TSTP Solution File: GEO223+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO223+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 08:59:41 EST 2010
% Result : Theorem 4.86s
% Output : CNFRefutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 38 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 145 ( 53 ~; 78 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 157 ( 19 sgn 82 !; 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/tmpLtVNii/sel_GEO223+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/tmpLtVNii/sel_GEO223+1.p_1',ouo1) ).
fof(3,axiom,
! [X5,X6,X7] :
( convergent_lines(X5,X6)
=> ( convergent_lines(X5,X7)
| convergent_lines(X6,X7) ) ),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',ax6) ).
fof(4,axiom,
! [X5,X6,X7] :
( convergent_lines(X5,X6)
=> ( distinct_lines(X6,X7)
| convergent_lines(X5,X7) ) ),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',ceq3) ).
fof(6,axiom,
! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',ooc1) ).
fof(7,axiom,
! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',ooc2) ).
fof(8,axiom,
! [X5,X6] : ~ apart_point_and_line(X5,parallel_through_point(X6,X5)),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',cp2) ).
fof(9,axiom,
! [X5,X6] : ~ convergent_lines(parallel_through_point(X6,X5),X6),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',cp1) ).
fof(11,axiom,
! [X5] : ~ distinct_lines(X5,X5),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',apart2) ).
fof(12,axiom,
! [X5] : ~ convergent_lines(X5,X5),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',apart3) ).
fof(14,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',occu1) ).
fof(15,conjecture,
! [X4,X1] : ~ distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
file('/tmp/tmpLtVNii/sel_GEO223+1.p_1',con) ).
fof(16,negated_conjecture,
~ ! [X4,X1] : ~ distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(assume_negation,[status(cth)],[15]) ).
fof(17,plain,
! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(18,plain,
! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(19,plain,
! [X5,X6] : ~ apart_point_and_line(X5,parallel_through_point(X6,X5)),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(20,plain,
! [X5,X6] : ~ convergent_lines(parallel_through_point(X6,X5),X6),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(21,plain,
! [X5] : ~ distinct_lines(X5,X5),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(22,plain,
! [X5] : ~ convergent_lines(X5,X5),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(23,negated_conjecture,
~ ! [X4,X1] : ~ distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).
fof(24,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(25,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)],[24]) ).
fof(26,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)],[25]) ).
cnf(29,plain,
( convergent_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(31,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(32,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)],[31]) ).
cnf(33,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)],[32]) ).
fof(34,plain,
! [X5,X6,X7] :
( ~ convergent_lines(X5,X6)
| convergent_lines(X5,X7)
| convergent_lines(X6,X7) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(35,plain,
! [X8,X9,X10] :
( ~ convergent_lines(X8,X9)
| convergent_lines(X8,X10)
| convergent_lines(X9,X10) ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X5,X6,X7] :
( ~ convergent_lines(X5,X6)
| distinct_lines(X6,X7)
| convergent_lines(X5,X7) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(38,plain,
! [X8,X9,X10] :
( ~ convergent_lines(X8,X9)
| distinct_lines(X9,X10)
| convergent_lines(X8,X10) ),
inference(variable_rename,[status(thm)],[37]) ).
cnf(39,plain,
( convergent_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(43,plain,
! [X5,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X5),X6),
inference(variable_rename,[status(thm)],[17]) ).
cnf(44,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,plain,
! [X5,X6] : ~ apart_point_and_line(X5,orthogonal_through_point(X6,X5)),
inference(variable_rename,[status(thm)],[18]) ).
cnf(46,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X7,X8] : ~ apart_point_and_line(X7,parallel_through_point(X8,X7)),
inference(variable_rename,[status(thm)],[19]) ).
cnf(48,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[47]) ).
fof(49,plain,
! [X7,X8] : ~ convergent_lines(parallel_through_point(X8,X7),X8),
inference(variable_rename,[status(thm)],[20]) ).
cnf(50,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[49]) ).
fof(54,plain,
! [X6] : ~ distinct_lines(X6,X6),
inference(variable_rename,[status(thm)],[21]) ).
cnf(55,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[54]) ).
fof(56,plain,
! [X6] : ~ convergent_lines(X6,X6),
inference(variable_rename,[status(thm)],[22]) ).
cnf(57,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[56]) ).
fof(61,plain,
! [X3,X4] :
( convergent_lines(X3,X4)
| unorthogonal_lines(X3,X4) ),
inference(variable_rename,[status(thm)],[14]) ).
cnf(62,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,negated_conjecture,
? [X4,X1] : distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
inference(fof_nnf,[status(thm)],[23]) ).
fof(64,negated_conjecture,
? [X5,X6] : distinct_lines(parallel_through_point(X6,X5),orthogonal_through_point(orthogonal_through_point(X6,X5),X5)),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,negated_conjecture,
distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(skolemize,[status(esa)],[64]) ).
cnf(66,negated_conjecture,
distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(68,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[44,62,theory(equality)]) ).
cnf(74,negated_conjecture,
( apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X2)
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X2) ),
inference(spm,[status(thm)],[33,66,theory(equality)]) ).
cnf(76,plain,
( distinct_lines(X1,X2)
| convergent_lines(orthogonal_through_point(X1,X3),X2) ),
inference(spm,[status(thm)],[39,68,theory(equality)]) ).
cnf(78,plain,
( convergent_lines(X1,X2)
| convergent_lines(orthogonal_through_point(X3,X4),X2)
| distinct_lines(X3,X1) ),
inference(spm,[status(thm)],[36,76,theory(equality)]) ).
cnf(148,negated_conjecture,
( apart_point_and_line(esk1_0,parallel_through_point(esk2_0,esk1_0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[46,74,theory(equality)]) ).
cnf(154,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
inference(sr,[status(thm)],[148,48,theory(equality)]) ).
cnf(190,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| distinct_lines(X4,X3)
| convergent_lines(orthogonal_through_point(X4,X5),X1) ),
inference(spm,[status(thm)],[36,78,theory(equality)]) ).
cnf(1647,negated_conjecture,
unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)),
inference(spm,[status(thm)],[44,154,theory(equality)]) ).
cnf(1652,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| ~ convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[29,1647,theory(equality)]) ).
cnf(2508,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| convergent_lines(X1,X4)
| convergent_lines(X3,X4) ),
inference(spm,[status(thm)],[55,190,theory(equality)]) ).
cnf(8907,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| convergent_lines(X3,X1) ),
inference(spm,[status(thm)],[57,2508,theory(equality)]) ).
cnf(8982,plain,
( distinct_lines(X1,X2)
| convergent_lines(orthogonal_through_point(X3,X4),X2)
| convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[39,8907,theory(equality)]) ).
cnf(8996,plain,
( distinct_lines(parallel_through_point(X1,X2),X3)
| convergent_lines(orthogonal_through_point(X1,X4),X3) ),
inference(spm,[status(thm)],[50,8982,theory(equality)]) ).
cnf(9317,plain,
convergent_lines(orthogonal_through_point(X1,X3),parallel_through_point(X1,X2)),
inference(spm,[status(thm)],[55,8996,theory(equality)]) ).
cnf(9334,plain,
( convergent_lines(parallel_through_point(X1,X2),X3)
| convergent_lines(orthogonal_through_point(X1,X4),X3) ),
inference(spm,[status(thm)],[36,9317,theory(equality)]) ).
cnf(9346,plain,
convergent_lines(parallel_through_point(X1,X3),orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[57,9334,theory(equality)]) ).
cnf(66818,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| $false ),
inference(rw,[status(thm)],[1652,9346,theory(equality)]) ).
cnf(66819,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
inference(cn,[status(thm)],[66818,theory(equality)]) ).
cnf(66820,negated_conjecture,
convergent_lines(parallel_through_point(esk2_0,esk1_0),esk2_0),
inference(spm,[status(thm)],[44,66819,theory(equality)]) ).
cnf(66824,negated_conjecture,
$false,
inference(sr,[status(thm)],[66820,50,theory(equality)]) ).
cnf(66825,negated_conjecture,
$false,
66824,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO223+1.p
% --creating new selector for [GEO006+0.ax, GEO006+2.ax, GEO006+3.ax]
% -running prover on /tmp/tmpLtVNii/sel_GEO223+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO223+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO223+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO223+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
%
%------------------------------------------------------------------------------