TSTP Solution File: GRA007+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA007+1 : TPTP v5.0.0. Bugfixed v3.2.0.
% 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 09:55:06 EST 2010
% Result : Theorem 239.81s
% Output : CNFRefutation 239.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 132 ( 18 unt; 0 def)
% Number of atoms : 668 ( 206 equ)
% Maximal formula atoms : 37 ( 5 avg)
% Number of connectives : 876 ( 340 ~; 361 |; 145 &)
% ( 6 <=>; 21 =>; 1 <=; 2 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 308 ( 24 sgn 194 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( edge(X1)
=> ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',edge_ends_are_vertices) ).
fof(2,axiom,
! [X2,X3] :
( sequential(X2,X3)
<=> ( edge(X2)
& edge(X3)
& X2 != X3
& head_of(X2) = tail_of(X3) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',sequential_defn) ).
fof(3,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',no_loops) ).
fof(4,axiom,
! [X4,X5,X6] :
( shortest_path(X4,X5,X6)
<=> ( path(X4,X5,X6)
& X4 != X5
& ! [X7] :
( path(X4,X5,X7)
=> less_or_equal(length_of(X6),length_of(X7)) ) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',shortest_path_defn) ).
fof(5,axiom,
( complete
=> ! [X4,X5] :
( ( vertex(X4)
& vertex(X5)
& X4 != X5 )
=> ? [X1] :
( edge(X1)
& ( ( X4 = head_of(X1)
& X5 = tail_of(X1) )
<~> ( X5 = head_of(X1)
& X4 = tail_of(X1) ) ) ) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',complete_properties) ).
fof(6,axiom,
! [X7,X4,X5] :
( path(X4,X5,X7)
=> ! [X2,X3] :
( precedes(X2,X3,X7)
=> ( on_path(X2,X7)
& on_path(X3,X7)
& ( sequential(X2,X3)
<~> ? [X8] :
( sequential(X2,X8)
& precedes(X8,X3,X7) ) ) ) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',precedes_properties) ).
fof(8,axiom,
! [X4,X5,X7,X1] :
( ( path(X4,X5,X7)
& on_path(X1,X7) )
=> ( edge(X1)
& in_path(head_of(X1),X7)
& in_path(tail_of(X1),X7) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',on_path_properties) ).
fof(9,axiom,
! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7) )
=> ( ~ ? [X8] :
( tail_of(X8) = tail_of(X2)
& head_of(X8) = head_of(X3) )
& ~ precedes(X3,X2,X7) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',shortest_path_properties) ).
fof(10,axiom,
! [X7,X4,X5] :
( path(X4,X5,X7)
=> ! [X2,X3] :
( precedes(X2,X3,X7)
<= ( on_path(X2,X7)
& on_path(X3,X7)
& ( sequential(X2,X3)
| ? [X8] :
( sequential(X2,X8)
& precedes(X8,X3,X7) ) ) ) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',precedes_defn) ).
fof(11,conjecture,
( complete
=> ! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7) )
=> ? [X8] :
( edge(X8)
& tail_of(X8) = head_of(X3)
& head_of(X8) = tail_of(X2) ) ) ),
file('/tmp/tmpa17TkQ/sel_GRA007+1.p_5',back_edge) ).
fof(17,negated_conjecture,
~ ( complete
=> ! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7) )
=> ? [X8] :
( edge(X8)
& tail_of(X8) = head_of(X3)
& head_of(X8) = tail_of(X2) ) ) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(18,plain,
( complete
=> ! [X4,X5] :
( ( vertex(X4)
& vertex(X5)
& X4 != X5 )
=> ? [X1] :
( edge(X1)
& ~ ( ( X4 = head_of(X1)
& X5 = tail_of(X1) )
<=> ( X5 = head_of(X1)
& X4 = tail_of(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(19,plain,
! [X7,X4,X5] :
( path(X4,X5,X7)
=> ! [X2,X3] :
( precedes(X2,X3,X7)
=> ( on_path(X2,X7)
& on_path(X3,X7)
& ~ ( sequential(X2,X3)
<=> ? [X8] :
( sequential(X2,X8)
& precedes(X8,X3,X7) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(20,plain,
! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7) )
=> ( ~ ? [X8] :
( tail_of(X8) = tail_of(X2)
& head_of(X8) = head_of(X3) )
& ~ precedes(X3,X2,X7) ) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(21,plain,
! [X7,X4,X5] :
( path(X4,X5,X7)
=> ! [X2,X3] :
( ( on_path(X2,X7)
& on_path(X3,X7)
& ( sequential(X2,X3)
| ? [X8] :
( sequential(X2,X8)
& precedes(X8,X3,X7) ) ) )
=> precedes(X2,X3,X7) ) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(22,plain,
! [X1] :
( ~ edge(X1)
| ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(23,plain,
! [X2] :
( ~ edge(X2)
| ( vertex(head_of(X2))
& vertex(tail_of(X2)) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X2] :
( ( vertex(head_of(X2))
| ~ edge(X2) )
& ( vertex(tail_of(X2))
| ~ edge(X2) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(25,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(26,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(27,plain,
! [X2,X3] :
( ( ~ sequential(X2,X3)
| ( edge(X2)
& edge(X3)
& X2 != X3
& head_of(X2) = tail_of(X3) ) )
& ( ~ edge(X2)
| ~ edge(X3)
| X2 = X3
| head_of(X2) != tail_of(X3)
| sequential(X2,X3) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(28,plain,
! [X4,X5] :
( ( ~ sequential(X4,X5)
| ( edge(X4)
& edge(X5)
& X4 != X5
& head_of(X4) = tail_of(X5) ) )
& ( ~ edge(X4)
| ~ edge(X5)
| X4 = X5
| head_of(X4) != tail_of(X5)
| sequential(X4,X5) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5] :
( ( edge(X4)
| ~ sequential(X4,X5) )
& ( edge(X5)
| ~ sequential(X4,X5) )
& ( X4 != X5
| ~ sequential(X4,X5) )
& ( head_of(X4) = tail_of(X5)
| ~ sequential(X4,X5) )
& ( ~ edge(X4)
| ~ edge(X5)
| X4 = X5
| head_of(X4) != tail_of(X5)
| sequential(X4,X5) ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(30,plain,
( sequential(X1,X2)
| X1 = X2
| head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(35,plain,
! [X1] :
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(36,plain,
! [X2] :
( ~ edge(X2)
| head_of(X2) != tail_of(X2) ),
inference(variable_rename,[status(thm)],[35]) ).
cnf(37,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5,X6] :
( ( ~ shortest_path(X4,X5,X6)
| ( path(X4,X5,X6)
& X4 != X5
& ! [X7] :
( ~ path(X4,X5,X7)
| less_or_equal(length_of(X6),length_of(X7)) ) ) )
& ( ~ path(X4,X5,X6)
| X4 = X5
| ? [X7] :
( path(X4,X5,X7)
& ~ less_or_equal(length_of(X6),length_of(X7)) )
| shortest_path(X4,X5,X6) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(39,plain,
! [X8,X9,X10] :
( ( ~ shortest_path(X8,X9,X10)
| ( path(X8,X9,X10)
& X8 != X9
& ! [X11] :
( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11)) ) ) )
& ( ~ path(X8,X9,X10)
| X8 = X9
| ? [X12] :
( path(X8,X9,X12)
& ~ less_or_equal(length_of(X10),length_of(X12)) )
| shortest_path(X8,X9,X10) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,plain,
! [X8,X9,X10] :
( ( ~ shortest_path(X8,X9,X10)
| ( path(X8,X9,X10)
& X8 != X9
& ! [X11] :
( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11)) ) ) )
& ( ~ path(X8,X9,X10)
| X8 = X9
| ( path(X8,X9,esk1_3(X8,X9,X10))
& ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10))) )
| shortest_path(X8,X9,X10) ) ),
inference(skolemize,[status(esa)],[39]) ).
fof(41,plain,
! [X8,X9,X10,X11] :
( ( ( ( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11)) )
& path(X8,X9,X10)
& X8 != X9 )
| ~ shortest_path(X8,X9,X10) )
& ( ~ path(X8,X9,X10)
| X8 = X9
| ( path(X8,X9,esk1_3(X8,X9,X10))
& ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10))) )
| shortest_path(X8,X9,X10) ) ),
inference(shift_quantors,[status(thm)],[40]) ).
fof(42,plain,
! [X8,X9,X10,X11] :
( ( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11))
| ~ shortest_path(X8,X9,X10) )
& ( path(X8,X9,X10)
| ~ shortest_path(X8,X9,X10) )
& ( X8 != X9
| ~ shortest_path(X8,X9,X10) )
& ( path(X8,X9,esk1_3(X8,X9,X10))
| ~ path(X8,X9,X10)
| X8 = X9
| shortest_path(X8,X9,X10) )
& ( ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10)))
| ~ path(X8,X9,X10)
| X8 = X9
| shortest_path(X8,X9,X10) ) ),
inference(distribute,[status(thm)],[41]) ).
cnf(46,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(48,plain,
( ~ complete
| ! [X4,X5] :
( ~ vertex(X4)
| ~ vertex(X5)
| X4 = X5
| ? [X1] :
( edge(X1)
& ( X4 != head_of(X1)
| X5 != tail_of(X1)
| X5 != head_of(X1)
| X4 != tail_of(X1) )
& ( ( X4 = head_of(X1)
& X5 = tail_of(X1) )
| ( X5 = head_of(X1)
& X4 = tail_of(X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(49,plain,
( ~ complete
| ! [X6,X7] :
( ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ? [X8] :
( edge(X8)
& ( X6 != head_of(X8)
| X7 != tail_of(X8)
| X7 != head_of(X8)
| X6 != tail_of(X8) )
& ( ( X6 = head_of(X8)
& X7 = tail_of(X8) )
| ( X7 = head_of(X8)
& X6 = tail_of(X8) ) ) ) ) ),
inference(variable_rename,[status(thm)],[48]) ).
fof(50,plain,
( ~ complete
| ! [X6,X7] :
( ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ( edge(esk2_2(X6,X7))
& ( X6 != head_of(esk2_2(X6,X7))
| X7 != tail_of(esk2_2(X6,X7))
| X7 != head_of(esk2_2(X6,X7))
| X6 != tail_of(esk2_2(X6,X7)) )
& ( ( X6 = head_of(esk2_2(X6,X7))
& X7 = tail_of(esk2_2(X6,X7)) )
| ( X7 = head_of(esk2_2(X6,X7))
& X6 = tail_of(esk2_2(X6,X7)) ) ) ) ) ),
inference(skolemize,[status(esa)],[49]) ).
fof(51,plain,
! [X6,X7] :
( ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ( edge(esk2_2(X6,X7))
& ( X6 != head_of(esk2_2(X6,X7))
| X7 != tail_of(esk2_2(X6,X7))
| X7 != head_of(esk2_2(X6,X7))
| X6 != tail_of(esk2_2(X6,X7)) )
& ( ( X6 = head_of(esk2_2(X6,X7))
& X7 = tail_of(esk2_2(X6,X7)) )
| ( X7 = head_of(esk2_2(X6,X7))
& X6 = tail_of(esk2_2(X6,X7)) ) ) )
| ~ complete ),
inference(shift_quantors,[status(thm)],[50]) ).
fof(52,plain,
! [X6,X7] :
( ( edge(esk2_2(X6,X7))
| ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ~ complete )
& ( X6 != head_of(esk2_2(X6,X7))
| X7 != tail_of(esk2_2(X6,X7))
| X7 != head_of(esk2_2(X6,X7))
| X6 != tail_of(esk2_2(X6,X7))
| ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ~ complete )
& ( X7 = head_of(esk2_2(X6,X7))
| X6 = head_of(esk2_2(X6,X7))
| ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ~ complete )
& ( X6 = tail_of(esk2_2(X6,X7))
| X6 = head_of(esk2_2(X6,X7))
| ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ~ complete )
& ( X7 = head_of(esk2_2(X6,X7))
| X7 = tail_of(esk2_2(X6,X7))
| ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ~ complete )
& ( X6 = tail_of(esk2_2(X6,X7))
| X7 = tail_of(esk2_2(X6,X7))
| ~ vertex(X6)
| ~ vertex(X7)
| X6 = X7
| ~ complete ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(53,plain,
( X1 = X2
| X2 = tail_of(esk2_2(X1,X2))
| X1 = tail_of(esk2_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(54,plain,
( X1 = X2
| X2 = tail_of(esk2_2(X1,X2))
| X2 = head_of(esk2_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(56,plain,
( X1 = X2
| X1 = head_of(esk2_2(X1,X2))
| X2 = head_of(esk2_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(58,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(59,plain,
! [X7,X4,X5] :
( ~ path(X4,X5,X7)
| ! [X2,X3] :
( ~ precedes(X2,X3,X7)
| ( on_path(X2,X7)
& on_path(X3,X7)
& ( ~ sequential(X2,X3)
| ! [X8] :
( ~ sequential(X2,X8)
| ~ precedes(X8,X3,X7) ) )
& ( sequential(X2,X3)
| ? [X8] :
( sequential(X2,X8)
& precedes(X8,X3,X7) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(60,plain,
! [X9,X10,X11] :
( ~ path(X10,X11,X9)
| ! [X12,X13] :
( ~ precedes(X12,X13,X9)
| ( on_path(X12,X9)
& on_path(X13,X9)
& ( ~ sequential(X12,X13)
| ! [X14] :
( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9) ) )
& ( sequential(X12,X13)
| ? [X15] :
( sequential(X12,X15)
& precedes(X15,X13,X9) ) ) ) ) ),
inference(variable_rename,[status(thm)],[59]) ).
fof(61,plain,
! [X9,X10,X11] :
( ~ path(X10,X11,X9)
| ! [X12,X13] :
( ~ precedes(X12,X13,X9)
| ( on_path(X12,X9)
& on_path(X13,X9)
& ( ~ sequential(X12,X13)
| ! [X14] :
( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9) ) )
& ( sequential(X12,X13)
| ( sequential(X12,esk3_5(X9,X10,X11,X12,X13))
& precedes(esk3_5(X9,X10,X11,X12,X13),X13,X9) ) ) ) ) ),
inference(skolemize,[status(esa)],[60]) ).
fof(62,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9)
| ~ sequential(X12,X13) )
& ( sequential(X12,X13)
| ( sequential(X12,esk3_5(X9,X10,X11,X12,X13))
& precedes(esk3_5(X9,X10,X11,X12,X13),X13,X9) ) )
& on_path(X12,X9)
& on_path(X13,X9) )
| ~ precedes(X12,X13,X9)
| ~ path(X10,X11,X9) ),
inference(shift_quantors,[status(thm)],[61]) ).
fof(63,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9)
| ~ sequential(X12,X13)
| ~ precedes(X12,X13,X9)
| ~ path(X10,X11,X9) )
& ( sequential(X12,esk3_5(X9,X10,X11,X12,X13))
| sequential(X12,X13)
| ~ precedes(X12,X13,X9)
| ~ path(X10,X11,X9) )
& ( precedes(esk3_5(X9,X10,X11,X12,X13),X13,X9)
| sequential(X12,X13)
| ~ precedes(X12,X13,X9)
| ~ path(X10,X11,X9) )
& ( on_path(X12,X9)
| ~ precedes(X12,X13,X9)
| ~ path(X10,X11,X9) )
& ( on_path(X13,X9)
| ~ precedes(X12,X13,X9)
| ~ path(X10,X11,X9) ) ),
inference(distribute,[status(thm)],[62]) ).
cnf(64,plain,
( on_path(X5,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[63]) ).
cnf(65,plain,
( on_path(X4,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(76,plain,
! [X4,X5,X7,X1] :
( ~ path(X4,X5,X7)
| ~ on_path(X1,X7)
| ( edge(X1)
& in_path(head_of(X1),X7)
& in_path(tail_of(X1),X7) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(77,plain,
! [X8,X9,X10,X11] :
( ~ path(X8,X9,X10)
| ~ on_path(X11,X10)
| ( edge(X11)
& in_path(head_of(X11),X10)
& in_path(tail_of(X11),X10) ) ),
inference(variable_rename,[status(thm)],[76]) ).
fof(78,plain,
! [X8,X9,X10,X11] :
( ( edge(X11)
| ~ path(X8,X9,X10)
| ~ on_path(X11,X10) )
& ( in_path(head_of(X11),X10)
| ~ path(X8,X9,X10)
| ~ on_path(X11,X10) )
& ( in_path(tail_of(X11),X10)
| ~ path(X8,X9,X10)
| ~ on_path(X11,X10) ) ),
inference(distribute,[status(thm)],[77]) ).
cnf(81,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(82,plain,
! [X4,X5,X2,X3,X7] :
( ~ shortest_path(X4,X5,X7)
| ~ precedes(X2,X3,X7)
| ( ! [X8] :
( tail_of(X8) != tail_of(X2)
| head_of(X8) != head_of(X3) )
& ~ precedes(X3,X2,X7) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(83,plain,
! [X9,X10,X11,X12,X13] :
( ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ( ! [X14] :
( tail_of(X14) != tail_of(X11)
| head_of(X14) != head_of(X12) )
& ~ precedes(X12,X11,X13) ) ),
inference(variable_rename,[status(thm)],[82]) ).
fof(84,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ( tail_of(X14) != tail_of(X11)
| head_of(X14) != head_of(X12) )
& ~ precedes(X12,X11,X13) )
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13) ),
inference(shift_quantors,[status(thm)],[83]) ).
fof(85,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( tail_of(X14) != tail_of(X11)
| head_of(X14) != head_of(X12)
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13) )
& ( ~ precedes(X12,X11,X13)
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13) ) ),
inference(distribute,[status(thm)],[84]) ).
cnf(86,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(87,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| head_of(X6) != head_of(X2)
| tail_of(X6) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[85]) ).
fof(88,plain,
! [X7,X4,X5] :
( ~ path(X4,X5,X7)
| ! [X2,X3] :
( ~ on_path(X2,X7)
| ~ on_path(X3,X7)
| ( ~ sequential(X2,X3)
& ! [X8] :
( ~ sequential(X2,X8)
| ~ precedes(X8,X3,X7) ) )
| precedes(X2,X3,X7) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(89,plain,
! [X9,X10,X11] :
( ~ path(X10,X11,X9)
| ! [X12,X13] :
( ~ on_path(X12,X9)
| ~ on_path(X13,X9)
| ( ~ sequential(X12,X13)
& ! [X14] :
( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9) ) )
| precedes(X12,X13,X9) ) ),
inference(variable_rename,[status(thm)],[88]) ).
fof(90,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9) )
& ~ sequential(X12,X13) )
| ~ on_path(X12,X9)
| ~ on_path(X13,X9)
| precedes(X12,X13,X9)
| ~ path(X10,X11,X9) ),
inference(shift_quantors,[status(thm)],[89]) ).
fof(91,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9)
| ~ on_path(X12,X9)
| ~ on_path(X13,X9)
| precedes(X12,X13,X9)
| ~ path(X10,X11,X9) )
& ( ~ sequential(X12,X13)
| ~ on_path(X12,X9)
| ~ on_path(X13,X9)
| precedes(X12,X13,X9)
| ~ path(X10,X11,X9) ) ),
inference(distribute,[status(thm)],[90]) ).
cnf(92,plain,
( precedes(X4,X5,X3)
| ~ path(X1,X2,X3)
| ~ on_path(X5,X3)
| ~ on_path(X4,X3)
| ~ sequential(X4,X5) ),
inference(split_conjunct,[status(thm)],[91]) ).
fof(94,negated_conjecture,
( complete
& ? [X4,X5,X2,X3,X7] :
( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7)
& ! [X8] :
( ~ edge(X8)
| tail_of(X8) != head_of(X3)
| head_of(X8) != tail_of(X2) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(95,negated_conjecture,
( complete
& ? [X9,X10,X11,X12,X13] :
( shortest_path(X9,X10,X13)
& precedes(X11,X12,X13)
& ! [X14] :
( ~ edge(X14)
| tail_of(X14) != head_of(X12)
| head_of(X14) != tail_of(X11) ) ) ),
inference(variable_rename,[status(thm)],[94]) ).
fof(96,negated_conjecture,
( complete
& shortest_path(esk5_0,esk6_0,esk9_0)
& precedes(esk7_0,esk8_0,esk9_0)
& ! [X14] :
( ~ edge(X14)
| tail_of(X14) != head_of(esk8_0)
| head_of(X14) != tail_of(esk7_0) ) ),
inference(skolemize,[status(esa)],[95]) ).
fof(97,negated_conjecture,
! [X14] :
( ( ~ edge(X14)
| tail_of(X14) != head_of(esk8_0)
| head_of(X14) != tail_of(esk7_0) )
& shortest_path(esk5_0,esk6_0,esk9_0)
& precedes(esk7_0,esk8_0,esk9_0)
& complete ),
inference(shift_quantors,[status(thm)],[96]) ).
cnf(98,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[97]) ).
cnf(99,negated_conjecture,
precedes(esk7_0,esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[97]) ).
cnf(100,negated_conjecture,
shortest_path(esk5_0,esk6_0,esk9_0),
inference(split_conjunct,[status(thm)],[97]) ).
cnf(101,negated_conjecture,
( head_of(X1) != tail_of(esk7_0)
| tail_of(X1) != head_of(esk8_0)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[97]) ).
cnf(131,negated_conjecture,
path(esk5_0,esk6_0,esk9_0),
inference(spm,[status(thm)],[46,100,theory(equality)]) ).
cnf(132,negated_conjecture,
( ~ precedes(esk8_0,esk7_0,esk9_0)
| ~ shortest_path(X1,X2,esk9_0) ),
inference(spm,[status(thm)],[86,99,theory(equality)]) ).
cnf(133,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| $false
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(rw,[status(thm)],[58,98,theory(equality)]) ).
cnf(134,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[133,theory(equality)]) ).
cnf(135,negated_conjecture,
( on_path(esk8_0,esk9_0)
| ~ path(X1,X2,esk9_0) ),
inference(spm,[status(thm)],[64,99,theory(equality)]) ).
cnf(136,negated_conjecture,
( on_path(esk7_0,esk9_0)
| ~ path(X1,X2,esk9_0) ),
inference(spm,[status(thm)],[65,99,theory(equality)]) ).
cnf(137,negated_conjecture,
( head_of(esk8_0) != head_of(X1)
| tail_of(esk7_0) != tail_of(X1)
| ~ shortest_path(X2,X3,esk9_0) ),
inference(spm,[status(thm)],[87,99,theory(equality)]) ).
cnf(138,plain,
( X1 = X2
| head_of(esk2_2(X1,X2)) = X2
| head_of(esk2_2(X1,X2)) = X1
| $false
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(rw,[status(thm)],[56,98,theory(equality)]) ).
cnf(139,plain,
( X1 = X2
| head_of(esk2_2(X1,X2)) = X2
| head_of(esk2_2(X1,X2)) = X1
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[138,theory(equality)]) ).
cnf(140,plain,
( head_of(esk2_2(X1,head_of(X2))) = X1
| head_of(esk2_2(X1,head_of(X2))) = head_of(X2)
| X1 = head_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[139,26,theory(equality)]) ).
cnf(151,plain,
( X1 = X2
| head_of(esk2_2(X1,X2)) = X2
| tail_of(esk2_2(X1,X2)) = X2
| $false
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(rw,[status(thm)],[54,98,theory(equality)]) ).
cnf(152,plain,
( X1 = X2
| head_of(esk2_2(X1,X2)) = X2
| tail_of(esk2_2(X1,X2)) = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[151,theory(equality)]) ).
cnf(162,plain,
( X1 = X2
| tail_of(esk2_2(X1,X2)) = X2
| tail_of(esk2_2(X1,X2)) = X1
| $false
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(rw,[status(thm)],[53,98,theory(equality)]) ).
cnf(163,plain,
( X1 = X2
| tail_of(esk2_2(X1,X2)) = X2
| tail_of(esk2_2(X1,X2)) = X1
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[162,theory(equality)]) ).
cnf(192,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[81,131,theory(equality)]) ).
cnf(199,negated_conjecture,
( precedes(X1,X2,esk9_0)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0)
| ~ sequential(X1,X2) ),
inference(spm,[status(thm)],[92,131,theory(equality)]) ).
cnf(201,negated_conjecture,
~ precedes(esk8_0,esk7_0,esk9_0),
inference(spm,[status(thm)],[132,100,theory(equality)]) ).
fof(202,plain,
( ~ epred1_0
<=> ! [X1] :
( tail_of(esk7_0) != tail_of(X1)
| head_of(esk8_0) != head_of(X1) ) ),
introduced(definition),
[split] ).
cnf(203,plain,
( epred1_0
| tail_of(esk7_0) != tail_of(X1)
| head_of(esk8_0) != head_of(X1) ),
inference(split_equiv,[status(thm)],[202]) ).
fof(204,plain,
( ~ epred2_0
<=> ! [X3,X2] : ~ shortest_path(X2,X3,esk9_0) ),
introduced(definition),
[split] ).
cnf(205,plain,
( epred2_0
| ~ shortest_path(X2,X3,esk9_0) ),
inference(split_equiv,[status(thm)],[204]) ).
cnf(206,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[137,202,theory(equality)]),204,theory(equality)]),
[split] ).
cnf(208,negated_conjecture,
epred2_0,
inference(spm,[status(thm)],[205,100,theory(equality)]) ).
cnf(210,negated_conjecture,
( $false
| ~ epred1_0 ),
inference(rw,[status(thm)],[206,208,theory(equality)]) ).
cnf(211,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[210,theory(equality)]) ).
cnf(212,negated_conjecture,
on_path(esk8_0,esk9_0),
inference(spm,[status(thm)],[135,131,theory(equality)]) ).
cnf(213,negated_conjecture,
( tail_of(esk7_0) != tail_of(X1)
| head_of(esk8_0) != head_of(X1) ),
inference(sr,[status(thm)],[203,211,theory(equality)]) ).
cnf(214,negated_conjecture,
tail_of(esk7_0) != tail_of(esk8_0),
inference(er,[status(thm)],[213,theory(equality)]) ).
cnf(224,negated_conjecture,
edge(esk8_0),
inference(spm,[status(thm)],[192,212,theory(equality)]) ).
cnf(228,negated_conjecture,
on_path(esk7_0,esk9_0),
inference(spm,[status(thm)],[136,131,theory(equality)]) ).
cnf(236,negated_conjecture,
edge(esk7_0),
inference(spm,[status(thm)],[192,228,theory(equality)]) ).
cnf(240,plain,
( head_of(esk2_2(tail_of(X1),head_of(X2))) = head_of(X2)
| head_of(esk2_2(tail_of(X1),head_of(X2))) = tail_of(X1)
| tail_of(X1) = head_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[140,25,theory(equality)]) ).
cnf(279,negated_conjecture,
( precedes(X1,esk7_0,esk9_0)
| ~ on_path(X1,esk9_0)
| ~ sequential(X1,esk7_0) ),
inference(spm,[status(thm)],[199,228,theory(equality)]) ).
cnf(292,negated_conjecture,
( precedes(esk8_0,esk7_0,esk9_0)
| ~ sequential(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[279,212,theory(equality)]) ).
cnf(297,negated_conjecture,
~ sequential(esk8_0,esk7_0),
inference(sr,[status(thm)],[292,201,theory(equality)]) ).
cnf(689,negated_conjecture,
( head_of(esk2_2(tail_of(X1),head_of(esk8_0))) = tail_of(X1)
| head_of(esk2_2(tail_of(X1),head_of(esk8_0))) = head_of(esk8_0)
| tail_of(X1) = head_of(esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[240,224,theory(equality)]) ).
cnf(760,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = head_of(esk8_0)
| head_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = tail_of(esk7_0)
| tail_of(esk7_0) = head_of(esk8_0) ),
inference(spm,[status(thm)],[689,236,theory(equality)]) ).
cnf(811,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0)))
| ~ edge(esk2_2(tail_of(esk7_0),head_of(esk8_0))) ),
inference(spm,[status(thm)],[37,760,theory(equality)]) ).
cnf(815,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk7_0) != tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) ),
inference(spm,[status(thm)],[213,760,theory(equality)]) ).
cnf(823,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = head_of(esk8_0)
| tail_of(esk7_0) = head_of(esk8_0)
| ~ vertex(head_of(esk8_0))
| ~ vertex(tail_of(esk7_0))
| tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) != tail_of(esk7_0) ),
inference(spm,[status(thm)],[152,815,theory(equality)]) ).
cnf(898,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) != head_of(esk8_0)
| ~ edge(esk2_2(tail_of(esk7_0),head_of(esk8_0))) ),
inference(csr,[status(thm)],[811,101]) ).
cnf(930,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| ~ vertex(head_of(esk8_0))
| ~ vertex(tail_of(esk7_0)) ),
inference(csr,[status(thm)],[823,163]) ).
cnf(943,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| ~ edge(esk2_2(tail_of(esk7_0),head_of(esk8_0)))
| ~ vertex(head_of(esk8_0))
| ~ vertex(tail_of(esk7_0)) ),
inference(spm,[status(thm)],[898,930,theory(equality)]) ).
cnf(944,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| ~ vertex(head_of(esk8_0))
| ~ vertex(tail_of(esk7_0)) ),
inference(csr,[status(thm)],[943,134]) ).
cnf(945,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0))
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[944,26,theory(equality)]) ).
cnf(947,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[945,224,theory(equality)]) ).
cnf(948,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(cn,[status(thm)],[947,theory(equality)]) ).
cnf(951,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| ~ edge(esk7_0) ),
inference(spm,[status(thm)],[948,25,theory(equality)]) ).
cnf(953,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| $false ),
inference(rw,[status(thm)],[951,236,theory(equality)]) ).
cnf(954,negated_conjecture,
head_of(esk8_0) = tail_of(esk7_0),
inference(cn,[status(thm)],[953,theory(equality)]) ).
cnf(959,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk7_0)
| ~ edge(X1)
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[30,954,theory(equality)]) ).
cnf(1285,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk7_0)
| ~ edge(X1)
| $false ),
inference(rw,[status(thm)],[959,224,theory(equality)]) ).
cnf(1286,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk7_0)
| ~ edge(X1) ),
inference(cn,[status(thm)],[1285,theory(equality)]) ).
cnf(1308,negated_conjecture,
( esk8_0 = esk7_0
| sequential(esk8_0,esk7_0)
| ~ edge(esk7_0) ),
inference(er,[status(thm)],[1286,theory(equality)]) ).
cnf(1310,negated_conjecture,
( esk8_0 = esk7_0
| sequential(esk8_0,esk7_0)
| $false ),
inference(rw,[status(thm)],[1308,236,theory(equality)]) ).
cnf(1311,negated_conjecture,
( esk8_0 = esk7_0
| sequential(esk8_0,esk7_0) ),
inference(cn,[status(thm)],[1310,theory(equality)]) ).
cnf(1312,negated_conjecture,
esk8_0 = esk7_0,
inference(sr,[status(thm)],[1311,297,theory(equality)]) ).
cnf(1320,negated_conjecture,
$false,
inference(rw,[status(thm)],[214,1312,theory(equality)]) ).
cnf(1321,negated_conjecture,
$false,
inference(cn,[status(thm)],[1320,theory(equality)]) ).
cnf(1322,negated_conjecture,
$false,
1321,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA007+1.p
% --creating new selector for [GRA001+0.ax]
% eprover: CPU time limit exceeded, terminating
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpa17TkQ/sel_GRA007+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpa17TkQ/sel_GRA007+1.p_2 with time limit 81
% -prover status ResourceOut
% --creating new selector for [GRA001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpa17TkQ/sel_GRA007+1.p_3 with time limit 74
% -prover status ResourceOut
% --creating new selector for [GRA001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpa17TkQ/sel_GRA007+1.p_4 with time limit 55
% -prover status ResourceOut
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmpa17TkQ/sel_GRA007+1.p_5 with time limit 54
% -prover status Theorem
% Problem GRA007+1.p solved in phase 4.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA007+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA007+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
%
%------------------------------------------------------------------------------