TSTP Solution File: GEO202+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO202+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 08:54:22 EST 2010
% Result : Theorem 13.47s
% Output : CNFRefutation 13.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 14 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 152 ( 53 ~; 71 |; 16 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,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/tmp3K6RTY/sel_GEO202+3.p_1',cu1) ).
fof(6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ceq3) ).
fof(9,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ci3) ).
fof(11,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ci1) ).
fof(12,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ax1) ).
fof(14,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ci4) ).
fof(17,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',apart3) ).
fof(20,conjecture,
! [X1,X2,X3] :
( ( distinct_points(X1,X2)
& distinct_points(X1,X3)
& convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
=> equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',con) ).
fof(21,negated_conjecture,
~ ! [X1,X2,X3] :
( ( distinct_points(X1,X2)
& distinct_points(X1,X3)
& convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
=> equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
inference(assume_negation,[status(cth)],[20]) ).
fof(23,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(25,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(26,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(27,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(29,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[17,theory(equality)]) ).
fof(38,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)],[4]) ).
fof(39,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)],[38]) ).
cnf(40,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)],[39]) ).
fof(44,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| distinct_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(45,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| distinct_lines(X5,X6)
| convergent_lines(X4,X6) ),
inference(variable_rename,[status(thm)],[44]) ).
cnf(46,plain,
( convergent_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(53,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(54,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[53]) ).
cnf(55,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(59,plain,
! [X1,X2] :
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(60,plain,
! [X3,X4] :
( ~ distinct_points(X3,X4)
| ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
inference(variable_rename,[status(thm)],[59]) ).
cnf(61,plain,
( ~ apart_point_and_line(X1,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(62,plain,
! [X1,X2] :
( ( ~ equal_points(X1,X2)
| ~ distinct_points(X1,X2) )
& ( distinct_points(X1,X2)
| equal_points(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(63,plain,
! [X3,X4] :
( ( ~ equal_points(X3,X4)
| ~ distinct_points(X3,X4) )
& ( distinct_points(X3,X4)
| equal_points(X3,X4) ) ),
inference(variable_rename,[status(thm)],[62]) ).
cnf(64,plain,
( equal_points(X1,X2)
| distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(69,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(70,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[69]) ).
cnf(71,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(77,plain,
! [X2] : ~ convergent_lines(X2,X2),
inference(variable_rename,[status(thm)],[29]) ).
cnf(78,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[77]) ).
fof(85,negated_conjecture,
? [X1,X2,X3] :
( distinct_points(X1,X2)
& distinct_points(X1,X3)
& convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3))
& ~ equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(86,negated_conjecture,
? [X4,X5,X6] :
( distinct_points(X4,X5)
& distinct_points(X4,X6)
& convergent_lines(line_connecting(X4,X5),line_connecting(X4,X6))
& ~ equal_points(intersection_point(line_connecting(X4,X5),line_connecting(X4,X6)),X4) ),
inference(variable_rename,[status(thm)],[85]) ).
fof(87,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& distinct_points(esk1_0,esk3_0)
& convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
& ~ equal_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0) ),
inference(skolemize,[status(esa)],[86]) ).
cnf(88,negated_conjecture,
~ equal_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(89,negated_conjecture,
convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(90,negated_conjecture,
distinct_points(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(91,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(96,negated_conjecture,
distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0),
inference(spm,[status(thm)],[88,64,theory(equality)]) ).
cnf(97,negated_conjecture,
( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| distinct_lines(line_connecting(esk1_0,esk3_0),X1) ),
inference(spm,[status(thm)],[46,89,theory(equality)]) ).
cnf(139,negated_conjecture,
( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,line_connecting(esk1_0,esk3_0))
| convergent_lines(line_connecting(esk1_0,esk2_0),X2)
| ~ distinct_points(X3,X1) ),
inference(spm,[status(thm)],[40,97,theory(equality)]) ).
cnf(474,negated_conjecture,
( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
| apart_point_and_line(esk1_0,X1)
| convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[139,96,theory(equality)]) ).
cnf(3103,negated_conjecture,
( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,X1)
| convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| ~ convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[71,474,theory(equality)]) ).
cnf(3106,negated_conjecture,
( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,X1)
| convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| $false ),
inference(rw,[status(thm)],[3103,89,theory(equality)]) ).
cnf(3107,negated_conjecture,
( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,X1)
| convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(cn,[status(thm)],[3106,theory(equality)]) ).
cnf(175210,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk2_0))
| ~ convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[55,3107,theory(equality)]) ).
cnf(175214,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[175210,89,theory(equality)]) ).
cnf(175215,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[175214,theory(equality)]) ).
cnf(175216,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[175215,78,theory(equality)]) ).
cnf(175218,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| ~ distinct_points(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[61,175216,theory(equality)]) ).
cnf(175220,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[175218,90,theory(equality)]) ).
cnf(175221,negated_conjecture,
apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)),
inference(cn,[status(thm)],[175220,theory(equality)]) ).
cnf(175223,negated_conjecture,
~ distinct_points(esk1_0,esk2_0),
inference(spm,[status(thm)],[61,175221,theory(equality)]) ).
cnf(175226,negated_conjecture,
$false,
inference(rw,[status(thm)],[175223,91,theory(equality)]) ).
cnf(175227,negated_conjecture,
$false,
inference(cn,[status(thm)],[175226,theory(equality)]) ).
cnf(175228,negated_conjecture,
$false,
175227,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO202+3.p
% --creating new selector for [GEO006+3.ax, GEO006+0.ax, GEO006+1.ax, GEO006+2.ax, GEO006+4.ax, GEO006+5.ax, GEO006+6.ax]
% -running prover on /tmp/tmp3K6RTY/sel_GEO202+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO202+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO202+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO202+3.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
%
%------------------------------------------------------------------------------