%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO174+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 11:57:48 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 65 ( 24 ~; 26 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(ceq2,plain,
! [A,B,C] :
( ~ apart_point_and_line(A,B)
| distinct_lines(B,C)
| apart_point_and_line(A,C) ),
file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),
[] ).
cnf(150919904,plain,
( ~ apart_point_and_line(A,B)
| distinct_lines(B,C)
| apart_point_and_line(A,C) ),
inference(rewrite,[status(thm)],[ceq2]),
[] ).
fof(con,plain,
( ( ~ distinct_lines(u,line_connecting(x,y))
| apart_point_and_line(x,u) )
& ( apart_point_and_line(y,u)
| apart_point_and_line(x,u) )
& ( convergent_lines(u,v)
| apart_point_and_line(x,u) )
& ( distinct_points(x,y)
| apart_point_and_line(x,u) )
& ( ~ distinct_lines(u,line_connecting(x,y))
| convergent_lines(u,v) )
& ( apart_point_and_line(y,u)
| convergent_lines(u,v) )
& ( convergent_lines(u,v)
| convergent_lines(u,v) )
& ( distinct_points(x,y)
| convergent_lines(u,v) )
& ( ~ distinct_lines(u,line_connecting(x,y))
| distinct_points(x,y) )
& ( apart_point_and_line(y,u)
| distinct_points(x,y) )
& ( convergent_lines(u,v)
| distinct_points(x,y) )
& ( distinct_points(x,y)
| distinct_points(x,y) )
& ( ~ distinct_lines(u,line_connecting(x,y))
| ~ distinct_lines(u,line_connecting(x,y)) )
& ( apart_point_and_line(y,u)
| ~ distinct_lines(u,line_connecting(x,y)) )
& ( convergent_lines(u,v)
| ~ distinct_lines(u,line_connecting(x,y)) )
& ( distinct_points(x,y)
| ~ distinct_lines(u,line_connecting(x,y)) ) ),
file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),
[] ).
cnf(151112648,plain,
~ distinct_lines(u,line_connecting(x,y)),
inference(rewrite,[status(thm)],[con]),
[] ).
cnf(175027040,plain,
( ~ apart_point_and_line(A,u)
| apart_point_and_line(A,line_connecting(x,y)) ),
inference(resolution,[status(thm)],[150919904,151112648]),
[] ).
fof(ci2,plain,
! [A,B] :
( ~ distinct_points(A,B)
| ~ apart_point_and_line(B,line_connecting(A,B)) ),
file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),
[] ).
cnf(150881368,plain,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(B,line_connecting(A,B)) ),
inference(rewrite,[status(thm)],[ci2]),
[] ).
cnf(151116184,plain,
distinct_points(x,y),
inference(rewrite,[status(thm)],[con]),
[] ).
cnf(174754000,plain,
~ apart_point_and_line(y,line_connecting(x,y)),
inference(resolution,[status(thm)],[150881368,151116184]),
[] ).
cnf(175115312,plain,
~ apart_point_and_line(y,u),
inference(resolution,[status(thm)],[175027040,174754000]),
[] ).
fof(ci1,plain,
! [A,B] :
( ~ distinct_points(A,B)
| ~ apart_point_and_line(A,line_connecting(A,B)) ),
file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),
[] ).
cnf(150864128,plain,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(A,line_connecting(A,B)) ),
inference(rewrite,[status(thm)],[ci1]),
[] ).
cnf(174740344,plain,
~ apart_point_and_line(x,line_connecting(x,y)),
inference(resolution,[status(thm)],[150864128,151116184]),
[] ).
cnf(175091800,plain,
~ apart_point_and_line(x,u),
inference(resolution,[status(thm)],[175027040,174740344]),
[] ).
cnf(151129152,plain,
( apart_point_and_line(y,u)
| apart_point_and_line(x,u) ),
inference(rewrite,[status(thm)],[con]),
[] ).
cnf(177572800,plain,
apart_point_and_line(y,u),
inference(resolution,[status(thm)],[175091800,151129152]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[175115312,177572800]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(ceq2,plain,(~apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C)),file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),[]).
%
% cnf(150919904,plain,(~apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C)),inference(rewrite,[status(thm)],[ceq2]),[]).
%
% fof(con,plain,(((~distinct_lines(u,line_connecting(x,y))|apart_point_and_line(x,u))&(apart_point_and_line(y,u)|apart_point_and_line(x,u))&(convergent_lines(u,v)|apart_point_and_line(x,u))&(distinct_points(x,y)|apart_point_and_line(x,u))&(~distinct_lines(u,line_connecting(x,y))|convergent_lines(u,v))&(apart_point_and_line(y,u)|convergent_lines(u,v))&(convergent_lines(u,v)|convergent_lines(u,v))&(distinct_points(x,y)|convergent_lines(u,v))&(~distinct_lines(u,line_connecting(x,y))|distinct_points(x,y))&(apart_point_and_line(y,u)|distinct_points(x,y))&(convergent_lines(u,v)|distinct_points(x,y))&(distinct_points(x,y)|distinct_points(x,y))&(~distinct_lines(u,line_connecting(x,y))|~distinct_lines(u,line_connecting(x,y)))&(apart_point_and_line(y,u)|~distinct_lines(u,line_connecting(x,y)))&(convergent_lines(u,v)|~distinct_lines(u,line_connecting(x,y)))&(distinct_points(x,y)|~distinct_lines(u,line_connecting(x,y))))),file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),[]).
%
% cnf(151112648,plain,(~distinct_lines(u,line_connecting(x,y))),inference(rewrite,[status(thm)],[con]),[]).
%
% cnf(175027040,plain,(~apart_point_and_line(A,u)|apart_point_and_line(A,line_connecting(x,y))),inference(resolution,[status(thm)],[150919904,151112648]),[]).
%
% fof(ci2,plain,(~distinct_points(A,B)|~apart_point_and_line(B,line_connecting(A,B))),file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),[]).
%
% cnf(150881368,plain,(~distinct_points(A,B)|~apart_point_and_line(B,line_connecting(A,B))),inference(rewrite,[status(thm)],[ci2]),[]).
%
% cnf(151116184,plain,(distinct_points(x,y)),inference(rewrite,[status(thm)],[con]),[]).
%
% cnf(174754000,plain,(~apart_point_and_line(y,line_connecting(x,y))),inference(resolution,[status(thm)],[150881368,151116184]),[]).
%
% cnf(175115312,plain,(~apart_point_and_line(y,u)),inference(resolution,[status(thm)],[175027040,174754000]),[]).
%
% fof(ci1,plain,(~distinct_points(A,B)|~apart_point_and_line(A,line_connecting(A,B))),file('/tmp/SystemOnTPTP12481/GEO174+1.p',unknown),[]).
%
% cnf(150864128,plain,(~distinct_points(A,B)|~apart_point_and_line(A,line_connecting(A,B))),inference(rewrite,[status(thm)],[ci1]),[]).
%
% cnf(174740344,plain,(~apart_point_and_line(x,line_connecting(x,y))),inference(resolution,[status(thm)],[150864128,151116184]),[]).
%
% cnf(175091800,plain,(~apart_point_and_line(x,u)),inference(resolution,[status(thm)],[175027040,174740344]),[]).
%
% cnf(151129152,plain,(apart_point_and_line(y,u)|apart_point_and_line(x,u)),inference(rewrite,[status(thm)],[con]),[]).
%
% cnf(177572800,plain,(apart_point_and_line(y,u)),inference(resolution,[status(thm)],[175091800,151129152]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[175115312,177572800]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------