%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO173+2 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 11:57:43 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 67 ( 30 ~; 32 |; 5 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 34 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(con,plain,
( distinct_points(x,y)
& convergent_lines(u,v)
& distinct_lines(u,line_connecting(x,y))
& ~ apart_point_and_line(x,u)
& ~ apart_point_and_line(y,u) ),
file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),
[] ).
cnf(148764592,plain,
~ apart_point_and_line(y,u),
inference(rewrite,[status(thm)],[con]),
[] ).
cnf(148784656,plain,
distinct_lines(u,line_connecting(x,y)),
inference(rewrite,[status(thm)],[con]),
[] ).
fof(cu1,plain,
! [A,B,C,D] :
( ~ distinct_points(A,B)
| ~ distinct_lines(C,D)
| apart_point_and_line(A,C)
| apart_point_and_line(A,D)
| apart_point_and_line(B,C)
| apart_point_and_line(B,D) ),
file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),
[] ).
cnf(148671888,plain,
( ~ distinct_points(A,B)
| ~ distinct_lines(C,D)
| apart_point_and_line(A,C)
| apart_point_and_line(A,D)
| apart_point_and_line(B,C)
| apart_point_and_line(B,D) ),
inference(rewrite,[status(thm)],[cu1]),
[] ).
fof(con1,plain,
! [C,A,B] :
( ( distinct_points(C,A)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) )
& ( distinct_points(C,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ) ),
file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),
[] ).
cnf(148636584,plain,
( distinct_points(C,A)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(rewrite,[status(thm)],[con1]),
[] ).
fof(apart1,plain,
! [A] : ~ distinct_points(A,A),
file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),
[] ).
cnf(148576080,plain,
~ distinct_points(A,A),
inference(rewrite,[status(thm)],[apart1]),
[] ).
cnf(167364856,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(resolution,[status(thm)],[148636584,148576080]),
[] ).
cnf(148800864,plain,
distinct_points(x,y),
inference(rewrite,[status(thm)],[con]),
[] ).
cnf(167378288,plain,
~ apart_point_and_line(x,line_connecting(x,y)),
inference(resolution,[status(thm)],[167364856,148800864]),
[] ).
cnf(167710680,plain,
( ~ distinct_points(A,x)
| ~ distinct_lines(B,line_connecting(x,y))
| apart_point_and_line(A,B)
| apart_point_and_line(A,line_connecting(x,y))
| apart_point_and_line(x,B) ),
inference(resolution,[status(thm)],[148671888,167378288]),
[] ).
cnf(148771968,plain,
~ apart_point_and_line(x,u),
inference(rewrite,[status(thm)],[con]),
[] ).
cnf(167769904,plain,
( ~ distinct_points(A,x)
| apart_point_and_line(A,u)
| apart_point_and_line(A,line_connecting(x,y)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[148784656,167710680,148771968]),
[] ).
fof(apart4,plain,
! [A,B,C] :
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),
[] ).
cnf(148593104,plain,
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(rewrite,[status(thm)],[apart4]),
[] ).
cnf(167303368,plain,
( ~ distinct_points(A,B)
| distinct_points(B,A) ),
inference(resolution,[status(thm)],[148593104,148576080]),
[] ).
cnf(167316832,plain,
distinct_points(y,x),
inference(resolution,[status(thm)],[167303368,148800864]),
[] ).
cnf(167774320,plain,
( apart_point_and_line(y,u)
| apart_point_and_line(y,line_connecting(x,y)) ),
inference(resolution,[status(thm)],[167769904,167316832]),
[] ).
cnf(148632272,plain,
( distinct_points(C,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(rewrite,[status(thm)],[con1]),
[] ).
cnf(167336856,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(resolution,[status(thm)],[148632272,148576080]),
[] ).
cnf(167350424,plain,
~ apart_point_and_line(y,line_connecting(x,y)),
inference(resolution,[status(thm)],[167336856,148800864]),
[] ).
cnf(167778408,plain,
apart_point_and_line(y,u),
inference(resolution,[status(thm)],[167774320,167350424]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[148764592,167778408]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(con,plain,((distinct_points(x,y)&convergent_lines(u,v)&distinct_lines(u,line_connecting(x,y))&~apart_point_and_line(x,u)&~apart_point_and_line(y,u))),file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),[]).
%
% cnf(148764592,plain,(~apart_point_and_line(y,u)),inference(rewrite,[status(thm)],[con]),[]).
%
% cnf(148784656,plain,(distinct_lines(u,line_connecting(x,y))),inference(rewrite,[status(thm)],[con]),[]).
%
% fof(cu1,plain,(~distinct_points(A,B)|~distinct_lines(C,D)|apart_point_and_line(A,C)|apart_point_and_line(A,D)|apart_point_and_line(B,C)|apart_point_and_line(B,D)),file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),[]).
%
% cnf(148671888,plain,(~distinct_points(A,B)|~distinct_lines(C,D)|apart_point_and_line(A,C)|apart_point_and_line(A,D)|apart_point_and_line(B,C)|apart_point_and_line(B,D)),inference(rewrite,[status(thm)],[cu1]),[]).
%
% fof(con1,plain,(((distinct_points(C,A)|~apart_point_and_line(C,line_connecting(A,B))|~distinct_points(A,B))&(distinct_points(C,B)|~apart_point_and_line(C,line_connecting(A,B))|~distinct_points(A,B)))),file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),[]).
%
% cnf(148636584,plain,(distinct_points(C,A)|~apart_point_and_line(C,line_connecting(A,B))|~distinct_points(A,B)),inference(rewrite,[status(thm)],[con1]),[]).
%
% fof(apart1,plain,(~distinct_points(A,A)),file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),[]).
%
% cnf(148576080,plain,(~distinct_points(A,A)),inference(rewrite,[status(thm)],[apart1]),[]).
%
% cnf(167364856,plain,(~apart_point_and_line(A,line_connecting(A,B))|~distinct_points(A,B)),inference(resolution,[status(thm)],[148636584,148576080]),[]).
%
% cnf(148800864,plain,(distinct_points(x,y)),inference(rewrite,[status(thm)],[con]),[]).
%
% cnf(167378288,plain,(~apart_point_and_line(x,line_connecting(x,y))),inference(resolution,[status(thm)],[167364856,148800864]),[]).
%
% cnf(167710680,plain,(~distinct_points(A,x)|~distinct_lines(B,line_connecting(x,y))|apart_point_and_line(A,B)|apart_point_and_line(A,line_connecting(x,y))|apart_point_and_line(x,B)),inference(resolution,[status(thm)],[148671888,167378288]),[]).
%
% cnf(148771968,plain,(~apart_point_and_line(x,u)),inference(rewrite,[status(thm)],[con]),[]).
%
% cnf(167769904,plain,(~distinct_points(A,x)|apart_point_and_line(A,u)|apart_point_and_line(A,line_connecting(x,y))),inference(forward_subsumption_resolution__resolution,[status(thm)],[148784656,167710680,148771968]),[]).
%
% fof(apart4,plain,(~distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C)),file('/tmp/SystemOnTPTP28198/GEO173+2.p',unknown),[]).
%
% cnf(148593104,plain,(~distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C)),inference(rewrite,[status(thm)],[apart4]),[]).
%
% cnf(167303368,plain,(~distinct_points(A,B)|distinct_points(B,A)),inference(resolution,[status(thm)],[148593104,148576080]),[]).
%
% cnf(167316832,plain,(distinct_points(y,x)),inference(resolution,[status(thm)],[167303368,148800864]),[]).
%
% cnf(167774320,plain,(apart_point_and_line(y,u)|apart_point_and_line(y,line_connecting(x,y))),inference(resolution,[status(thm)],[167769904,167316832]),[]).
%
% cnf(148632272,plain,(distinct_points(C,B)|~apart_point_and_line(C,line_connecting(A,B))|~distinct_points(A,B)),inference(rewrite,[status(thm)],[con1]),[]).
%
% cnf(167336856,plain,(~apart_point_and_line(B,line_connecting(A,B))|~distinct_points(A,B)),inference(resolution,[status(thm)],[148632272,148576080]),[]).
%
% cnf(167350424,plain,(~apart_point_and_line(y,line_connecting(x,y))),inference(resolution,[status(thm)],[167336856,148800864]),[]).
%
% cnf(167778408,plain,(apart_point_and_line(y,u)),inference(resolution,[status(thm)],[167774320,167350424]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[148764592,167778408]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------