TSTP Solution File: GEO204+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO204+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 08:55:04 EST 2010
% Result : Theorem 0.76s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 14 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 179 ( 63 ~; 88 |; 15 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 71 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',ax2) ).
fof(5,axiom,
! [X1,X2,X6,X7] :
( ( distinct_points(X1,X2)
& distinct_lines(X6,X7) )
=> ( apart_point_and_line(X1,X6)
| apart_point_and_line(X1,X7)
| apart_point_and_line(X2,X6)
| apart_point_and_line(X2,X7) ) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',cu1) ).
fof(8,axiom,
! [X1,X2,X5] :
( apart_point_and_line(X1,X2)
=> ( distinct_points(X1,X5)
| apart_point_and_line(X5,X2) ) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',ceq1) ).
fof(9,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',ci2) ).
fof(10,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',ci1) ).
fof(11,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',ax1) ).
fof(12,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',apart1) ).
fof(16,axiom,
! [X1,X2,X5] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X5)
| distinct_points(X2,X5) ) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',apart4) ).
fof(18,conjecture,
! [X1,X2,X5] :
( ( distinct_points(X1,X2)
& equal_points(X2,X5) )
=> ( distinct_points(X1,X5)
& equal_lines(line_connecting(X1,X2),line_connecting(X1,X5)) ) ),
file('/tmp/tmpIxJnkL/sel_GEO204+3.p_1',con) ).
fof(19,negated_conjecture,
~ ! [X1,X2,X5] :
( ( distinct_points(X1,X2)
& equal_points(X2,X5) )
=> ( distinct_points(X1,X5)
& equal_lines(line_connecting(X1,X2),line_connecting(X1,X5)) ) ),
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(21,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(22,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(23,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(24,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[12,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(29,plain,
( equal_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(40,plain,
! [X1,X2,X6,X7] :
( ~ distinct_points(X1,X2)
| ~ distinct_lines(X6,X7)
| apart_point_and_line(X1,X6)
| apart_point_and_line(X1,X7)
| apart_point_and_line(X2,X6)
| apart_point_and_line(X2,X7) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(41,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)],[40]) ).
cnf(42,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)],[41]) ).
fof(49,plain,
! [X1,X2,X5] :
( ~ apart_point_and_line(X1,X2)
| distinct_points(X1,X5)
| apart_point_and_line(X5,X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(50,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)],[49]) ).
cnf(51,plain,
( apart_point_and_line(X1,X2)
| distinct_points(X3,X1)
| ~ apart_point_and_line(X3,X2) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,plain,
! [X1,X2] :
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(53,plain,
! [X3,X4] :
( ~ distinct_points(X3,X4)
| ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
inference(variable_rename,[status(thm)],[52]) ).
cnf(54,plain,
( ~ apart_point_and_line(X1,line_connecting(X2,X1))
| ~ distinct_points(X2,X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(55,plain,
! [X1,X2] :
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(56,plain,
! [X3,X4] :
( ~ distinct_points(X3,X4)
| ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
inference(variable_rename,[status(thm)],[55]) ).
cnf(57,plain,
( ~ apart_point_and_line(X1,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(58,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(59,plain,
! [X3,X4] :
( ( ~ equal_points(X3,X4)
| ~ distinct_points(X3,X4) )
& ( distinct_points(X3,X4)
| equal_points(X3,X4) ) ),
inference(variable_rename,[status(thm)],[58]) ).
cnf(61,plain,
( ~ distinct_points(X1,X2)
| ~ equal_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(62,plain,
! [X2] : ~ distinct_points(X2,X2),
inference(variable_rename,[status(thm)],[24]) ).
cnf(63,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[62]) ).
fof(71,plain,
! [X1,X2,X5] :
( ~ distinct_points(X1,X2)
| distinct_points(X1,X5)
| distinct_points(X2,X5) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(72,plain,
! [X6,X7,X8] :
( ~ distinct_points(X6,X7)
| distinct_points(X6,X8)
| distinct_points(X7,X8) ),
inference(variable_rename,[status(thm)],[71]) ).
cnf(73,plain,
( distinct_points(X1,X2)
| distinct_points(X3,X2)
| ~ distinct_points(X3,X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(77,negated_conjecture,
? [X1,X2,X5] :
( distinct_points(X1,X2)
& equal_points(X2,X5)
& ( ~ distinct_points(X1,X5)
| ~ equal_lines(line_connecting(X1,X2),line_connecting(X1,X5)) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(78,negated_conjecture,
? [X6,X7,X8] :
( distinct_points(X6,X7)
& equal_points(X7,X8)
& ( ~ distinct_points(X6,X8)
| ~ equal_lines(line_connecting(X6,X7),line_connecting(X6,X8)) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& equal_points(esk2_0,esk3_0)
& ( ~ distinct_points(esk1_0,esk3_0)
| ~ equal_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[78]) ).
cnf(80,negated_conjecture,
( ~ equal_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
| ~ distinct_points(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(81,negated_conjecture,
equal_points(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(82,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(83,negated_conjecture,
( distinct_points(esk2_0,X1)
| distinct_points(esk1_0,X1) ),
inference(spm,[status(thm)],[73,82,theory(equality)]) ).
cnf(85,negated_conjecture,
~ distinct_points(esk2_0,esk3_0),
inference(spm,[status(thm)],[61,81,theory(equality)]) ).
cnf(116,negated_conjecture,
distinct_points(esk1_0,esk3_0),
inference(spm,[status(thm)],[85,83,theory(equality)]) ).
cnf(119,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk3_0,X2)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk1_0,X2)
| ~ distinct_lines(X2,X1) ),
inference(spm,[status(thm)],[42,116,theory(equality)]) ).
cnf(120,negated_conjecture,
( $false
| ~ equal_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ),
inference(rw,[status(thm)],[80,116,theory(equality)]) ).
cnf(121,negated_conjecture,
~ equal_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
inference(cn,[status(thm)],[120,theory(equality)]) ).
cnf(146,negated_conjecture,
distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
inference(spm,[status(thm)],[121,29,theory(equality)]) ).
cnf(530,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[119,146,theory(equality)]) ).
cnf(3910,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| ~ distinct_points(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[54,530,theory(equality)]) ).
cnf(3913,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[3910,116,theory(equality)]) ).
cnf(3914,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[3913,theory(equality)]) ).
cnf(9037,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,X1)
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[51,3914,theory(equality)]) ).
cnf(10243,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,esk2_0)
| ~ distinct_points(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[54,9037,theory(equality)]) ).
cnf(10249,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[10243,82,theory(equality)]) ).
cnf(10250,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,esk2_0) ),
inference(cn,[status(thm)],[10249,theory(equality)]) ).
cnf(10339,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,esk2_0)
| ~ distinct_points(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[57,10250,theory(equality)]) ).
cnf(10342,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[10339,116,theory(equality)]) ).
cnf(10343,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,esk2_0) ),
inference(cn,[status(thm)],[10342,theory(equality)]) ).
cnf(10344,negated_conjecture,
( distinct_points(esk3_0,esk2_0)
| ~ distinct_points(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[57,10343,theory(equality)]) ).
cnf(10347,negated_conjecture,
( distinct_points(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[10344,82,theory(equality)]) ).
cnf(10348,negated_conjecture,
distinct_points(esk3_0,esk2_0),
inference(cn,[status(thm)],[10347,theory(equality)]) ).
cnf(10349,negated_conjecture,
( distinct_points(esk2_0,X1)
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[73,10348,theory(equality)]) ).
cnf(10352,negated_conjecture,
distinct_points(esk2_0,esk3_0),
inference(spm,[status(thm)],[63,10349,theory(equality)]) ).
cnf(10355,negated_conjecture,
$false,
inference(sr,[status(thm)],[10352,85,theory(equality)]) ).
cnf(10356,negated_conjecture,
$false,
10355,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO204+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/tmpIxJnkL/sel_GEO204+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO204+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO204+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO204+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
%
%------------------------------------------------------------------------------