%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO172+1 : TPTP v5.0.0. Released v3.3.0.
% 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 08:43:23 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 12 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 54 ~; 65 |; 16 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 89 ( 0 sgn 58 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/tmp/tmpYQlOd2/sel_GEO172+1.p_1',ax6) ).
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/tmpYQlOd2/sel_GEO172+1.p_1',cu1) ).
fof(3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/tmp/tmpYQlOd2/sel_GEO172+1.p_1',ceq3) ).
fof(6,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/tmp/tmpYQlOd2/sel_GEO172+1.p_1',ci3) ).
fof(7,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/tmp/tmpYQlOd2/sel_GEO172+1.p_1',ci4) ).
fof(10,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/tmp/tmpYQlOd2/sel_GEO172+1.p_1',apart3) ).
fof(13,conjecture,
! [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/tmpYQlOd2/sel_GEO172+1.p_1',con) ).
fof(14,negated_conjecture,
~ ! [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(assume_negation,[status(cth)],[13]) ).
fof(15,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(16,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(19,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(20,negated_conjecture,
~ ! [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_simplification,[status(thm)],[14,theory(equality)]) ).
fof(21,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(22,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| convergent_lines(X4,X6)
| convergent_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[21]) ).
cnf(23,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,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(25,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)],[24]) ).
cnf(26,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)],[25]) ).
fof(27,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| distinct_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(28,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| distinct_lines(X5,X6)
| convergent_lines(X4,X6) ),
inference(variable_rename,[status(thm)],[27]) ).
cnf(29,plain,
( convergent_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(36,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(37,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[36]) ).
cnf(38,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(40,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[39]) ).
cnf(41,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(46,plain,
! [X2] : ~ convergent_lines(X2,X2),
inference(variable_rename,[status(thm)],[19]) ).
cnf(47,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[46]) ).
fof(54,negated_conjecture,
? [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)],[20]) ).
fof(55,negated_conjecture,
? [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)],[54]) ).
fof(56,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ apart_point_and_line(esk3_0,esk1_0)
& ~ apart_point_and_line(esk3_0,esk2_0)
& distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[55]) ).
cnf(57,negated_conjecture,
distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,negated_conjecture,
~ apart_point_and_line(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(59,negated_conjecture,
~ apart_point_and_line(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(60,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(61,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[23,60,theory(equality)]) ).
cnf(64,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[47,61,theory(equality)]) ).
cnf(71,negated_conjecture,
( distinct_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[29,64,theory(equality)]) ).
cnf(74,negated_conjecture,
( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,esk1_0)
| convergent_lines(esk2_0,X2)
| ~ distinct_points(X3,X1) ),
inference(spm,[status(thm)],[26,71,theory(equality)]) ).
cnf(196,negated_conjecture,
( apart_point_and_line(esk3_0,esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[74,57,theory(equality)]) ).
cnf(202,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| convergent_lines(esk2_0,X1) ),
inference(sr,[status(thm)],[196,59,theory(equality)]) ).
cnf(257,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| apart_point_and_line(esk3_0,X1)
| convergent_lines(esk2_0,X1)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[38,202,theory(equality)]) ).
cnf(264,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| apart_point_and_line(esk3_0,X1)
| convergent_lines(esk2_0,X1)
| $false ),
inference(rw,[status(thm)],[257,60,theory(equality)]) ).
cnf(265,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| apart_point_and_line(esk3_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(cn,[status(thm)],[264,theory(equality)]) ).
cnf(266,negated_conjecture,
( apart_point_and_line(esk3_0,esk2_0)
| convergent_lines(esk2_0,esk2_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[41,265,theory(equality)]) ).
cnf(270,negated_conjecture,
( apart_point_and_line(esk3_0,esk2_0)
| convergent_lines(esk2_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[266,60,theory(equality)]) ).
cnf(271,negated_conjecture,
( apart_point_and_line(esk3_0,esk2_0)
| convergent_lines(esk2_0,esk2_0) ),
inference(cn,[status(thm)],[270,theory(equality)]) ).
cnf(272,negated_conjecture,
convergent_lines(esk2_0,esk2_0),
inference(sr,[status(thm)],[271,58,theory(equality)]) ).
cnf(273,negated_conjecture,
$false,
inference(sr,[status(thm)],[272,47,theory(equality)]) ).
cnf(274,negated_conjecture,
$false,
273,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO172+1.p
% --creating new selector for [GEO006+0.ax]
% -running prover on /tmp/tmpYQlOd2/sel_GEO172+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO172+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO172+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO172+1.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
%
%------------------------------------------------------------------------------