [] ).

cnf(147744680,plain,
    ( ~ equidistant(A,B,C,D)
    | ~ equidistant(A,B,E,F)
    | equidistant(C,D,E,F) ),
    inference(rewrite,[status(thm)],[transitivity_for_equidistance]),
    [] ).

fof(w_to_x_equals_y_to_z,plain,
    equidistant(w,x,y,z),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),
    [] ).

cnf(148014480,plain,
    equidistant(w,x,y,z),
    inference(rewrite,[status(thm)],[w_to_x_equals_y_to_z]),
    [] ).

cnf(157540232,plain,
    ( ~ equidistant(w,x,A,B)
    | equidistant(y,z,A,B) ),
    inference(resolution,[status(thm)],[147744680,148014480]),
    [] ).

fof(prove_transitivity,plain,
    ~ equidistant(u,v,y,z),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),
    [] ).

cnf(148018264,plain,
    ~ equidistant(u,v,y,z),
    inference(rewrite,[status(thm)],[prove_transitivity]),
    [] ).

cnf(156427928,plain,
    ~ equidistant(y,z,u,v),
    inference(resolution,[status(thm)],[147980664,148018264]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[156690360,157540232,156427928]),
    [] ).

%------------------------------------------------------------------------------
%----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/GEO022-3.tptp',unknown),[]).
% 
% cnf(147980664,plain,(~equidistant(A,B,C,D)|equidistant(C,D,A,B)),inference(rewrite,[status(thm)],[d2]),[]).
% 
% fof(u_to_v_equals_w_to_x,plain,(equidistant(u,v,w,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),[]).
% 
% cnf(148006368,plain,(equidistant(u,v,w,x)),inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),[]).
% 
% cnf(156690360,plain,(equidistant(w,x,u,v)),inference(resolution,[status(thm)],[147980664,148006368]),[]).
% 
% fof(transitivity_for_equidistance,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),[]).
% 
% cnf(147744680,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),inference(rewrite,[status(thm)],[transitivity_for_equidistance]),[]).
% 
% fof(w_to_x_equals_y_to_z,plain,(equidistant(w,x,y,z)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),[]).
% 
% cnf(148014480,plain,(equidistant(w,x,y,z)),inference(rewrite,[status(thm)],[w_to_x_equals_y_to_z]),[]).
% 
% cnf(157540232,plain,(~equidistant(w,x,A,B)|equidistant(y,z,A,B)),inference(resolution,[status(thm)],[147744680,148014480]),[]).
% 
% fof(prove_transitivity,plain,(~equidistant(u,v,y,z)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO022-3.tptp',unknown),[]).
% 
% cnf(148018264,plain,(~equidistant(u,v,y,z)),inference(rewrite,[status(thm)],[prove_transitivity]),[]).
% 
% cnf(156427928,plain,(~equidistant(y,z,u,v)),inference(resolution,[status(thm)],[147980664,148018264]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[156690360,157540232,156427928]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------