TSTP Solution File: GEO172+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO172+3 : TPTP v5.0.0. Released v4.0.0.
% 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 08:43:32 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 14 unt; 0 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 166 ( 56 ~; 79 |; 18 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 11 sgn 71 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',ax6) ).
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/tmpbQOZWn/sel_GEO172+3.p_1',cu1) ).
fof(5,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',ceq3) ).
fof(8,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',ci3) ).
fof(9,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',ax1) ).
fof(11,axiom,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',a4) ).
fof(12,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',ci4) ).
fof(15,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',apart3) ).
fof(18,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& incident_point_and_line(X3,X1)
& incident_point_and_line(X3,X2) )
=> equal_points(X3,intersection_point(X1,X2)) ),
file('/tmp/tmpbQOZWn/sel_GEO172+3.p_1',con) ).
fof(19,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& incident_point_and_line(X3,X1)
& incident_point_and_line(X3,X2) )
=> equal_points(X3,intersection_point(X1,X2)) ),
inference(assume_negation,[status(cth)],[18]) ).
fof(21,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(22,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(23,plain,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(24,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(26,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(32,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(33,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| convergent_lines(X4,X6)
| convergent_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[32]) ).
cnf(34,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,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(36,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)],[35]) ).
cnf(37,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)],[36]) ).
fof(38,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| distinct_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(39,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| distinct_lines(X5,X6)
| convergent_lines(X4,X6) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( convergent_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(47,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(48,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[47]) ).
cnf(49,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,plain,
! [X1,X2] :
( ( ~ equal_points(X1,X2)
| ~ distinct_points(X1,X2) )
& ( distinct_points(X1,X2)
| equal_points(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(51,plain,
! [X3,X4] :
( ( ~ equal_points(X3,X4)
| ~ distinct_points(X3,X4) )
& ( distinct_points(X3,X4)
| equal_points(X3,X4) ) ),
inference(variable_rename,[status(thm)],[50]) ).
cnf(52,plain,
( equal_points(X1,X2)
| distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(57,plain,
! [X1,X2] :
( ( ~ incident_point_and_line(X1,X2)
| ~ apart_point_and_line(X1,X2) )
& ( apart_point_and_line(X1,X2)
| incident_point_and_line(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(58,plain,
! [X3,X4] :
( ( ~ incident_point_and_line(X3,X4)
| ~ apart_point_and_line(X3,X4) )
& ( apart_point_and_line(X3,X4)
| incident_point_and_line(X3,X4) ) ),
inference(variable_rename,[status(thm)],[57]) ).
cnf(60,plain,
( ~ apart_point_and_line(X1,X2)
| ~ incident_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(61,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(62,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[61]) ).
cnf(63,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[62]) ).
fof(69,plain,
! [X2] : ~ convergent_lines(X2,X2),
inference(variable_rename,[status(thm)],[26]) ).
cnf(70,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[69]) ).
fof(77,negated_conjecture,
? [X1,X2,X3] :
( convergent_lines(X1,X2)
& incident_point_and_line(X3,X1)
& incident_point_and_line(X3,X2)
& ~ equal_points(X3,intersection_point(X1,X2)) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(78,negated_conjecture,
? [X4,X5,X6] :
( convergent_lines(X4,X5)
& incident_point_and_line(X6,X4)
& incident_point_and_line(X6,X5)
& ~ equal_points(X6,intersection_point(X4,X5)) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& incident_point_and_line(esk3_0,esk1_0)
& incident_point_and_line(esk3_0,esk2_0)
& ~ equal_points(esk3_0,intersection_point(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[78]) ).
cnf(80,negated_conjecture,
~ equal_points(esk3_0,intersection_point(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(81,negated_conjecture,
incident_point_and_line(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(82,negated_conjecture,
incident_point_and_line(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(83,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(84,negated_conjecture,
distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)),
inference(spm,[status(thm)],[80,52,theory(equality)]) ).
cnf(86,negated_conjecture,
~ apart_point_and_line(esk3_0,esk1_0),
inference(spm,[status(thm)],[60,82,theory(equality)]) ).
cnf(87,negated_conjecture,
~ apart_point_and_line(esk3_0,esk2_0),
inference(spm,[status(thm)],[60,81,theory(equality)]) ).
cnf(89,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[34,83,theory(equality)]) ).
cnf(94,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(esk1_0,X2)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[34,89,theory(equality)]) ).
cnf(111,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(X1,esk1_0) ),
inference(spm,[status(thm)],[70,94,theory(equality)]) ).
cnf(123,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(esk2_0,X2)
| convergent_lines(X1,esk1_0) ),
inference(spm,[status(thm)],[34,111,theory(equality)]) ).
cnf(138,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[70,123,theory(equality)]) ).
cnf(154,negated_conjecture,
( convergent_lines(X1,X2)
| distinct_lines(esk1_0,X2)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[40,138,theory(equality)]) ).
cnf(223,negated_conjecture,
( convergent_lines(X3,esk2_0)
| distinct_lines(esk1_0,esk2_0) ),
inference(ef,[status(thm)],[154,theory(equality)]) ).
cnf(238,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X2,esk1_0)
| convergent_lines(X3,esk2_0)
| ~ distinct_points(X2,X1) ),
inference(spm,[status(thm)],[37,223,theory(equality)]) ).
cnf(1268,negated_conjecture,
( apart_point_and_line(esk3_0,esk1_0)
| apart_point_and_line(esk3_0,esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[238,84,theory(equality)]) ).
cnf(1275,negated_conjecture,
( apart_point_and_line(esk3_0,esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| convergent_lines(X1,esk2_0) ),
inference(sr,[status(thm)],[1268,86,theory(equality)]) ).
cnf(1276,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| convergent_lines(X1,esk2_0) ),
inference(sr,[status(thm)],[1275,87,theory(equality)]) ).
cnf(1317,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| convergent_lines(X1,esk2_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[49,1276,theory(equality)]) ).
cnf(1319,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| convergent_lines(X1,esk2_0)
| $false ),
inference(rw,[status(thm)],[1317,83,theory(equality)]) ).
cnf(1320,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| convergent_lines(X1,esk2_0) ),
inference(cn,[status(thm)],[1319,theory(equality)]) ).
cnf(1324,negated_conjecture,
( convergent_lines(X1,esk2_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[63,1320,theory(equality)]) ).
cnf(1326,negated_conjecture,
( convergent_lines(X1,esk2_0)
| $false ),
inference(rw,[status(thm)],[1324,83,theory(equality)]) ).
cnf(1327,negated_conjecture,
convergent_lines(X1,esk2_0),
inference(cn,[status(thm)],[1326,theory(equality)]) ).
cnf(1350,negated_conjecture,
$false,
inference(spm,[status(thm)],[70,1327,theory(equality)]) ).
cnf(1380,negated_conjecture,
$false,
1350,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO172+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/tmpbQOZWn/sel_GEO172+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO172+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO172+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO172+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
%
%------------------------------------------------------------------------------