TSTP Solution File: GEO205+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO205+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 08:55:25 EST 2010
% Result : Theorem 71.26s
% Output : CNFRefutation 71.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 18 unt; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 67 ~; 96 |; 16 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 72 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,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/tmpBQluW6/sel_GEO205+2.p_2',con2) ).
fof(2,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/tmpBQluW6/sel_GEO205+2.p_2',cu1) ).
fof(3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/tmp/tmpBQluW6/sel_GEO205+2.p_2',ceq3) ).
fof(4,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/tmp/tmpBQluW6/sel_GEO205+2.p_2',ceq2) ).
fof(6,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/tmp/tmpBQluW6/sel_GEO205+2.p_2',apart1) ).
fof(7,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/tmp/tmpBQluW6/sel_GEO205+2.p_2',apart2) ).
fof(10,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/tmp/tmpBQluW6/sel_GEO205+2.p_2',apart5) ).
fof(11,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/tmp/tmpBQluW6/sel_GEO205+2.p_2',apart6) ).
fof(12,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& ~ distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
file('/tmp/tmpBQluW6/sel_GEO205+2.p_2',con) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& ~ distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(14,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(15,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(17,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& ~ distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).
fof(18,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)],[1]) ).
fof(19,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)],[18]) ).
fof(20,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)],[19]) ).
cnf(21,plain,
( distinct_points(X3,intersection_point(X1,X2))
| ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(X3,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( distinct_points(X3,intersection_point(X1,X2))
| ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(X3,X1) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(23,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)],[2]) ).
fof(24,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)],[23]) ).
cnf(25,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)],[24]) ).
fof(26,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(27,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| distinct_lines(X3,X4) ),
inference(variable_rename,[status(thm)],[26]) ).
cnf(28,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X1,X2,X3] :
( ~ apart_point_and_line(X1,X2)
| distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(30,plain,
! [X4,X5,X6] :
( ~ apart_point_and_line(X4,X5)
| distinct_lines(X5,X6)
| apart_point_and_line(X4,X6) ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(31,plain,
( apart_point_and_line(X1,X2)
| distinct_lines(X3,X2)
| ~ apart_point_and_line(X1,X3) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(35,plain,
! [X2] : ~ distinct_points(X2,X2),
inference(variable_rename,[status(thm)],[14]) ).
cnf(36,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X2] : ~ distinct_lines(X2,X2),
inference(variable_rename,[status(thm)],[15]) ).
cnf(38,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[37]) ).
fof(44,plain,
! [X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(45,plain,
! [X4,X5,X6] :
( ~ distinct_lines(X4,X5)
| distinct_lines(X4,X6)
| distinct_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[44]) ).
cnf(46,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ distinct_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(48,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| convergent_lines(X4,X6)
| convergent_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[47]) ).
cnf(49,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,negated_conjecture,
? [X1,X2,X3] :
( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3)
& ( ~ convergent_lines(X1,X3)
| distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(51,negated_conjecture,
? [X4,X5,X6] :
( convergent_lines(X4,X5)
& ~ distinct_lines(X5,X6)
& ( ~ convergent_lines(X4,X6)
| distinct_points(intersection_point(X4,X5),intersection_point(X4,X6)) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ distinct_lines(esk2_0,esk3_0)
& ( ~ convergent_lines(esk1_0,esk3_0)
| distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[51]) ).
cnf(53,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(54,negated_conjecture,
~ distinct_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(55,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(56,negated_conjecture,
~ convergent_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[54,28,theory(equality)]) ).
cnf(57,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[49,55,theory(equality)]) ).
cnf(60,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(spm,[status(thm)],[46,28,theory(equality)]) ).
cnf(61,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[36,21,theory(equality)]) ).
cnf(63,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[36,22,theory(equality)]) ).
cnf(69,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[56,57,theory(equality)]) ).
cnf(71,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| $false ),
inference(rw,[status(thm)],[53,69,theory(equality)]) ).
cnf(72,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
inference(cn,[status(thm)],[71,theory(equality)]) ).
cnf(96,negated_conjecture,
( distinct_lines(esk1_0,X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[60,69,theory(equality)]) ).
cnf(104,negated_conjecture,
distinct_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[38,96,theory(equality)]) ).
cnf(108,negated_conjecture,
( apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X2,esk3_0)
| apart_point_and_line(X2,esk1_0)
| ~ distinct_points(X2,X1) ),
inference(spm,[status(thm)],[25,104,theory(equality)]) ).
cnf(641,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk3_0) ),
inference(spm,[status(thm)],[108,72,theory(equality)]) ).
cnf(8897,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[61,641,theory(equality)]) ).
cnf(8902,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| $false ),
inference(rw,[status(thm)],[8897,69,theory(equality)]) ).
cnf(8903,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(cn,[status(thm)],[8902,theory(equality)]) ).
cnf(314139,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[63,8903,theory(equality)]) ).
cnf(314405,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| $false ),
inference(rw,[status(thm)],[314139,69,theory(equality)]) ).
cnf(314406,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0) ),
inference(cn,[status(thm)],[314405,theory(equality)]) ).
cnf(314408,negated_conjecture,
( distinct_lines(esk3_0,X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[31,314406,theory(equality)]) ).
cnf(314867,negated_conjecture,
( distinct_lines(esk3_0,esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[61,314408,theory(equality)]) ).
cnf(315403,negated_conjecture,
( distinct_lines(esk3_0,esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| $false ),
inference(rw,[status(thm)],[314867,55,theory(equality)]) ).
cnf(315404,negated_conjecture,
( distinct_lines(esk3_0,esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(cn,[status(thm)],[315403,theory(equality)]) ).
cnf(315410,negated_conjecture,
( distinct_lines(esk3_0,esk2_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[63,315404,theory(equality)]) ).
cnf(315676,negated_conjecture,
( distinct_lines(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[315410,55,theory(equality)]) ).
cnf(315677,negated_conjecture,
distinct_lines(esk3_0,esk2_0),
inference(cn,[status(thm)],[315676,theory(equality)]) ).
cnf(315678,negated_conjecture,
( distinct_lines(esk2_0,X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[46,315677,theory(equality)]) ).
cnf(315681,negated_conjecture,
distinct_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[38,315678,theory(equality)]) ).
cnf(315684,negated_conjecture,
$false,
inference(sr,[status(thm)],[315681,54,theory(equality)]) ).
cnf(315685,negated_conjecture,
$false,
315684,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO205+2.p
% --creating new selector for [GEO008+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpBQluW6/sel_GEO205+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpBQluW6/sel_GEO205+2.p_2 with time limit 80
% -prover status Theorem
% Problem GEO205+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO205+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO205+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
%
%------------------------------------------------------------------------------