%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO203+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 08:54:34 EST 2010
% Result : Theorem 4.53s
% Output : CNFRefutation 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 150 ( 46 ~; 73 |; 23 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ) ),
file('/tmp/tmpSIs0Wt/sel_GEO203+2.p_1',con1) ).
fof(2,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( ( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2) )
=> distinct_points(X3,intersection_point(X1,X2)) ) ),
file('/tmp/tmpSIs0Wt/sel_GEO203+2.p_1',con2) ).
fof(3,axiom,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_lines(X4,X5) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X5) ) ),
file('/tmp/tmpSIs0Wt/sel_GEO203+2.p_1',cu1) ).
fof(7,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/tmp/tmpSIs0Wt/sel_GEO203+2.p_1',apart1) ).
fof(13,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
=> ~ distinct_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
file('/tmp/tmpSIs0Wt/sel_GEO203+2.p_1',con) ).
fof(14,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
=> ~ distinct_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
inference(assume_negation,[status(cth)],[13]) ).
fof(15,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(18,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
=> ~ distinct_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(19,plain,
! [X1,X2,X3] :
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X3,line_connecting(X1,X2))
| ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(20,plain,
! [X4,X5,X6] :
( ~ distinct_points(X4,X5)
| ~ apart_point_and_line(X6,line_connecting(X4,X5))
| ( distinct_points(X6,X4)
& distinct_points(X6,X5) ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,plain,
! [X4,X5,X6] :
( ( distinct_points(X6,X4)
| ~ apart_point_and_line(X6,line_connecting(X4,X5))
| ~ distinct_points(X4,X5) )
& ( distinct_points(X6,X5)
| ~ apart_point_and_line(X6,line_connecting(X4,X5))
| ~ distinct_points(X4,X5) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(22,plain,
( distinct_points(X3,X2)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X3,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(23,plain,
( distinct_points(X3,X1)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X3,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(24,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| ( ~ apart_point_and_line(X3,X1)
& ~ apart_point_and_line(X3,X2) )
| distinct_points(X3,intersection_point(X1,X2)) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(25,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| ( ~ apart_point_and_line(X6,X4)
& ~ apart_point_and_line(X6,X5) )
| distinct_points(X6,intersection_point(X4,X5)) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ apart_point_and_line(X6,X4)
| distinct_points(X6,intersection_point(X4,X5))
| ~ convergent_lines(X4,X5) )
& ( ~ apart_point_and_line(X6,X5)
| distinct_points(X6,intersection_point(X4,X5))
| ~ convergent_lines(X4,X5) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(28,plain,
( distinct_points(X3,intersection_point(X1,X2))
| ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(X3,X1) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(29,plain,
! [X1,X2,X4,X5] :
( ~ distinct_points(X1,X2)
| ~ distinct_lines(X4,X5)
| apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X5) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(30,plain,
! [X6,X7,X8,X9] :
( ~ distinct_points(X6,X7)
| ~ distinct_lines(X8,X9)
| apart_point_and_line(X6,X8)
| apart_point_and_line(X6,X9)
| apart_point_and_line(X7,X8)
| apart_point_and_line(X7,X9) ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(31,plain,
( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X4,X3)
| ~ distinct_lines(X3,X2)
| ~ distinct_points(X4,X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(41,plain,
! [X2] : ~ distinct_points(X2,X2),
inference(variable_rename,[status(thm)],[15]) ).
cnf(42,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[41]) ).
fof(56,negated_conjecture,
? [X1,X2,X3] :
( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3))
& distinct_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(57,negated_conjecture,
? [X4,X5,X6] :
( convergent_lines(X4,X5)
& convergent_lines(X4,X6)
& distinct_points(intersection_point(X4,X5),intersection_point(X4,X6))
& distinct_lines(line_connecting(intersection_point(X4,X5),intersection_point(X4,X6)),X4) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& convergent_lines(esk1_0,esk3_0)
& distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
& distinct_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0) ),
inference(skolemize,[status(esa)],[57]) ).
cnf(59,negated_conjecture,
distinct_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(61,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(62,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(71,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(spm,[status(thm)],[42,28,theory(equality)]) ).
cnf(73,negated_conjecture,
( apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(X2,esk1_0)
| apart_point_and_line(X2,line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| ~ distinct_points(X2,X1) ),
inference(spm,[status(thm)],[31,59,theory(equality)]) ).
cnf(241,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk3_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
inference(spm,[status(thm)],[73,60,theory(equality)]) ).
cnf(2039,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk3_0),intersection_point(esk1_0,esk3_0))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| ~ distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[22,241,theory(equality)]) ).
cnf(2043,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk3_0),intersection_point(esk1_0,esk3_0))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| $false ),
inference(rw,[status(thm)],[2039,60,theory(equality)]) ).
cnf(2044,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk3_0),intersection_point(esk1_0,esk3_0))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(cn,[status(thm)],[2043,theory(equality)]) ).
cnf(2045,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(sr,[status(thm)],[2044,42,theory(equality)]) ).
cnf(54689,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk2_0))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| ~ distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[23,2045,theory(equality)]) ).
cnf(54727,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk2_0))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| $false ),
inference(rw,[status(thm)],[54689,60,theory(equality)]) ).
cnf(54728,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk2_0))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
inference(cn,[status(thm)],[54727,theory(equality)]) ).
cnf(54729,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
inference(sr,[status(thm)],[54728,42,theory(equality)]) ).
cnf(54732,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[71,54729,theory(equality)]) ).
cnf(54767,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| $false ),
inference(rw,[status(thm)],[54732,61,theory(equality)]) ).
cnf(54768,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0),
inference(cn,[status(thm)],[54767,theory(equality)]) ).
cnf(54771,negated_conjecture,
~ convergent_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[71,54768,theory(equality)]) ).
cnf(54812,negated_conjecture,
$false,
inference(rw,[status(thm)],[54771,62,theory(equality)]) ).
cnf(54813,negated_conjecture,
$false,
inference(cn,[status(thm)],[54812,theory(equality)]) ).
cnf(54814,negated_conjecture,
$false,
54813,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO203+2.p
% --creating new selector for [GEO008+0.ax]
% -running prover on /tmp/tmpSIs0Wt/sel_GEO203+2.p_1 with time limit 29
% -prover status Theorem
% Problem GEO203+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO203+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO203+2.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------