TSTP Solution File: GEO222+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO222+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 08:59:36 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 21 unt; 0 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 194 ( 79 ~; 82 |; 25 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 118 ( 5 sgn 77 !; 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/tmpA51HqF/sel_GEO222+3.p_1',oac1) ).
fof(4,axiom,
! [X5,X6,X7] :
( convergent_lines(X5,X6)
=> ( convergent_lines(X5,X7)
| convergent_lines(X6,X7) ) ),
file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',ax6) ).
fof(5,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/tmpA51HqF/sel_GEO222+3.p_1',cotno1) ).
fof(10,axiom,
! [X5,X6] :
( parallel_lines(X5,X6)
<=> ~ convergent_lines(X5,X6) ),
file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',a3) ).
fof(11,axiom,
! [X1,X2] :
~ ( ~ convergent_lines(X1,X2)
& ~ unorthogonal_lines(X1,X2) ),
file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',coipo1) ).
fof(12,axiom,
! [X1,X2,X3] :
( ( ~ unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X1,X3) )
=> ~ convergent_lines(X2,X3) ),
file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',couo1) ).
fof(15,axiom,
! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',ooc1) ).
fof(16,axiom,
! [X5] : ~ convergent_lines(X5,X5),
file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',apart3) ).
fof(19,conjecture,
! [X4,X1] : parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',con) ).
fof(20,negated_conjecture,
~ ! [X4,X1] : parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(assume_negation,[status(cth)],[19]) ).
fof(21,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_simplification,[status(thm)],[5,theory(equality)]) ).
fof(22,plain,
! [X5,X6] :
( parallel_lines(X5,X6)
<=> ~ convergent_lines(X5,X6) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(23,plain,
! [X1,X2] :
~ ( ~ convergent_lines(X1,X2)
& ~ unorthogonal_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(24,plain,
! [X1,X2,X3] :
( ( ~ unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X1,X3) )
=> ~ convergent_lines(X2,X3) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(26,plain,
! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(27,plain,
! [X5] : ~ convergent_lines(X5,X5),
inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).
fof(29,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(30,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)],[29]) ).
fof(31,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)],[30]) ).
cnf(32,plain,
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(42,plain,
! [X5,X6,X7] :
( ~ convergent_lines(X5,X6)
| convergent_lines(X5,X7)
| convergent_lines(X6,X7) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(43,plain,
! [X8,X9,X10] :
( ~ convergent_lines(X8,X9)
| convergent_lines(X8,X10)
| convergent_lines(X9,X10) ),
inference(variable_rename,[status(thm)],[42]) ).
cnf(44,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,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)],[21]) ).
fof(46,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)],[45]) ).
fof(47,plain,
! [X4,X5,X6] :
( ( convergent_lines(X4,X6)
| convergent_lines(X4,X5)
| ~ convergent_lines(X5,X6)
| ~ unorthogonal_lines(X5,X6) )
& ( unorthogonal_lines(X4,X6)
| convergent_lines(X4,X5)
| ~ convergent_lines(X5,X6)
| ~ unorthogonal_lines(X5,X6) )
& ( convergent_lines(X4,X6)
| unorthogonal_lines(X4,X5)
| ~ convergent_lines(X5,X6)
| ~ unorthogonal_lines(X5,X6) )
& ( unorthogonal_lines(X4,X6)
| unorthogonal_lines(X4,X5)
| ~ convergent_lines(X5,X6)
| ~ unorthogonal_lines(X5,X6) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(49,plain,
( unorthogonal_lines(X3,X1)
| convergent_lines(X3,X2)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(64,plain,
! [X5,X6] :
( ( ~ parallel_lines(X5,X6)
| ~ convergent_lines(X5,X6) )
& ( convergent_lines(X5,X6)
| parallel_lines(X5,X6) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(65,plain,
! [X7,X8] :
( ( ~ parallel_lines(X7,X8)
| ~ convergent_lines(X7,X8) )
& ( convergent_lines(X7,X8)
| parallel_lines(X7,X8) ) ),
inference(variable_rename,[status(thm)],[64]) ).
cnf(66,plain,
( parallel_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(68,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(69,plain,
! [X3,X4] :
( convergent_lines(X3,X4)
| unorthogonal_lines(X3,X4) ),
inference(variable_rename,[status(thm)],[68]) ).
cnf(70,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(71,plain,
! [X1,X2,X3] :
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(72,plain,
! [X4,X5,X6] :
( unorthogonal_lines(X4,X5)
| unorthogonal_lines(X4,X6)
| ~ convergent_lines(X5,X6) ),
inference(variable_rename,[status(thm)],[71]) ).
cnf(73,plain,
( unorthogonal_lines(X3,X2)
| unorthogonal_lines(X3,X1)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(79,plain,
! [X5,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X5),X6),
inference(variable_rename,[status(thm)],[26]) ).
cnf(80,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[79]) ).
fof(81,plain,
! [X6] : ~ convergent_lines(X6,X6),
inference(variable_rename,[status(thm)],[27]) ).
cnf(82,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[81]) ).
fof(87,negated_conjecture,
? [X4,X1] : ~ parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(fof_nnf,[status(thm)],[20]) ).
fof(88,negated_conjecture,
? [X5,X6] : ~ parallel_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X5),X5)),
inference(variable_rename,[status(thm)],[87]) ).
fof(89,negated_conjecture,
~ parallel_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(skolemize,[status(esa)],[88]) ).
cnf(90,negated_conjecture,
~ parallel_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[89]) ).
cnf(91,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[80,70,theory(equality)]) ).
cnf(92,negated_conjecture,
convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(spm,[status(thm)],[90,66,theory(equality)]) ).
cnf(104,plain,
( convergent_lines(X1,X2)
| convergent_lines(orthogonal_through_point(X1,X3),X2) ),
inference(spm,[status(thm)],[44,91,theory(equality)]) ).
cnf(106,plain,
( unorthogonal_lines(X1,orthogonal_through_point(X2,X3))
| unorthogonal_lines(X1,X2) ),
inference(spm,[status(thm)],[73,91,theory(equality)]) ).
cnf(110,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[82,104,theory(equality)]) ).
cnf(141,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(orthogonal_through_point(X3,X4),X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X1,orthogonal_through_point(X3,X4)) ),
inference(spm,[status(thm)],[32,106,theory(equality)]) ).
cnf(697,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0))
| unorthogonal_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[141,92,theory(equality)]) ).
cnf(728,negated_conjecture,
unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)),
inference(spm,[status(thm)],[80,697,theory(equality)]) ).
cnf(736,negated_conjecture,
( unorthogonal_lines(X1,esk2_0)
| convergent_lines(X1,orthogonal_through_point(esk2_0,esk1_0))
| ~ convergent_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[49,728,theory(equality)]) ).
cnf(754,negated_conjecture,
( unorthogonal_lines(X1,esk2_0)
| convergent_lines(X1,orthogonal_through_point(esk2_0,esk1_0))
| $false ),
inference(rw,[status(thm)],[736,110,theory(equality)]) ).
cnf(755,negated_conjecture,
( unorthogonal_lines(X1,esk2_0)
| convergent_lines(X1,orthogonal_through_point(esk2_0,esk1_0)) ),
inference(cn,[status(thm)],[754,theory(equality)]) ).
cnf(775,negated_conjecture,
unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),esk2_0),
inference(spm,[status(thm)],[82,755,theory(equality)]) ).
cnf(785,negated_conjecture,
$false,
inference(sr,[status(thm)],[775,80,theory(equality)]) ).
cnf(786,negated_conjecture,
$false,
785,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO222+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/tmpA51HqF/sel_GEO222+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO222+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO222+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO222+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
%
%------------------------------------------------------------------------------