%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO205+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 08:55:29 EST 2010
% Result : Theorem 1.10s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 21 unt; 0 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 213 ( 72 ~; 111 |; 15 &)
% ( 4 <=>; 11 =>; 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 : 141 ( 0 sgn 92 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',ax2) ).
fof(4,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',ax6) ).
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/tmps-NqiZ/sel_GEO205+3.p_1',cu1) ).
fof(6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',ceq3) ).
fof(7,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',ceq2) ).
fof(9,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',ci3) ).
fof(10,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',ax1) ).
fof(12,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',ci4) ).
fof(14,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',apart2) ).
fof(15,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',apart3) ).
fof(17,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',apart5) ).
fof(18,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& equal_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& equal_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
file('/tmp/tmps-NqiZ/sel_GEO205+3.p_1',con) ).
fof(19,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& equal_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& equal_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(assume_negation,[status(cth)],[18]) ).
fof(20,plain,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(22,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(23,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[10,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(25,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(26,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(27,plain,
! [X1,X2] :
( ( ~ equal_lines(X1,X2)
| ~ distinct_lines(X1,X2) )
& ( distinct_lines(X1,X2)
| equal_lines(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(28,plain,
! [X3,X4] :
( ( ~ equal_lines(X3,X4)
| ~ distinct_lines(X3,X4) )
& ( distinct_lines(X3,X4)
| equal_lines(X3,X4) ) ),
inference(variable_rename,[status(thm)],[27]) ).
cnf(30,plain,
( ~ distinct_lines(X1,X2)
| ~ equal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(36,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(37,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| convergent_lines(X4,X6)
| convergent_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[36]) ).
cnf(38,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,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(40,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)],[39]) ).
cnf(41,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)],[40]) ).
fof(42,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| distinct_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(43,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| distinct_lines(X5,X6)
| convergent_lines(X4,X6) ),
inference(variable_rename,[status(thm)],[42]) ).
cnf(44,plain,
( convergent_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,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)],[7]) ).
fof(46,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)],[45]) ).
cnf(47,plain,
( apart_point_and_line(X1,X2)
| distinct_lines(X3,X2)
| ~ apart_point_and_line(X1,X3) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(51,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(52,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[51]) ).
cnf(53,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X1,X2] :
( ( ~ equal_points(X1,X2)
| ~ distinct_points(X1,X2) )
& ( distinct_points(X1,X2)
| equal_points(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(55,plain,
! [X3,X4] :
( ( ~ equal_points(X3,X4)
| ~ distinct_points(X3,X4) )
& ( distinct_points(X3,X4)
| equal_points(X3,X4) ) ),
inference(variable_rename,[status(thm)],[54]) ).
cnf(56,plain,
( equal_points(X1,X2)
| distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[55]) ).
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(67,plain,
! [X2] : ~ distinct_lines(X2,X2),
inference(variable_rename,[status(thm)],[25]) ).
cnf(68,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[67]) ).
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(74,plain,
! [X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(75,plain,
! [X4,X5,X6] :
( ~ distinct_lines(X4,X5)
| distinct_lines(X4,X6)
| distinct_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[74]) ).
cnf(76,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ distinct_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(77,negated_conjecture,
? [X1,X2,X3] :
( convergent_lines(X1,X2)
& equal_lines(X2,X3)
& ( ~ convergent_lines(X1,X3)
| ~ equal_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(78,negated_conjecture,
? [X4,X5,X6] :
( convergent_lines(X4,X5)
& equal_lines(X5,X6)
& ( ~ convergent_lines(X4,X6)
| ~ equal_points(intersection_point(X4,X5),intersection_point(X4,X6)) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& equal_lines(esk2_0,esk3_0)
& ( ~ convergent_lines(esk1_0,esk3_0)
| ~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[78]) ).
cnf(80,negated_conjecture,
( ~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(81,negated_conjecture,
equal_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(82,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(83,negated_conjecture,
~ distinct_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[30,81,theory(equality)]) ).
cnf(86,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[38,82,theory(equality)]) ).
cnf(87,negated_conjecture,
( convergent_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[44,82,theory(equality)]) ).
cnf(88,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[80,56,theory(equality)]) ).
cnf(92,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(esk2_0,X2)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[38,86,theory(equality)]) ).
cnf(99,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[83,87,theory(equality)]) ).
cnf(104,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| $false ),
inference(rw,[status(thm)],[88,99,theory(equality)]) ).
cnf(105,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
inference(cn,[status(thm)],[104,theory(equality)]) ).
cnf(118,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[70,92,theory(equality)]) ).
cnf(130,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[38,118,theory(equality)]) ).
cnf(135,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)],[41,105,theory(equality)]) ).
cnf(163,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,esk1_0) ),
inference(spm,[status(thm)],[70,130,theory(equality)]) ).
cnf(177,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[70,163,theory(equality)]) ).
cnf(181,negated_conjecture,
( convergent_lines(esk2_0,X1)
| distinct_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[44,177,theory(equality)]) ).
cnf(189,negated_conjecture,
( distinct_lines(X1,X2)
| distinct_lines(esk1_0,X2)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[76,181,theory(equality)]) ).
cnf(603,negated_conjecture,
( convergent_lines(esk2_0,esk2_0)
| distinct_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[83,189,theory(equality)]) ).
cnf(612,negated_conjecture,
distinct_lines(esk1_0,esk3_0),
inference(sr,[status(thm)],[603,70,theory(equality)]) ).
cnf(637,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[76,612,theory(equality)]) ).
cnf(642,negated_conjecture,
( distinct_lines(X1,X2)
| distinct_lines(esk3_0,X2)
| distinct_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[76,637,theory(equality)]) ).
cnf(1483,negated_conjecture,
( distinct_lines(esk1_0,esk2_0)
| distinct_lines(esk3_0,esk3_0) ),
inference(spm,[status(thm)],[83,642,theory(equality)]) ).
cnf(1495,negated_conjecture,
distinct_lines(esk1_0,esk2_0),
inference(sr,[status(thm)],[1483,68,theory(equality)]) ).
cnf(1533,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)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[135,1495,theory(equality)]) ).
cnf(11263,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_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)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[63,1533,theory(equality)]) ).
cnf(11266,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_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)],[11263,82,theory(equality)]) ).
cnf(11267,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_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)],[11266,theory(equality)]) ).
cnf(14554,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[53,11267,theory(equality)]) ).
cnf(14557,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0)
| $false ),
inference(rw,[status(thm)],[14554,82,theory(equality)]) ).
cnf(14558,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0) ),
inference(cn,[status(thm)],[14557,theory(equality)]) ).
cnf(14559,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),X1)
| distinct_lines(esk2_0,X1)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
inference(spm,[status(thm)],[47,14558,theory(equality)]) ).
cnf(14722,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| distinct_lines(esk2_0,esk3_0)
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[63,14559,theory(equality)]) ).
cnf(14730,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| distinct_lines(esk2_0,esk3_0)
| $false ),
inference(rw,[status(thm)],[14722,99,theory(equality)]) ).
cnf(14731,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| distinct_lines(esk2_0,esk3_0) ),
inference(cn,[status(thm)],[14730,theory(equality)]) ).
cnf(14732,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0),
inference(sr,[status(thm)],[14731,83,theory(equality)]) ).
cnf(14735,negated_conjecture,
~ convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[53,14732,theory(equality)]) ).
cnf(14753,negated_conjecture,
$false,
inference(rw,[status(thm)],[14735,99,theory(equality)]) ).
cnf(14754,negated_conjecture,
$false,
inference(cn,[status(thm)],[14753,theory(equality)]) ).
cnf(14755,negated_conjecture,
$false,
14754,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO205+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/tmps-NqiZ/sel_GEO205+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO205+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO205+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO205+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
%
%------------------------------------------------------------------------------