TSTP Solution File: GEO225+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO225+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 12:03:44 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 64 ( 10 ~; 30 |; 24 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(ci2,plain,
! [A,B] :
( ~ distinct_points(A,B)
| ~ apart_point_and_line(B,line_connecting(A,B)) ),
file('/tmp/SystemOnTPTP14608/GEO225+1.p',unknown),
[] ).
cnf(174144072,plain,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(B,line_connecting(A,B)) ),
inference(rewrite,[status(thm)],[ci2]),
[] ).
fof(con,plain,
! [C] :
( ( point(a)
| apart_point_and_line(a,C) )
& ( point(b)
| apart_point_and_line(a,C) )
& ( distinct_points(a,b)
| apart_point_and_line(a,C) )
& ( apart_point_and_line(b,C)
| apart_point_and_line(a,C) )
& ( line(C)
| apart_point_and_line(a,C) )
& ( point(a)
| line(C) )
& ( point(b)
| line(C) )
& ( distinct_points(a,b)
| line(C) )
& ( apart_point_and_line(b,C)
| line(C) )
& ( line(C)
| line(C) )
& ( point(a)
| point(a) )
& ( point(b)
| point(a) )
& ( distinct_points(a,b)
| point(a) )
& ( apart_point_and_line(b,C)
| point(a) )
& ( line(C)
| point(a) )
& ( point(a)
| point(b) )
& ( point(b)
| point(b) )
& ( distinct_points(a,b)
| point(b) )
& ( apart_point_and_line(b,C)
| point(b) )
& ( line(C)
| point(b) )
& ( point(a)
| distinct_points(a,b) )
& ( point(b)
| distinct_points(a,b) )
& ( distinct_points(a,b)
| distinct_points(a,b) )
& ( apart_point_and_line(b,C)
| distinct_points(a,b) )
& ( line(C)
| distinct_points(a,b) ) ),
file('/tmp/SystemOnTPTP14608/GEO225+1.p',unknown),
[] ).
cnf(174457192,plain,
distinct_points(a,b),
inference(rewrite,[status(thm)],[con]),
[] ).
cnf(208766752,plain,
~ apart_point_and_line(b,line_connecting(a,b)),
inference(resolution,[status(thm)],[174144072,174457192]),
[] ).
cnf(174500744,plain,
( apart_point_and_line(b,C)
| apart_point_and_line(a,C) ),
inference(rewrite,[status(thm)],[con]),
[] ).
fof(ci1,plain,
! [A,B] :
( ~ distinct_points(A,B)
| ~ apart_point_and_line(A,line_connecting(A,B)) ),
file('/tmp/SystemOnTPTP14608/GEO225+1.p',unknown),
[] ).
cnf(174126608,plain,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(A,line_connecting(A,B)) ),
inference(rewrite,[status(thm)],[ci1]),
[] ).
cnf(208752888,plain,
~ apart_point_and_line(a,line_connecting(a,b)),
inference(resolution,[status(thm)],[174126608,174457192]),
[] ).
cnf(208808888,plain,
apart_point_and_line(b,line_connecting(a,b)),
inference(resolution,[status(thm)],[174500744,208752888]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[208766752,208808888]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(ci2,plain,(~distinct_points(A,B)|~apart_point_and_line(B,line_connecting(A,B))),file('/tmp/SystemOnTPTP14608/GEO225+1.p',unknown),[]).
%
% cnf(174144072,plain,(~distinct_points(A,B)|~apart_point_and_line(B,line_connecting(A,B))),inference(rewrite,[status(thm)],[ci2]),[]).
%
% fof(con,plain,(((point(a)|apart_point_and_line(a,C))&(point(b)|apart_point_and_line(a,C))&(distinct_points(a,b)|apart_point_and_line(a,C))&(apart_point_and_line(b,C)|apart_point_and_line(a,C))&(line(C)|apart_point_and_line(a,C))&(point(a)|line(C))&(point(b)|line(C))&(distinct_points(a,b)|line(C))&(apart_point_and_line(b,C)|line(C))&(line(C)|line(C))&(point(a)|point(a))&(point(b)|point(a))&(distinct_points(a,b)|point(a))&(apart_point_and_line(b,C)|point(a))&(line(C)|point(a))&(point(a)|point(b))&(point(b)|point(b))&(distinct_points(a,b)|point(b))&(apart_point_and_line(b,C)|point(b))&(line(C)|point(b))&(point(a)|distinct_points(a,b))&(point(b)|distinct_points(a,b))&(distinct_points(a,b)|distinct_points(a,b))&(apart_point_and_line(b,C)|distinct_points(a,b))&(line(C)|distinct_points(a,b)))),file('/tmp/SystemOnTPTP14608/GEO225+1.p',unknown),[]).
%
% cnf(174457192,plain,(distinct_points(a,b)),inference(rewrite,[status(thm)],[con]),[]).
%
% cnf(208766752,plain,(~apart_point_and_line(b,line_connecting(a,b))),inference(resolution,[status(thm)],[174144072,174457192]),[]).
%
% cnf(174500744,plain,(apart_point_and_line(b,C)|apart_point_and_line(a,C)),inference(rewrite,[status(thm)],[con]),[]).
%
% fof(ci1,plain,(~distinct_points(A,B)|~apart_point_and_line(A,line_connecting(A,B))),file('/tmp/SystemOnTPTP14608/GEO225+1.p',unknown),[]).
%
% cnf(174126608,plain,(~distinct_points(A,B)|~apart_point_and_line(A,line_connecting(A,B))),inference(rewrite,[status(thm)],[ci1]),[]).
%
% cnf(208752888,plain,(~apart_point_and_line(a,line_connecting(a,b))),inference(resolution,[status(thm)],[174126608,174457192]),[]).
%
% cnf(208808888,plain,(apart_point_and_line(b,line_connecting(a,b))),inference(resolution,[status(thm)],[174500744,208752888]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[208766752,208808888]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------