TSTP Solution File: GEO191+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO191+2 : TPTP v5.0.0. Released v3.3.0.
% 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 08:49:32 EST 2010
% Result : Theorem 0.50s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 23 unt; 0 def)
% Number of atoms : 243 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 228 ( 69 ~; 129 |; 20 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 83 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [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/tmpoXoBVw/sel_GEO191+2.p_1',con2) ).
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/tmpoXoBVw/sel_GEO191+2.p_1',cu1) ).
fof(3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',ceq3) ).
fof(5,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_points(X1,X3)
| apart_point_and_line(X3,X2) ) ),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',ceq1) ).
fof(6,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',apart1) ).
fof(7,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',apart2) ).
fof(8,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',apart3) ).
fof(9,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',apart4) ).
fof(10,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',apart5) ).
fof(11,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',apart6) ).
fof(12,conjecture,
! [X1,X2,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X4,X5)
& ( apart_point_and_line(intersection_point(X1,X2),X4)
| apart_point_and_line(intersection_point(X1,X2),X5) ) )
=> ( apart_point_and_line(intersection_point(X4,X5),X1)
| apart_point_and_line(intersection_point(X4,X5),X2) ) ),
file('/tmp/tmpoXoBVw/sel_GEO191+2.p_1',con) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X4,X5)
& ( apart_point_and_line(intersection_point(X1,X2),X4)
| apart_point_and_line(intersection_point(X1,X2),X5) ) )
=> ( apart_point_and_line(intersection_point(X4,X5),X1)
| apart_point_and_line(intersection_point(X4,X5),X2) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(14,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(15,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(16,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(17,plain,
! [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)],[1]) ).
fof(18,plain,
! [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)],[17]) ).
fof(19,plain,
! [X4,X5,X6] :
( ( ~ apart_point_and_line(X6,X4)
| distinct_points(X6,intersection_point(X4,X5))
| ~ convergent_lines(X4,X5) )
& ( ~ apart_point_and_line(X6,X5)
| distinct_points(X6,intersection_point(X4,X5))
| ~ convergent_lines(X4,X5) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(20,plain,
( distinct_points(X3,intersection_point(X1,X2))
| ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(X3,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( distinct_points(X3,intersection_point(X1,X2))
| ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(X3,X1) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(22,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(23,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)],[22]) ).
cnf(24,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)],[23]) ).
fof(25,plain,
! [X1,X2] :
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(26,plain,
! [X3,X4] :
( ~ convergent_lines(X3,X4)
| distinct_lines(X3,X4) ),
inference(variable_rename,[status(thm)],[25]) ).
cnf(27,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(31,plain,
! [X1,X2,X3] :
( ~ apart_point_and_line(X1,X2)
| distinct_points(X1,X3)
| apart_point_and_line(X3,X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,plain,
! [X4,X5,X6] :
( ~ apart_point_and_line(X4,X5)
| distinct_points(X4,X6)
| apart_point_and_line(X6,X5) ),
inference(variable_rename,[status(thm)],[31]) ).
cnf(33,plain,
( apart_point_and_line(X1,X2)
| distinct_points(X3,X1)
| ~ apart_point_and_line(X3,X2) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X2] : ~ distinct_points(X2,X2),
inference(variable_rename,[status(thm)],[14]) ).
cnf(35,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,plain,
! [X2] : ~ distinct_lines(X2,X2),
inference(variable_rename,[status(thm)],[15]) ).
cnf(37,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X2] : ~ convergent_lines(X2,X2),
inference(variable_rename,[status(thm)],[16]) ).
cnf(39,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,plain,
! [X1,X2,X3] :
( ~ distinct_points(X1,X2)
| distinct_points(X1,X3)
| distinct_points(X2,X3) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(41,plain,
! [X4,X5,X6] :
( ~ distinct_points(X4,X5)
| distinct_points(X4,X6)
| distinct_points(X5,X6) ),
inference(variable_rename,[status(thm)],[40]) ).
cnf(42,plain,
( distinct_points(X1,X2)
| distinct_points(X3,X2)
| ~ distinct_points(X3,X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(44,plain,
! [X4,X5,X6] :
( ~ distinct_lines(X4,X5)
| distinct_lines(X4,X6)
| distinct_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(45,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ distinct_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(47,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| convergent_lines(X4,X6)
| convergent_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[46]) ).
cnf(48,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(49,negated_conjecture,
? [X1,X2,X4,X5] :
( convergent_lines(X1,X2)
& convergent_lines(X4,X5)
& ( apart_point_and_line(intersection_point(X1,X2),X4)
| apart_point_and_line(intersection_point(X1,X2),X5) )
& ~ apart_point_and_line(intersection_point(X4,X5),X1)
& ~ apart_point_and_line(intersection_point(X4,X5),X2) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(50,negated_conjecture,
? [X6,X7,X8,X9] :
( convergent_lines(X6,X7)
& convergent_lines(X8,X9)
& ( apart_point_and_line(intersection_point(X6,X7),X8)
| apart_point_and_line(intersection_point(X6,X7),X9) )
& ~ apart_point_and_line(intersection_point(X8,X9),X6)
& ~ apart_point_and_line(intersection_point(X8,X9),X7) ),
inference(variable_rename,[status(thm)],[49]) ).
fof(51,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& convergent_lines(esk3_0,esk4_0)
& ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0) )
& ~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
& ~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0) ),
inference(skolemize,[status(esa)],[50]) ).
cnf(52,negated_conjecture,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(53,negated_conjecture,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(54,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(55,negated_conjecture,
convergent_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(56,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(57,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[48,56,theory(equality)]) ).
cnf(62,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[35,20,theory(equality)]) ).
cnf(63,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[35,21,theory(equality)]) ).
cnf(64,plain,
( distinct_points(intersection_point(X1,X2),X3)
| distinct_points(X4,X3)
| ~ apart_point_and_line(X4,X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[42,20,theory(equality)]) ).
cnf(66,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(spm,[status(thm)],[45,27,theory(equality)]) ).
cnf(68,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[39,57,theory(equality)]) ).
cnf(197,negated_conjecture,
( distinct_points(intersection_point(X1,esk4_0),X2)
| distinct_points(intersection_point(esk1_0,esk2_0),X2)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| ~ convergent_lines(X1,esk4_0) ),
inference(spm,[status(thm)],[64,54,theory(equality)]) ).
cnf(259,negated_conjecture,
( distinct_lines(esk2_0,X1)
| distinct_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[66,68,theory(equality)]) ).
cnf(304,negated_conjecture,
distinct_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[37,259,theory(equality)]) ).
cnf(308,negated_conjecture,
( apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X2,esk1_0)
| apart_point_and_line(X2,esk2_0)
| ~ distinct_points(X2,X1) ),
inference(spm,[status(thm)],[24,304,theory(equality)]) ).
cnf(1104,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),X1)
| distinct_points(intersection_point(esk3_0,esk4_0),X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0) ),
inference(spm,[status(thm)],[197,55,theory(equality)]) ).
cnf(5989,negated_conjecture,
( distinct_points(intersection_point(esk3_0,esk4_0),intersection_point(esk1_0,esk2_0))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0) ),
inference(spm,[status(thm)],[35,1104,theory(equality)]) ).
cnf(6039,negated_conjecture,
( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0)
| apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_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),esk3_0) ),
inference(spm,[status(thm)],[308,5989,theory(equality)]) ).
cnf(6045,negated_conjecture,
( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_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),esk3_0) ),
inference(sr,[status(thm)],[6039,52,theory(equality)]) ).
cnf(6046,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_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),esk3_0) ),
inference(sr,[status(thm)],[6045,53,theory(equality)]) ).
cnf(6050,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[63,6046,theory(equality)]) ).
cnf(6053,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| $false ),
inference(rw,[status(thm)],[6050,56,theory(equality)]) ).
cnf(6054,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
inference(cn,[status(thm)],[6053,theory(equality)]) ).
cnf(6055,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),X1)
| apart_point_and_line(X1,esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[33,6054,theory(equality)]) ).
cnf(6063,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk3_0) ),
inference(spm,[status(thm)],[308,6055,theory(equality)]) ).
cnf(6528,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk2_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[63,6063,theory(equality)]) ).
cnf(6534,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk2_0)
| $false ),
inference(rw,[status(thm)],[6528,56,theory(equality)]) ).
cnf(6535,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk2_0) ),
inference(cn,[status(thm)],[6534,theory(equality)]) ).
cnf(6866,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk3_0)
| ~ convergent_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[62,6535,theory(equality)]) ).
cnf(6873,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk3_0)
| $false ),
inference(rw,[status(thm)],[6866,56,theory(equality)]) ).
cnf(6874,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk3_0) ),
inference(cn,[status(thm)],[6873,theory(equality)]) ).
cnf(6875,negated_conjecture,
( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0)
| apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0) ),
inference(spm,[status(thm)],[53,6874,theory(equality)]) ).
cnf(6882,negated_conjecture,
apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0),
inference(sr,[status(thm)],[6875,52,theory(equality)]) ).
cnf(6885,negated_conjecture,
~ convergent_lines(esk3_0,esk4_0),
inference(spm,[status(thm)],[63,6882,theory(equality)]) ).
cnf(6888,negated_conjecture,
$false,
inference(rw,[status(thm)],[6885,55,theory(equality)]) ).
cnf(6889,negated_conjecture,
$false,
inference(cn,[status(thm)],[6888,theory(equality)]) ).
cnf(6890,negated_conjecture,
$false,
6889,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO191+2.p
% --creating new selector for [GEO008+0.ax]
% -running prover on /tmp/tmpoXoBVw/sel_GEO191+2.p_1 with time limit 29
% -prover status Theorem
% Problem GEO191+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO191+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO191+2.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
%
%------------------------------------------------------------------------------