TSTP Solution File: GEO177+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO177+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 08:45:20 EST 2010
% Result : Theorem 3.34s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 14 unt; 0 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 195 ( 49 ~; 120 |; 15 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 57 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X3,X4,X6,X7] :
( ( distinct_points(X3,X4)
& distinct_lines(X6,X7) )
=> ( apart_point_and_line(X3,X6)
| apart_point_and_line(X3,X7)
| apart_point_and_line(X4,X6)
| apart_point_and_line(X4,X7) ) ),
file('/tmp/tmp9WDNLW/sel_GEO177+3.p_1',cu1) ).
fof(6,axiom,
! [X3,X4,X5] :
( apart_point_and_line(X3,X4)
=> ( distinct_lines(X4,X5)
| apart_point_and_line(X3,X5) ) ),
file('/tmp/tmp9WDNLW/sel_GEO177+3.p_1',ceq2) ).
fof(7,axiom,
! [X3,X4,X5] :
( apart_point_and_line(X3,X4)
=> ( distinct_points(X3,X5)
| apart_point_and_line(X5,X4) ) ),
file('/tmp/tmp9WDNLW/sel_GEO177+3.p_1',ceq1) ).
fof(8,axiom,
! [X3,X4] :
( distinct_points(X3,X4)
=> ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
file('/tmp/tmp9WDNLW/sel_GEO177+3.p_1',ci2) ).
fof(9,axiom,
! [X3,X4] :
( distinct_points(X3,X4)
=> ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
file('/tmp/tmp9WDNLW/sel_GEO177+3.p_1',ci1) ).
fof(10,axiom,
! [X3] : ~ distinct_points(X3,X3),
file('/tmp/tmp9WDNLW/sel_GEO177+3.p_1',apart1) ).
fof(16,conjecture,
! [X3,X4,X6,X7] :
( ( distinct_points(X3,X4)
& distinct_points(X6,X7) )
=> ( ( apart_point_and_line(X3,line_connecting(X6,X7))
| apart_point_and_line(X4,line_connecting(X6,X7)) )
=> ( apart_point_and_line(X6,line_connecting(X3,X4))
| apart_point_and_line(X7,line_connecting(X3,X4)) ) ) ),
file('/tmp/tmp9WDNLW/sel_GEO177+3.p_1',con) ).
fof(17,negated_conjecture,
~ ! [X3,X4,X6,X7] :
( ( distinct_points(X3,X4)
& distinct_points(X6,X7) )
=> ( ( apart_point_and_line(X3,line_connecting(X6,X7))
| apart_point_and_line(X4,line_connecting(X6,X7)) )
=> ( apart_point_and_line(X6,line_connecting(X3,X4))
| apart_point_and_line(X7,line_connecting(X3,X4)) ) ) ),
inference(assume_negation,[status(cth)],[16]) ).
fof(18,plain,
! [X3,X4] :
( distinct_points(X3,X4)
=> ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(19,plain,
! [X3,X4] :
( distinct_points(X3,X4)
=> ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(20,plain,
! [X3] : ~ distinct_points(X3,X3),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(32,plain,
! [X3,X4,X6,X7] :
( ~ distinct_points(X3,X4)
| ~ distinct_lines(X6,X7)
| apart_point_and_line(X3,X6)
| apart_point_and_line(X3,X7)
| apart_point_and_line(X4,X6)
| apart_point_and_line(X4,X7) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(33,plain,
! [X8,X9,X10,X11] :
( ~ distinct_points(X8,X9)
| ~ distinct_lines(X10,X11)
| apart_point_and_line(X8,X10)
| apart_point_and_line(X8,X11)
| apart_point_and_line(X9,X10)
| apart_point_and_line(X9,X11) ),
inference(variable_rename,[status(thm)],[32]) ).
cnf(34,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)],[33]) ).
fof(38,plain,
! [X3,X4,X5] :
( ~ apart_point_and_line(X3,X4)
| distinct_lines(X4,X5)
| apart_point_and_line(X3,X5) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(39,plain,
! [X6,X7,X8] :
( ~ apart_point_and_line(X6,X7)
| distinct_lines(X7,X8)
| apart_point_and_line(X6,X8) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( apart_point_and_line(X1,X2)
| distinct_lines(X3,X2)
| ~ apart_point_and_line(X1,X3) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X3,X4,X5] :
( ~ apart_point_and_line(X3,X4)
| distinct_points(X3,X5)
| apart_point_and_line(X5,X4) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(42,plain,
! [X6,X7,X8] :
( ~ apart_point_and_line(X6,X7)
| distinct_points(X6,X8)
| apart_point_and_line(X8,X7) ),
inference(variable_rename,[status(thm)],[41]) ).
cnf(43,plain,
( apart_point_and_line(X1,X2)
| distinct_points(X3,X1)
| ~ apart_point_and_line(X3,X2) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X3,X4] :
( ~ distinct_points(X3,X4)
| ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(45,plain,
! [X5,X6] :
( ~ distinct_points(X5,X6)
| ~ apart_point_and_line(X6,line_connecting(X5,X6)) ),
inference(variable_rename,[status(thm)],[44]) ).
cnf(46,plain,
( ~ apart_point_and_line(X1,line_connecting(X2,X1))
| ~ distinct_points(X2,X1) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X3,X4] :
( ~ distinct_points(X3,X4)
| ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(48,plain,
! [X5,X6] :
( ~ distinct_points(X5,X6)
| ~ apart_point_and_line(X5,line_connecting(X5,X6)) ),
inference(variable_rename,[status(thm)],[47]) ).
cnf(49,plain,
( ~ apart_point_and_line(X1,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,plain,
! [X4] : ~ distinct_points(X4,X4),
inference(variable_rename,[status(thm)],[20]) ).
cnf(51,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[50]) ).
fof(65,negated_conjecture,
? [X3,X4,X6,X7] :
( distinct_points(X3,X4)
& distinct_points(X6,X7)
& ( apart_point_and_line(X3,line_connecting(X6,X7))
| apart_point_and_line(X4,line_connecting(X6,X7)) )
& ~ apart_point_and_line(X6,line_connecting(X3,X4))
& ~ apart_point_and_line(X7,line_connecting(X3,X4)) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(66,negated_conjecture,
? [X8,X9,X10,X11] :
( distinct_points(X8,X9)
& distinct_points(X10,X11)
& ( apart_point_and_line(X8,line_connecting(X10,X11))
| apart_point_and_line(X9,line_connecting(X10,X11)) )
& ~ apart_point_and_line(X10,line_connecting(X8,X9))
& ~ apart_point_and_line(X11,line_connecting(X8,X9)) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& distinct_points(esk3_0,esk4_0)
& ( apart_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)) )
& ~ apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
& ~ apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[66]) ).
cnf(68,negated_conjecture,
~ apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[67]) ).
cnf(69,negated_conjecture,
~ apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[67]) ).
cnf(70,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[67]) ).
cnf(71,negated_conjecture,
distinct_points(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[67]) ).
cnf(72,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[67]) ).
cnf(77,negated_conjecture,
( apart_point_and_line(esk1_0,X1)
| distinct_lines(line_connecting(esk3_0,esk4_0),X1)
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[40,70,theory(equality)]) ).
cnf(120,negated_conjecture,
( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X2)
| ~ distinct_points(X3,X1) ),
inference(spm,[status(thm)],[34,77,theory(equality)]) ).
cnf(439,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk4_0,X1) ),
inference(spm,[status(thm)],[120,71,theory(equality)]) ).
cnf(6583,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk1_0,X1)
| ~ distinct_points(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[46,439,theory(equality)]) ).
cnf(6588,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk1_0,X1)
| $false ),
inference(rw,[status(thm)],[6583,71,theory(equality)]) ).
cnf(6589,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk1_0,X1) ),
inference(cn,[status(thm)],[6588,theory(equality)]) ).
cnf(13727,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk4_0,X1)
| ~ distinct_points(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[49,6589,theory(equality)]) ).
cnf(13731,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk4_0,X1)
| $false ),
inference(rw,[status(thm)],[13727,71,theory(equality)]) ).
cnf(13732,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk4_0,X1) ),
inference(cn,[status(thm)],[13731,theory(equality)]) ).
cnf(13765,negated_conjecture,
( apart_point_and_line(X1,X2)
| distinct_points(esk1_0,X1)
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,X2)
| apart_point_and_line(esk3_0,X2) ),
inference(spm,[status(thm)],[43,13732,theory(equality)]) ).
cnf(23690,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk1_0,X1) ),
inference(spm,[status(thm)],[68,13765,theory(equality)]) ).
cnf(23712,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk1_0,X1) ),
inference(sr,[status(thm)],[23690,69,theory(equality)]) ).
cnf(23806,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| distinct_points(esk1_0,esk1_0)
| ~ distinct_points(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[49,23712,theory(equality)]) ).
cnf(23812,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| distinct_points(esk1_0,esk1_0)
| $false ),
inference(rw,[status(thm)],[23806,72,theory(equality)]) ).
cnf(23813,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| distinct_points(esk1_0,esk1_0) ),
inference(cn,[status(thm)],[23812,theory(equality)]) ).
cnf(23814,negated_conjecture,
apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)),
inference(sr,[status(thm)],[23813,51,theory(equality)]) ).
cnf(23816,negated_conjecture,
( apart_point_and_line(esk2_0,X1)
| distinct_lines(line_connecting(esk3_0,esk4_0),X1) ),
inference(spm,[status(thm)],[40,23814,theory(equality)]) ).
cnf(23919,negated_conjecture,
( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,X2)
| ~ distinct_points(X3,X1) ),
inference(spm,[status(thm)],[34,23816,theory(equality)]) ).
cnf(48513,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk4_0,X1) ),
inference(spm,[status(thm)],[23919,71,theory(equality)]) ).
cnf(50609,negated_conjecture,
( apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[68,48513,theory(equality)]) ).
cnf(50619,negated_conjecture,
( apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[50609,69,theory(equality)]) ).
cnf(50623,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| ~ distinct_points(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[46,50619,theory(equality)]) ).
cnf(50625,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| $false ),
inference(rw,[status(thm)],[50623,71,theory(equality)]) ).
cnf(50626,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0)) ),
inference(cn,[status(thm)],[50625,theory(equality)]) ).
cnf(50628,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| ~ distinct_points(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[49,50626,theory(equality)]) ).
cnf(50630,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[50628,71,theory(equality)]) ).
cnf(50631,negated_conjecture,
apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)),
inference(cn,[status(thm)],[50630,theory(equality)]) ).
cnf(50633,negated_conjecture,
~ distinct_points(esk1_0,esk2_0),
inference(spm,[status(thm)],[46,50631,theory(equality)]) ).
cnf(50636,negated_conjecture,
$false,
inference(rw,[status(thm)],[50633,72,theory(equality)]) ).
cnf(50637,negated_conjecture,
$false,
inference(cn,[status(thm)],[50636,theory(equality)]) ).
cnf(50638,negated_conjecture,
$false,
50637,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO177+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/tmp9WDNLW/sel_GEO177+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO177+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO177+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO177+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
%
%------------------------------------------------------------------------------