TSTP Solution File: GEO111+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GEO111+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 08:15:30 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 65 ( 11 unt; 0 def)
% Number of atoms : 347 ( 51 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 439 ( 157 ~; 174 |; 99 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 177 ( 14 sgn 89 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( end_point(X1,X2)
<=> ( incident_c(X1,X2)
& ! [X3,X4] :
( ( part_of(X3,X2)
& part_of(X4,X2)
& incident_c(X1,X3)
& incident_c(X1,X4) )
=> ( part_of(X3,X4)
| part_of(X4,X3) ) ) ) ),
file('/tmp/tmp821C55/sel_GEO111+1.p_1',end_point_defn) ).
fof(2,axiom,
! [X2,X3] :
( part_of(X3,X2)
<=> ! [X1] :
( incident_c(X1,X3)
=> incident_c(X1,X2) ) ),
file('/tmp/tmp821C55/sel_GEO111+1.p_1',part_of_defn) ).
fof(3,axiom,
! [X1,X2] :
( inner_point(X1,X2)
<=> ( incident_c(X1,X2)
& ~ end_point(X1,X2) ) ),
file('/tmp/tmp821C55/sel_GEO111+1.p_1',inner_point_defn) ).
fof(4,axiom,
! [X2,X1,X5,X6] :
( between_c(X2,X1,X5,X6)
<=> ( X1 != X6
& ? [X7] :
( part_of(X7,X2)
& end_point(X1,X7)
& end_point(X6,X7)
& inner_point(X5,X7) ) ) ),
file('/tmp/tmp821C55/sel_GEO111+1.p_1',between_c_defn) ).
fof(14,conjecture,
! [X2,X1,X5,X6] :
( between_c(X2,X1,X5,X6)
=> ( incident_c(X1,X2)
& incident_c(X5,X2)
& incident_c(X6,X2)
& X1 != X5
& X5 != X6
& X1 != X6 ) ),
file('/tmp/tmp821C55/sel_GEO111+1.p_1',theorem_3_8_1) ).
fof(15,negated_conjecture,
~ ! [X2,X1,X5,X6] :
( between_c(X2,X1,X5,X6)
=> ( incident_c(X1,X2)
& incident_c(X5,X2)
& incident_c(X6,X2)
& X1 != X5
& X5 != X6
& X1 != X6 ) ),
inference(assume_negation,[status(cth)],[14]) ).
fof(16,plain,
! [X1,X2] :
( inner_point(X1,X2)
<=> ( incident_c(X1,X2)
& ~ end_point(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(17,plain,
! [X1,X2] :
( ( ~ end_point(X1,X2)
| ( incident_c(X1,X2)
& ! [X3,X4] :
( ~ part_of(X3,X2)
| ~ part_of(X4,X2)
| ~ incident_c(X1,X3)
| ~ incident_c(X1,X4)
| part_of(X3,X4)
| part_of(X4,X3) ) ) )
& ( ~ incident_c(X1,X2)
| ? [X3,X4] :
( part_of(X3,X2)
& part_of(X4,X2)
& incident_c(X1,X3)
& incident_c(X1,X4)
& ~ part_of(X3,X4)
& ~ part_of(X4,X3) )
| end_point(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(18,plain,
! [X5,X6] :
( ( ~ end_point(X5,X6)
| ( incident_c(X5,X6)
& ! [X7,X8] :
( ~ part_of(X7,X6)
| ~ part_of(X8,X6)
| ~ incident_c(X5,X7)
| ~ incident_c(X5,X8)
| part_of(X7,X8)
| part_of(X8,X7) ) ) )
& ( ~ incident_c(X5,X6)
| ? [X9,X10] :
( part_of(X9,X6)
& part_of(X10,X6)
& incident_c(X5,X9)
& incident_c(X5,X10)
& ~ part_of(X9,X10)
& ~ part_of(X10,X9) )
| end_point(X5,X6) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X5,X6] :
( ( ~ end_point(X5,X6)
| ( incident_c(X5,X6)
& ! [X7,X8] :
( ~ part_of(X7,X6)
| ~ part_of(X8,X6)
| ~ incident_c(X5,X7)
| ~ incident_c(X5,X8)
| part_of(X7,X8)
| part_of(X8,X7) ) ) )
& ( ~ incident_c(X5,X6)
| ( part_of(esk1_2(X5,X6),X6)
& part_of(esk2_2(X5,X6),X6)
& incident_c(X5,esk1_2(X5,X6))
& incident_c(X5,esk2_2(X5,X6))
& ~ part_of(esk1_2(X5,X6),esk2_2(X5,X6))
& ~ part_of(esk2_2(X5,X6),esk1_2(X5,X6)) )
| end_point(X5,X6) ) ),
inference(skolemize,[status(esa)],[18]) ).
fof(20,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ part_of(X7,X6)
| ~ part_of(X8,X6)
| ~ incident_c(X5,X7)
| ~ incident_c(X5,X8)
| part_of(X7,X8)
| part_of(X8,X7) )
& incident_c(X5,X6) )
| ~ end_point(X5,X6) )
& ( ~ incident_c(X5,X6)
| ( part_of(esk1_2(X5,X6),X6)
& part_of(esk2_2(X5,X6),X6)
& incident_c(X5,esk1_2(X5,X6))
& incident_c(X5,esk2_2(X5,X6))
& ~ part_of(esk1_2(X5,X6),esk2_2(X5,X6))
& ~ part_of(esk2_2(X5,X6),esk1_2(X5,X6)) )
| end_point(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[19]) ).
fof(21,plain,
! [X5,X6,X7,X8] :
( ( ~ part_of(X7,X6)
| ~ part_of(X8,X6)
| ~ incident_c(X5,X7)
| ~ incident_c(X5,X8)
| part_of(X7,X8)
| part_of(X8,X7)
| ~ end_point(X5,X6) )
& ( incident_c(X5,X6)
| ~ end_point(X5,X6) )
& ( part_of(esk1_2(X5,X6),X6)
| ~ incident_c(X5,X6)
| end_point(X5,X6) )
& ( part_of(esk2_2(X5,X6),X6)
| ~ incident_c(X5,X6)
| end_point(X5,X6) )
& ( incident_c(X5,esk1_2(X5,X6))
| ~ incident_c(X5,X6)
| end_point(X5,X6) )
& ( incident_c(X5,esk2_2(X5,X6))
| ~ incident_c(X5,X6)
| end_point(X5,X6) )
& ( ~ part_of(esk1_2(X5,X6),esk2_2(X5,X6))
| ~ incident_c(X5,X6)
| end_point(X5,X6) )
& ( ~ part_of(esk2_2(X5,X6),esk1_2(X5,X6))
| ~ incident_c(X5,X6)
| end_point(X5,X6) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(28,plain,
( incident_c(X1,X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(30,plain,
! [X2,X3] :
( ( ~ part_of(X3,X2)
| ! [X1] :
( ~ incident_c(X1,X3)
| incident_c(X1,X2) ) )
& ( ? [X1] :
( incident_c(X1,X3)
& ~ incident_c(X1,X2) )
| part_of(X3,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(31,plain,
! [X4,X5] :
( ( ~ part_of(X5,X4)
| ! [X6] :
( ~ incident_c(X6,X5)
| incident_c(X6,X4) ) )
& ( ? [X7] :
( incident_c(X7,X5)
& ~ incident_c(X7,X4) )
| part_of(X5,X4) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X4,X5] :
( ( ~ part_of(X5,X4)
| ! [X6] :
( ~ incident_c(X6,X5)
| incident_c(X6,X4) ) )
& ( ( incident_c(esk3_2(X4,X5),X5)
& ~ incident_c(esk3_2(X4,X5),X4) )
| part_of(X5,X4) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X4,X5,X6] :
( ( ~ incident_c(X6,X5)
| incident_c(X6,X4)
| ~ part_of(X5,X4) )
& ( ( incident_c(esk3_2(X4,X5),X5)
& ~ incident_c(esk3_2(X4,X5),X4) )
| part_of(X5,X4) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X4,X5,X6] :
( ( ~ incident_c(X6,X5)
| incident_c(X6,X4)
| ~ part_of(X5,X4) )
& ( incident_c(esk3_2(X4,X5),X5)
| part_of(X5,X4) )
& ( ~ incident_c(esk3_2(X4,X5),X4)
| part_of(X5,X4) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(37,plain,
( incident_c(X3,X2)
| ~ part_of(X1,X2)
| ~ incident_c(X3,X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(38,plain,
! [X1,X2] :
( ( ~ inner_point(X1,X2)
| ( incident_c(X1,X2)
& ~ end_point(X1,X2) ) )
& ( ~ incident_c(X1,X2)
| end_point(X1,X2)
| inner_point(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(39,plain,
! [X3,X4] :
( ( ~ inner_point(X3,X4)
| ( incident_c(X3,X4)
& ~ end_point(X3,X4) ) )
& ( ~ incident_c(X3,X4)
| end_point(X3,X4)
| inner_point(X3,X4) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,plain,
! [X3,X4] :
( ( incident_c(X3,X4)
| ~ inner_point(X3,X4) )
& ( ~ end_point(X3,X4)
| ~ inner_point(X3,X4) )
& ( ~ incident_c(X3,X4)
| end_point(X3,X4)
| inner_point(X3,X4) ) ),
inference(distribute,[status(thm)],[39]) ).
cnf(42,plain,
( ~ inner_point(X1,X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(43,plain,
( incident_c(X1,X2)
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(44,plain,
! [X2,X1,X5,X6] :
( ( ~ between_c(X2,X1,X5,X6)
| ( X1 != X6
& ? [X7] :
( part_of(X7,X2)
& end_point(X1,X7)
& end_point(X6,X7)
& inner_point(X5,X7) ) ) )
& ( X1 = X6
| ! [X7] :
( ~ part_of(X7,X2)
| ~ end_point(X1,X7)
| ~ end_point(X6,X7)
| ~ inner_point(X5,X7) )
| between_c(X2,X1,X5,X6) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(45,plain,
! [X8,X9,X10,X11] :
( ( ~ between_c(X8,X9,X10,X11)
| ( X9 != X11
& ? [X12] :
( part_of(X12,X8)
& end_point(X9,X12)
& end_point(X11,X12)
& inner_point(X10,X12) ) ) )
& ( X9 = X11
| ! [X13] :
( ~ part_of(X13,X8)
| ~ end_point(X9,X13)
| ~ end_point(X11,X13)
| ~ inner_point(X10,X13) )
| between_c(X8,X9,X10,X11) ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X8,X9,X10,X11] :
( ( ~ between_c(X8,X9,X10,X11)
| ( X9 != X11
& part_of(esk4_4(X8,X9,X10,X11),X8)
& end_point(X9,esk4_4(X8,X9,X10,X11))
& end_point(X11,esk4_4(X8,X9,X10,X11))
& inner_point(X10,esk4_4(X8,X9,X10,X11)) ) )
& ( X9 = X11
| ! [X13] :
( ~ part_of(X13,X8)
| ~ end_point(X9,X13)
| ~ end_point(X11,X13)
| ~ inner_point(X10,X13) )
| between_c(X8,X9,X10,X11) ) ),
inference(skolemize,[status(esa)],[45]) ).
fof(47,plain,
! [X8,X9,X10,X11,X13] :
( ( ~ part_of(X13,X8)
| ~ end_point(X9,X13)
| ~ end_point(X11,X13)
| ~ inner_point(X10,X13)
| X9 = X11
| between_c(X8,X9,X10,X11) )
& ( ~ between_c(X8,X9,X10,X11)
| ( X9 != X11
& part_of(esk4_4(X8,X9,X10,X11),X8)
& end_point(X9,esk4_4(X8,X9,X10,X11))
& end_point(X11,esk4_4(X8,X9,X10,X11))
& inner_point(X10,esk4_4(X8,X9,X10,X11)) ) ) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,plain,
! [X8,X9,X10,X11,X13] :
( ( ~ part_of(X13,X8)
| ~ end_point(X9,X13)
| ~ end_point(X11,X13)
| ~ inner_point(X10,X13)
| X9 = X11
| between_c(X8,X9,X10,X11) )
& ( X9 != X11
| ~ between_c(X8,X9,X10,X11) )
& ( part_of(esk4_4(X8,X9,X10,X11),X8)
| ~ between_c(X8,X9,X10,X11) )
& ( end_point(X9,esk4_4(X8,X9,X10,X11))
| ~ between_c(X8,X9,X10,X11) )
& ( end_point(X11,esk4_4(X8,X9,X10,X11))
| ~ between_c(X8,X9,X10,X11) )
& ( inner_point(X10,esk4_4(X8,X9,X10,X11))
| ~ between_c(X8,X9,X10,X11) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(49,plain,
( inner_point(X3,esk4_4(X1,X2,X3,X4))
| ~ between_c(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,plain,
( end_point(X4,esk4_4(X1,X2,X3,X4))
| ~ between_c(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(51,plain,
( end_point(X2,esk4_4(X1,X2,X3,X4))
| ~ between_c(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(52,plain,
( part_of(esk4_4(X1,X2,X3,X4),X1)
| ~ between_c(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(53,plain,
( ~ between_c(X1,X2,X3,X4)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(111,negated_conjecture,
? [X2,X1,X5,X6] :
( between_c(X2,X1,X5,X6)
& ( ~ incident_c(X1,X2)
| ~ incident_c(X5,X2)
| ~ incident_c(X6,X2)
| X1 = X5
| X5 = X6
| X1 = X6 ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(112,negated_conjecture,
? [X7,X8,X9,X10] :
( between_c(X7,X8,X9,X10)
& ( ~ incident_c(X8,X7)
| ~ incident_c(X9,X7)
| ~ incident_c(X10,X7)
| X8 = X9
| X9 = X10
| X8 = X10 ) ),
inference(variable_rename,[status(thm)],[111]) ).
fof(113,negated_conjecture,
( between_c(esk13_0,esk14_0,esk15_0,esk16_0)
& ( ~ incident_c(esk14_0,esk13_0)
| ~ incident_c(esk15_0,esk13_0)
| ~ incident_c(esk16_0,esk13_0)
| esk14_0 = esk15_0
| esk15_0 = esk16_0
| esk14_0 = esk16_0 ) ),
inference(skolemize,[status(esa)],[112]) ).
cnf(114,negated_conjecture,
( esk14_0 = esk16_0
| esk15_0 = esk16_0
| esk14_0 = esk15_0
| ~ incident_c(esk16_0,esk13_0)
| ~ incident_c(esk15_0,esk13_0)
| ~ incident_c(esk14_0,esk13_0) ),
inference(split_conjunct,[status(thm)],[113]) ).
cnf(115,negated_conjecture,
between_c(esk13_0,esk14_0,esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[113]) ).
cnf(116,plain,
~ between_c(X1,X2,X3,X2),
inference(er,[status(thm)],[53,theory(equality)]) ).
cnf(130,plain,
( incident_c(X1,esk4_4(X2,X3,X4,X1))
| ~ between_c(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[28,50,theory(equality)]) ).
cnf(134,plain,
( incident_c(X1,esk4_4(X2,X1,X3,X4))
| ~ between_c(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[28,51,theory(equality)]) ).
cnf(136,plain,
( incident_c(X1,esk4_4(X2,X3,X1,X4))
| ~ between_c(X2,X3,X1,X4) ),
inference(spm,[status(thm)],[43,49,theory(equality)]) ).
cnf(137,plain,
( ~ end_point(X1,esk4_4(X2,X3,X1,X4))
| ~ between_c(X2,X3,X1,X4) ),
inference(spm,[status(thm)],[42,49,theory(equality)]) ).
cnf(138,plain,
( incident_c(X1,X2)
| ~ incident_c(X1,esk4_4(X2,X3,X4,X5))
| ~ between_c(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[37,52,theory(equality)]) ).
cnf(174,plain,
~ between_c(X1,X2,X3,X3),
inference(spm,[status(thm)],[137,50,theory(equality)]) ).
cnf(175,plain,
~ between_c(X1,X2,X2,X3),
inference(spm,[status(thm)],[137,51,theory(equality)]) ).
cnf(319,plain,
( incident_c(X1,X2)
| ~ between_c(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[138,130,theory(equality)]) ).
cnf(320,plain,
( incident_c(X1,X2)
| ~ between_c(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[138,134,theory(equality)]) ).
cnf(321,plain,
( incident_c(X1,X2)
| ~ between_c(X2,X3,X1,X4) ),
inference(spm,[status(thm)],[138,136,theory(equality)]) ).
cnf(324,negated_conjecture,
incident_c(esk16_0,esk13_0),
inference(spm,[status(thm)],[319,115,theory(equality)]) ).
cnf(328,negated_conjecture,
( esk16_0 = esk15_0
| esk16_0 = esk14_0
| esk15_0 = esk14_0
| ~ incident_c(esk14_0,esk13_0)
| ~ incident_c(esk15_0,esk13_0)
| $false ),
inference(rw,[status(thm)],[114,324,theory(equality)]) ).
cnf(329,negated_conjecture,
( esk16_0 = esk15_0
| esk16_0 = esk14_0
| esk15_0 = esk14_0
| ~ incident_c(esk14_0,esk13_0)
| ~ incident_c(esk15_0,esk13_0) ),
inference(cn,[status(thm)],[328,theory(equality)]) ).
cnf(330,negated_conjecture,
incident_c(esk14_0,esk13_0),
inference(spm,[status(thm)],[320,115,theory(equality)]) ).
cnf(332,negated_conjecture,
incident_c(esk15_0,esk13_0),
inference(spm,[status(thm)],[321,115,theory(equality)]) ).
cnf(334,negated_conjecture,
( esk16_0 = esk15_0
| esk16_0 = esk14_0
| esk15_0 = esk14_0
| $false
| ~ incident_c(esk15_0,esk13_0) ),
inference(rw,[status(thm)],[329,330,theory(equality)]) ).
cnf(335,negated_conjecture,
( esk16_0 = esk15_0
| esk16_0 = esk14_0
| esk15_0 = esk14_0
| $false
| $false ),
inference(rw,[status(thm)],[334,332,theory(equality)]) ).
cnf(336,negated_conjecture,
( esk16_0 = esk15_0
| esk16_0 = esk14_0
| esk15_0 = esk14_0 ),
inference(cn,[status(thm)],[335,theory(equality)]) ).
cnf(338,negated_conjecture,
( between_c(esk13_0,esk14_0,esk15_0,esk15_0)
| esk15_0 = esk14_0
| esk16_0 = esk14_0 ),
inference(spm,[status(thm)],[115,336,theory(equality)]) ).
cnf(340,negated_conjecture,
( esk15_0 = esk14_0
| esk16_0 = esk14_0 ),
inference(sr,[status(thm)],[338,174,theory(equality)]) ).
cnf(342,negated_conjecture,
( between_c(esk13_0,esk14_0,esk15_0,esk14_0)
| esk15_0 = esk14_0 ),
inference(spm,[status(thm)],[115,340,theory(equality)]) ).
cnf(344,negated_conjecture,
esk15_0 = esk14_0,
inference(sr,[status(thm)],[342,116,theory(equality)]) ).
cnf(348,negated_conjecture,
between_c(esk13_0,esk14_0,esk14_0,esk16_0),
inference(rw,[status(thm)],[115,344,theory(equality)]) ).
cnf(349,negated_conjecture,
$false,
inference(sr,[status(thm)],[348,175,theory(equality)]) ).
cnf(350,negated_conjecture,
$false,
349,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO111+1.p
% --creating new selector for [GEO004+0.ax, GEO004+1.ax]
% -running prover on /tmp/tmp821C55/sel_GEO111+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO111+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO111+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO111+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
%
%------------------------------------------------------------------------------