TSTP Solution File: GEO222+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO222+1 : TPTP v5.0.0. Released v3.3.0.
% 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 08:59:24 EST 2010
% Result : Theorem 0.88s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 25 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 164 ( 45 ~; 105 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 147 ( 21 sgn 67 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
=> ( ( convergent_lines(X1,X3)
& unorthogonal_lines(X1,X3) )
| ( convergent_lines(X2,X3)
& unorthogonal_lines(X2,X3) ) ) ),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',oac1) ).
fof(2,axiom,
! [X4,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ) ),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',ouo1) ).
fof(3,axiom,
! [X5,X6,X7] :
( convergent_lines(X5,X6)
=> ( convergent_lines(X5,X7)
| convergent_lines(X6,X7) ) ),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',ax6) ).
fof(4,axiom,
! [X5,X6,X7] :
( convergent_lines(X5,X6)
=> ( distinct_lines(X6,X7)
| convergent_lines(X5,X7) ) ),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',ceq3) ).
fof(6,axiom,
! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',ooc1) ).
fof(7,axiom,
! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',ooc2) ).
fof(10,axiom,
! [X5] : ~ convergent_lines(X5,X5),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',apart3) ).
fof(12,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',occu1) ).
fof(13,conjecture,
! [X4,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
file('/tmp/tmpQ3lytR/sel_GEO222+1.p_1',con) ).
fof(14,negated_conjecture,
~ ! [X4,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(assume_negation,[status(cth)],[13]) ).
fof(15,plain,
! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(16,plain,
! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(18,plain,
! [X5] : ~ convergent_lines(X5,X5),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(19,negated_conjecture,
~ ! [X4,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(20,plain,
! [X1,X2,X3] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| ( convergent_lines(X1,X3)
& unorthogonal_lines(X1,X3) )
| ( convergent_lines(X2,X3)
& unorthogonal_lines(X2,X3) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(21,plain,
! [X4,X5,X6] :
( ~ convergent_lines(X4,X5)
| ~ unorthogonal_lines(X4,X5)
| ( convergent_lines(X4,X6)
& unorthogonal_lines(X4,X6) )
| ( convergent_lines(X5,X6)
& unorthogonal_lines(X5,X6) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X4,X5,X6] :
( ( convergent_lines(X5,X6)
| convergent_lines(X4,X6)
| ~ convergent_lines(X4,X5)
| ~ unorthogonal_lines(X4,X5) )
& ( unorthogonal_lines(X5,X6)
| convergent_lines(X4,X6)
| ~ convergent_lines(X4,X5)
| ~ unorthogonal_lines(X4,X5) )
& ( convergent_lines(X5,X6)
| unorthogonal_lines(X4,X6)
| ~ convergent_lines(X4,X5)
| ~ unorthogonal_lines(X4,X5) )
& ( unorthogonal_lines(X5,X6)
| unorthogonal_lines(X4,X6)
| ~ convergent_lines(X4,X5)
| ~ unorthogonal_lines(X4,X5) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(23,plain,
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(25,plain,
( convergent_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(27,plain,
! [X4,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(28,plain,
! [X5,X6,X7,X8] :
( ~ distinct_lines(X6,X7)
| apart_point_and_line(X5,X6)
| apart_point_and_line(X5,X7)
| unorthogonal_lines(X6,X8)
| unorthogonal_lines(X7,X8) ),
inference(variable_rename,[status(thm)],[27]) ).
cnf(29,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X3)
| ~ distinct_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X5,X6,X7] :
( ~ convergent_lines(X5,X6)
| convergent_lines(X5,X7)
| convergent_lines(X6,X7) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(31,plain,
! [X8,X9,X10] :
( ~ convergent_lines(X8,X9)
| convergent_lines(X8,X10)
| convergent_lines(X9,X10) ),
inference(variable_rename,[status(thm)],[30]) ).
cnf(32,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X5,X6,X7] :
( ~ convergent_lines(X5,X6)
| distinct_lines(X6,X7)
| convergent_lines(X5,X7) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(34,plain,
! [X8,X9,X10] :
( ~ convergent_lines(X8,X9)
| distinct_lines(X9,X10)
| convergent_lines(X8,X10) ),
inference(variable_rename,[status(thm)],[33]) ).
cnf(35,plain,
( convergent_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(39,plain,
! [X5,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X5),X6),
inference(variable_rename,[status(thm)],[15]) ).
cnf(40,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X5,X6] : ~ apart_point_and_line(X5,orthogonal_through_point(X6,X5)),
inference(variable_rename,[status(thm)],[16]) ).
cnf(42,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[41]) ).
fof(48,plain,
! [X6] : ~ convergent_lines(X6,X6),
inference(variable_rename,[status(thm)],[18]) ).
cnf(49,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[48]) ).
fof(53,plain,
! [X3,X4] :
( convergent_lines(X3,X4)
| unorthogonal_lines(X3,X4) ),
inference(variable_rename,[status(thm)],[12]) ).
cnf(54,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(55,negated_conjecture,
? [X4,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(fof_nnf,[status(thm)],[19]) ).
fof(56,negated_conjecture,
? [X5,X6] : convergent_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X5),X5)),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,negated_conjecture,
convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(skolemize,[status(esa)],[56]) ).
cnf(58,negated_conjecture,
convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(59,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[40,54,theory(equality)]) ).
cnf(60,negated_conjecture,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[32,58,theory(equality)]) ).
cnf(66,plain,
( convergent_lines(X1,X2)
| convergent_lines(orthogonal_through_point(X1,X3),X2) ),
inference(spm,[status(thm)],[32,59,theory(equality)]) ).
cnf(67,plain,
( distinct_lines(X1,X2)
| convergent_lines(orthogonal_through_point(X1,X3),X2) ),
inference(spm,[status(thm)],[35,59,theory(equality)]) ).
cnf(69,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X2)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[32,60,theory(equality)]) ).
cnf(72,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[49,66,theory(equality)]) ).
cnf(77,plain,
distinct_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[49,67,theory(equality)]) ).
cnf(82,plain,
( apart_point_and_line(X1,orthogonal_through_point(X2,X3))
| apart_point_and_line(X1,X2)
| unorthogonal_lines(orthogonal_through_point(X2,X3),X4)
| unorthogonal_lines(X2,X4) ),
inference(spm,[status(thm)],[29,77,theory(equality)]) ).
cnf(95,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X3) ),
inference(spm,[status(thm)],[32,69,theory(equality)]) ).
cnf(241,plain,
( apart_point_and_line(X1,X2)
| unorthogonal_lines(orthogonal_through_point(X2,X1),X3)
| unorthogonal_lines(X2,X3) ),
inference(spm,[status(thm)],[42,82,theory(equality)]) ).
cnf(396,negated_conjecture,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),esk2_0)
| convergent_lines(X6,X6)
| convergent_lines(esk2_0,X6) ),
inference(ef,[status(thm)],[95,theory(equality)]) ).
cnf(416,negated_conjecture,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),esk2_0)
| convergent_lines(esk2_0,X6) ),
inference(sr,[status(thm)],[396,49,theory(equality)]) ).
cnf(494,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(orthogonal_through_point(X3,X4),X2)
| apart_point_and_line(X4,X3)
| unorthogonal_lines(X3,X1)
| ~ convergent_lines(orthogonal_through_point(X3,X4),X1) ),
inference(spm,[status(thm)],[25,241,theory(equality)]) ).
cnf(12155,negated_conjecture,
( apart_point_and_line(esk1_0,orthogonal_through_point(esk2_0,esk1_0))
| unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),esk2_0)
| unorthogonal_lines(esk2_0,X1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X2) ),
inference(spm,[status(thm)],[494,416,theory(equality)]) ).
cnf(12672,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),esk2_0)
| unorthogonal_lines(esk2_0,X1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X2) ),
inference(sr,[status(thm)],[12155,42,theory(equality)]) ).
cnf(12673,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X2) ),
inference(sr,[status(thm)],[12672,40,theory(equality)]) ).
cnf(12722,negated_conjecture,
( unorthogonal_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[49,12673,theory(equality)]) ).
cnf(12753,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X2)
| ~ convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[23,12722,theory(equality)]) ).
cnf(12761,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X2)
| $false ),
inference(rw,[status(thm)],[12753,58,theory(equality)]) ).
cnf(12762,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(esk2_0,X2) ),
inference(cn,[status(thm)],[12761,theory(equality)]) ).
cnf(13378,negated_conjecture,
( unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0))
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[40,12762,theory(equality)]) ).
cnf(13393,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,X1)
| convergent_lines(esk2_0,X2)
| ~ convergent_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[25,13378,theory(equality)]) ).
cnf(13400,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,X1)
| convergent_lines(esk2_0,X2)
| $false ),
inference(rw,[status(thm)],[13393,72,theory(equality)]) ).
cnf(13401,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,X1)
| convergent_lines(esk2_0,X2) ),
inference(cn,[status(thm)],[13400,theory(equality)]) ).
cnf(13430,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk2_0,esk2_0) ),
inference(spm,[status(thm)],[40,13401,theory(equality)]) ).
cnf(13439,negated_conjecture,
convergent_lines(esk2_0,X1),
inference(sr,[status(thm)],[13430,49,theory(equality)]) ).
cnf(13443,negated_conjecture,
$false,
inference(spm,[status(thm)],[49,13439,theory(equality)]) ).
cnf(13571,negated_conjecture,
$false,
13443,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO222+1.p
% --creating new selector for [GEO006+0.ax, GEO006+2.ax, GEO006+3.ax]
% -running prover on /tmp/tmpQ3lytR/sel_GEO222+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO222+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO222+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO222+1.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
%
%------------------------------------------------------------------------------