TSTP Solution File: GEO187+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO187+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 08:48:15 EST 2010
% Result : Theorem 9.06s
% Output : CNFRefutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 12 unt; 0 def)
% Number of atoms : 224 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 218 ( 54 ~; 128 |; 29 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 88 ( 0 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ) ),
file('/tmp/tmpGLFvwF/sel_GEO187+2.p_1',con1) ).
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/tmpGLFvwF/sel_GEO187+2.p_1',cu1) ).
fof(3,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/tmp/tmpGLFvwF/sel_GEO187+2.p_1',ceq2) ).
fof(5,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/tmp/tmpGLFvwF/sel_GEO187+2.p_1',apart1) ).
fof(9,conjecture,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_points(X4,X5)
& ~ apart_point_and_line(X1,line_connecting(X4,X5))
& ~ apart_point_and_line(X2,line_connecting(X4,X5)) )
=> ( ~ apart_point_and_line(X4,line_connecting(X1,X2))
& ~ apart_point_and_line(X5,line_connecting(X1,X2)) ) ),
file('/tmp/tmpGLFvwF/sel_GEO187+2.p_1',con) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_points(X4,X5)
& ~ apart_point_and_line(X1,line_connecting(X4,X5))
& ~ apart_point_and_line(X2,line_connecting(X4,X5)) )
=> ( ~ apart_point_and_line(X4,line_connecting(X1,X2))
& ~ apart_point_and_line(X5,line_connecting(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(11,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_points(X4,X5)
& ~ apart_point_and_line(X1,line_connecting(X4,X5))
& ~ apart_point_and_line(X2,line_connecting(X4,X5)) )
=> ( ~ apart_point_and_line(X4,line_connecting(X1,X2))
& ~ apart_point_and_line(X5,line_connecting(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(14,plain,
! [X1,X2,X3] :
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X3,line_connecting(X1,X2))
| ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(15,plain,
! [X4,X5,X6] :
( ~ distinct_points(X4,X5)
| ~ apart_point_and_line(X6,line_connecting(X4,X5))
| ( distinct_points(X6,X4)
& distinct_points(X6,X5) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( distinct_points(X6,X4)
| ~ apart_point_and_line(X6,line_connecting(X4,X5))
| ~ distinct_points(X4,X5) )
& ( distinct_points(X6,X5)
| ~ apart_point_and_line(X6,line_connecting(X4,X5))
| ~ distinct_points(X4,X5) ) ),
inference(distribute,[status(thm)],[15]) ).
cnf(17,plain,
( distinct_points(X3,X2)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X3,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,plain,
( distinct_points(X3,X1)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X3,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(19,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(20,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)],[19]) ).
cnf(21,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)],[20]) ).
fof(22,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)],[3]) ).
fof(23,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)],[22]) ).
cnf(24,plain,
( apart_point_and_line(X1,X2)
| distinct_lines(X3,X2)
| ~ apart_point_and_line(X1,X3) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(28,plain,
! [X2] : ~ distinct_points(X2,X2),
inference(variable_rename,[status(thm)],[11]) ).
cnf(29,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[28]) ).
fof(38,negated_conjecture,
? [X1,X2,X4,X5] :
( distinct_points(X1,X2)
& distinct_points(X4,X5)
& ~ apart_point_and_line(X1,line_connecting(X4,X5))
& ~ apart_point_and_line(X2,line_connecting(X4,X5))
& ( apart_point_and_line(X4,line_connecting(X1,X2))
| apart_point_and_line(X5,line_connecting(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(39,negated_conjecture,
? [X6,X7,X8,X9] :
( distinct_points(X6,X7)
& distinct_points(X8,X9)
& ~ apart_point_and_line(X6,line_connecting(X8,X9))
& ~ apart_point_and_line(X7,line_connecting(X8,X9))
& ( apart_point_and_line(X8,line_connecting(X6,X7))
| apart_point_and_line(X9,line_connecting(X6,X7)) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,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)],[39]) ).
cnf(41,negated_conjecture,
( apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(42,negated_conjecture,
~ apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(43,negated_conjecture,
~ apart_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(44,negated_conjecture,
distinct_points(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(45,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(49,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[24,41,theory(equality)]) ).
cnf(108,negated_conjecture,
( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X2)
| ~ distinct_points(X3,X1) ),
inference(spm,[status(thm)],[21,49,theory(equality)]) ).
cnf(472,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,X1) ),
inference(spm,[status(thm)],[108,45,theory(equality)]) ).
cnf(7010,negated_conjecture,
( distinct_points(esk1_0,esk1_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk4_0,X1)
| ~ distinct_points(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[18,472,theory(equality)]) ).
cnf(7015,negated_conjecture,
( distinct_points(esk1_0,esk1_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk4_0,X1)
| $false ),
inference(rw,[status(thm)],[7010,45,theory(equality)]) ).
cnf(7016,negated_conjecture,
( distinct_points(esk1_0,esk1_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk4_0,X1) ),
inference(cn,[status(thm)],[7015,theory(equality)]) ).
cnf(7017,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk4_0,X1) ),
inference(sr,[status(thm)],[7016,29,theory(equality)]) ).
cnf(19530,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[43,7017,theory(equality)]) ).
cnf(19539,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0)) ),
inference(sr,[status(thm)],[19530,42,theory(equality)]) ).
cnf(19546,negated_conjecture,
( distinct_points(esk4_0,esk4_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| ~ distinct_points(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[17,19539,theory(equality)]) ).
cnf(19548,negated_conjecture,
( distinct_points(esk4_0,esk4_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[19546,44,theory(equality)]) ).
cnf(19549,negated_conjecture,
( distinct_points(esk4_0,esk4_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[19548,theory(equality)]) ).
cnf(19550,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[19549,29,theory(equality)]) ).
cnf(19555,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[24,19550,theory(equality)]) ).
cnf(20623,negated_conjecture,
( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,X2)
| ~ distinct_points(X3,X1) ),
inference(spm,[status(thm)],[21,19555,theory(equality)]) ).
cnf(138708,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,X1) ),
inference(spm,[status(thm)],[20623,45,theory(equality)]) ).
cnf(141250,negated_conjecture,
( distinct_points(esk1_0,esk1_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| ~ distinct_points(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[18,138708,theory(equality)]) ).
cnf(141255,negated_conjecture,
( distinct_points(esk1_0,esk1_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| $false ),
inference(rw,[status(thm)],[141250,45,theory(equality)]) ).
cnf(141256,negated_conjecture,
( distinct_points(esk1_0,esk1_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1) ),
inference(cn,[status(thm)],[141255,theory(equality)]) ).
cnf(141257,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1) ),
inference(sr,[status(thm)],[141256,29,theory(equality)]) ).
cnf(141258,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))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[43,141257,theory(equality)]) ).
cnf(141267,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(sr,[status(thm)],[141258,42,theory(equality)]) ).
cnf(141277,negated_conjecture,
( distinct_points(esk3_0,esk3_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| ~ distinct_points(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[18,141267,theory(equality)]) ).
cnf(141281,negated_conjecture,
( distinct_points(esk3_0,esk3_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[141277,44,theory(equality)]) ).
cnf(141282,negated_conjecture,
( distinct_points(esk3_0,esk3_0)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[141281,theory(equality)]) ).
cnf(141283,negated_conjecture,
apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)),
inference(sr,[status(thm)],[141282,29,theory(equality)]) ).
cnf(141286,negated_conjecture,
( distinct_points(esk2_0,esk2_0)
| ~ distinct_points(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[17,141283,theory(equality)]) ).
cnf(141295,negated_conjecture,
( distinct_points(esk2_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[141286,45,theory(equality)]) ).
cnf(141296,negated_conjecture,
distinct_points(esk2_0,esk2_0),
inference(cn,[status(thm)],[141295,theory(equality)]) ).
cnf(141297,negated_conjecture,
$false,
inference(sr,[status(thm)],[141296,29,theory(equality)]) ).
cnf(141298,negated_conjecture,
$false,
141297,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO187+2.p
% --creating new selector for [GEO008+0.ax]
% -running prover on /tmp/tmpGLFvwF/sel_GEO187+2.p_1 with time limit 29
% -prover status Theorem
% Problem GEO187+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO187+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO187+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
%
%------------------------------------------------------------------------------