TSTP Solution File: GEO203+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO203+3 : TPTP v5.0.0. Released v4.0.0.
% 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 08:54:42 EST 2010
% Result : Theorem 0.43s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 46 ~; 54 |; 16 &)
% ( 2 <=>; 9 =>; 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 : 70 ( 0 sgn 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ax2) ).
fof(5,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/tmpkmOnKC/sel_GEO203+3.p_1',cu1) ).
fof(10,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ci3) ).
fof(11,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ci2) ).
fof(12,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ci1) ).
fof(20,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
=> equal_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',con) ).
fof(21,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
=> equal_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
inference(assume_negation,[status(cth)],[20]) ).
fof(22,plain,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(24,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(25,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(26,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(30,plain,
! [X1,X2] :
( ( ~ equal_lines(X1,X2)
| ~ distinct_lines(X1,X2) )
& ( distinct_lines(X1,X2)
| equal_lines(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(31,plain,
! [X3,X4] :
( ( ~ equal_lines(X3,X4)
| ~ distinct_lines(X3,X4) )
& ( distinct_lines(X3,X4)
| equal_lines(X3,X4) ) ),
inference(variable_rename,[status(thm)],[30]) ).
cnf(32,plain,
( equal_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(42,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)],[5]) ).
fof(43,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)],[42]) ).
cnf(44,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)],[43]) ).
fof(57,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(58,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[57]) ).
cnf(59,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(60,plain,
! [X1,X2] :
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(61,plain,
! [X3,X4] :
( ~ distinct_points(X3,X4)
| ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
inference(variable_rename,[status(thm)],[60]) ).
cnf(62,plain,
( ~ apart_point_and_line(X1,line_connecting(X2,X1))
| ~ distinct_points(X2,X1) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,plain,
! [X1,X2] :
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(64,plain,
! [X3,X4] :
( ~ distinct_points(X3,X4)
| ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
inference(variable_rename,[status(thm)],[63]) ).
cnf(65,plain,
( ~ apart_point_and_line(X1,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(85,negated_conjecture,
? [X1,X2,X3] :
( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3))
& ~ equal_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(86,negated_conjecture,
? [X4,X5,X6] :
( convergent_lines(X4,X5)
& convergent_lines(X4,X6)
& distinct_points(intersection_point(X4,X5),intersection_point(X4,X6))
& ~ equal_lines(line_connecting(intersection_point(X4,X5),intersection_point(X4,X6)),X4) ),
inference(variable_rename,[status(thm)],[85]) ).
fof(87,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))
& ~ equal_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0) ),
inference(skolemize,[status(esa)],[86]) ).
cnf(88,negated_conjecture,
~ equal_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(89,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(90,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(91,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(96,negated_conjecture,
distinct_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0),
inference(spm,[status(thm)],[88,32,theory(equality)]) ).
cnf(101,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),X1)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),X2)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X2)
| ~ distinct_lines(X2,X1) ),
inference(spm,[status(thm)],[44,89,theory(equality)]) ).
cnf(131,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,esk2_0),esk1_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,esk3_0),esk1_0) ),
inference(spm,[status(thm)],[101,96,theory(equality)]) ).
cnf(494,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)
| ~ distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[62,131,theory(equality)]) ).
cnf(497,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)
| $false ),
inference(rw,[status(thm)],[494,89,theory(equality)]) ).
cnf(498,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(cn,[status(thm)],[497,theory(equality)]) ).
cnf(5628,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)
| ~ distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[65,498,theory(equality)]) ).
cnf(5630,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)
| $false ),
inference(rw,[status(thm)],[5628,89,theory(equality)]) ).
cnf(5631,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(cn,[status(thm)],[5630,theory(equality)]) ).
cnf(5634,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[59,5631,theory(equality)]) ).
cnf(5635,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| $false ),
inference(rw,[status(thm)],[5634,90,theory(equality)]) ).
cnf(5636,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0),
inference(cn,[status(thm)],[5635,theory(equality)]) ).
cnf(5639,negated_conjecture,
~ convergent_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[59,5636,theory(equality)]) ).
cnf(5641,negated_conjecture,
$false,
inference(rw,[status(thm)],[5639,91,theory(equality)]) ).
cnf(5642,negated_conjecture,
$false,
inference(cn,[status(thm)],[5641,theory(equality)]) ).
cnf(5643,negated_conjecture,
$false,
5642,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO203+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/tmpkmOnKC/sel_GEO203+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO203+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO203+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO203+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
%
%------------------------------------------------------------------------------