TSTP Solution File: GRA004+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA004+1 : TPTP v5.0.0. Bugfixed v3.2.0.
% 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 09:53:16 EST 2010
% Result : Theorem 239.71s
% Output : CNFRefutation 239.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 89 ( 17 unt; 0 def)
% Number of atoms : 419 ( 97 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 538 ( 208 ~; 198 |; 112 &)
% ( 5 <=>; 13 =>; 1 <=; 1 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-5 aty)
% Number of variables : 245 ( 24 sgn 169 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X2,X3] :
( sequential(X2,X3)
<=> ( edge(X2)
& edge(X3)
& X2 != X3
& head_of(X2) = tail_of(X3) ) ),
file('/tmp/tmpbcCnJD/sel_GRA004+1.p_5',sequential_defn) ).
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/tmpbcCnJD/sel_GRA004+1.p_5',shortest_path_defn) ).
fof(5,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/tmpbcCnJD/sel_GRA004+1.p_5',precedes_properties) ).
fof(7,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/tmpbcCnJD/sel_GRA004+1.p_5',on_path_properties) ).
fof(8,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/tmpbcCnJD/sel_GRA004+1.p_5',shortest_path_properties) ).
fof(9,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/tmpbcCnJD/sel_GRA004+1.p_5',precedes_defn) ).
fof(11,conjecture,
! [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) )
& head_of(X3) != tail_of(X2)
& head_of(X3) != head_of(X2) ) ),
file('/tmp/tmpbcCnJD/sel_GRA004+1.p_5',shortest_path_properties_lemma) ).
fof(16,negated_conjecture,
~ ! [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) )
& head_of(X3) != tail_of(X2)
& head_of(X3) != head_of(X2) ) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(17,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)],[5,theory(equality)]) ).
fof(18,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)],[8,theory(equality)]) ).
fof(19,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)],[9,theory(equality)]) ).
fof(25,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(26,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)],[25]) ).
fof(27,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)],[26]) ).
cnf(28,plain,
( sequential(X1,X2)
| X1 = X2
| head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(36,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(37,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)],[36]) ).
fof(38,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)],[37]) ).
fof(39,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)],[38]) ).
fof(40,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)],[39]) ).
cnf(44,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(46,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)],[17]) ).
fof(47,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)],[46]) ).
fof(48,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,esk2_5(X9,X10,X11,X12,X13))
& precedes(esk2_5(X9,X10,X11,X12,X13),X13,X9) ) ) ) ) ),
inference(skolemize,[status(esa)],[47]) ).
fof(49,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ( ~ sequential(X12,X14)
| ~ precedes(X14,X13,X9)
| ~ sequential(X12,X13) )
& ( sequential(X12,X13)
| ( sequential(X12,esk2_5(X9,X10,X11,X12,X13))
& precedes(esk2_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)],[48]) ).
fof(50,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,esk2_5(X9,X10,X11,X12,X13))
| sequential(X12,X13)
| ~ precedes(X12,X13,X9)
| ~ path(X10,X11,X9) )
& ( precedes(esk2_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)],[49]) ).
cnf(51,plain,
( on_path(X5,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(52,plain,
( on_path(X4,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(63,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)],[7]) ).
fof(64,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)],[63]) ).
fof(65,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)],[64]) ).
cnf(68,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(69,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)],[18]) ).
fof(70,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)],[69]) ).
fof(71,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)],[70]) ).
fof(72,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)],[71]) ).
cnf(73,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,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)],[72]) ).
fof(75,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)],[19]) ).
fof(76,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)],[75]) ).
fof(77,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)],[76]) ).
fof(78,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)],[77]) ).
cnf(79,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)],[78]) ).
fof(84,negated_conjecture,
? [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) )
| head_of(X3) = tail_of(X2)
| head_of(X3) = head_of(X2) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(85,negated_conjecture,
? [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) )
| head_of(X12) = tail_of(X11)
| head_of(X12) = head_of(X11) ) ),
inference(variable_rename,[status(thm)],[84]) ).
fof(86,negated_conjecture,
( shortest_path(esk4_0,esk5_0,esk8_0)
& precedes(esk6_0,esk7_0,esk8_0)
& ( ( tail_of(esk9_0) = tail_of(esk6_0)
& head_of(esk9_0) = head_of(esk7_0) )
| head_of(esk7_0) = tail_of(esk6_0)
| head_of(esk7_0) = head_of(esk6_0) ) ),
inference(skolemize,[status(esa)],[85]) ).
fof(87,negated_conjecture,
( shortest_path(esk4_0,esk5_0,esk8_0)
& precedes(esk6_0,esk7_0,esk8_0)
& ( tail_of(esk9_0) = tail_of(esk6_0)
| head_of(esk7_0) = tail_of(esk6_0)
| head_of(esk7_0) = head_of(esk6_0) )
& ( head_of(esk9_0) = head_of(esk7_0)
| head_of(esk7_0) = tail_of(esk6_0)
| head_of(esk7_0) = head_of(esk6_0) ) ),
inference(distribute,[status(thm)],[86]) ).
cnf(88,negated_conjecture,
( head_of(esk7_0) = head_of(esk6_0)
| head_of(esk7_0) = tail_of(esk6_0)
| head_of(esk9_0) = head_of(esk7_0) ),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(89,negated_conjecture,
( head_of(esk7_0) = head_of(esk6_0)
| head_of(esk7_0) = tail_of(esk6_0)
| tail_of(esk9_0) = tail_of(esk6_0) ),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(90,negated_conjecture,
precedes(esk6_0,esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(91,negated_conjecture,
shortest_path(esk4_0,esk5_0,esk8_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(122,negated_conjecture,
path(esk4_0,esk5_0,esk8_0),
inference(spm,[status(thm)],[44,91,theory(equality)]) ).
cnf(123,negated_conjecture,
( ~ precedes(esk7_0,esk6_0,esk8_0)
| ~ shortest_path(X1,X2,esk8_0) ),
inference(spm,[status(thm)],[73,90,theory(equality)]) ).
cnf(124,negated_conjecture,
( on_path(esk7_0,esk8_0)
| ~ path(X1,X2,esk8_0) ),
inference(spm,[status(thm)],[51,90,theory(equality)]) ).
cnf(125,negated_conjecture,
( on_path(esk6_0,esk8_0)
| ~ path(X1,X2,esk8_0) ),
inference(spm,[status(thm)],[52,90,theory(equality)]) ).
cnf(126,negated_conjecture,
( head_of(esk7_0) != head_of(X1)
| tail_of(esk6_0) != tail_of(X1)
| ~ shortest_path(X2,X3,esk8_0) ),
inference(spm,[status(thm)],[74,90,theory(equality)]) ).
cnf(161,negated_conjecture,
~ precedes(esk7_0,esk6_0,esk8_0),
inference(spm,[status(thm)],[123,91,theory(equality)]) ).
cnf(163,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk8_0) ),
inference(spm,[status(thm)],[68,122,theory(equality)]) ).
cnf(169,negated_conjecture,
( precedes(X1,X2,esk8_0)
| ~ on_path(X2,esk8_0)
| ~ on_path(X1,esk8_0)
| ~ sequential(X1,X2) ),
inference(spm,[status(thm)],[79,122,theory(equality)]) ).
fof(173,plain,
( ~ epred1_0
<=> ! [X1] :
( tail_of(esk6_0) != tail_of(X1)
| head_of(esk7_0) != head_of(X1) ) ),
introduced(definition),
[split] ).
cnf(174,plain,
( epred1_0
| tail_of(esk6_0) != tail_of(X1)
| head_of(esk7_0) != head_of(X1) ),
inference(split_equiv,[status(thm)],[173]) ).
fof(175,plain,
( ~ epred2_0
<=> ! [X3,X2] : ~ shortest_path(X2,X3,esk8_0) ),
introduced(definition),
[split] ).
cnf(176,plain,
( epred2_0
| ~ shortest_path(X2,X3,esk8_0) ),
inference(split_equiv,[status(thm)],[175]) ).
cnf(177,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[126,173,theory(equality)]),175,theory(equality)]),
[split] ).
cnf(178,negated_conjecture,
epred2_0,
inference(spm,[status(thm)],[176,91,theory(equality)]) ).
cnf(180,negated_conjecture,
( $false
| ~ epred1_0 ),
inference(rw,[status(thm)],[177,178,theory(equality)]) ).
cnf(181,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[180,theory(equality)]) ).
cnf(182,negated_conjecture,
( epred1_0
| head_of(esk7_0) != head_of(esk6_0) ),
inference(er,[status(thm)],[174,theory(equality)]) ).
cnf(187,negated_conjecture,
head_of(esk7_0) != head_of(esk6_0),
inference(sr,[status(thm)],[182,181,theory(equality)]) ).
cnf(188,negated_conjecture,
( tail_of(esk6_0) = head_of(esk7_0)
| head_of(esk9_0) = head_of(esk7_0) ),
inference(sr,[status(thm)],[88,187,theory(equality)]) ).
cnf(189,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk6_0)
| tail_of(esk6_0) = head_of(esk7_0) ),
inference(sr,[status(thm)],[89,187,theory(equality)]) ).
cnf(198,negated_conjecture,
( epred1_0
| tail_of(esk6_0) = head_of(esk7_0)
| head_of(esk7_0) != head_of(esk9_0) ),
inference(spm,[status(thm)],[174,189,theory(equality)]) ).
cnf(199,negated_conjecture,
( tail_of(esk6_0) = head_of(esk7_0)
| head_of(esk9_0) != head_of(esk7_0) ),
inference(sr,[status(thm)],[198,181,theory(equality)]) ).
cnf(200,negated_conjecture,
tail_of(esk6_0) = head_of(esk7_0),
inference(csr,[status(thm)],[199,188]) ).
cnf(217,negated_conjecture,
on_path(esk7_0,esk8_0),
inference(spm,[status(thm)],[124,122,theory(equality)]) ).
cnf(223,negated_conjecture,
edge(esk7_0),
inference(spm,[status(thm)],[163,217,theory(equality)]) ).
cnf(225,negated_conjecture,
( esk7_0 = X1
| sequential(esk7_0,X1)
| tail_of(X1) != head_of(esk7_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[28,223,theory(equality)]) ).
cnf(235,negated_conjecture,
( esk7_0 = esk6_0
| sequential(esk7_0,esk6_0)
| ~ edge(esk6_0) ),
inference(spm,[status(thm)],[225,200,theory(equality)]) ).
cnf(237,negated_conjecture,
on_path(esk6_0,esk8_0),
inference(spm,[status(thm)],[125,122,theory(equality)]) ).
cnf(242,negated_conjecture,
edge(esk6_0),
inference(spm,[status(thm)],[163,237,theory(equality)]) ).
cnf(247,negated_conjecture,
( esk7_0 = esk6_0
| sequential(esk7_0,esk6_0)
| $false ),
inference(rw,[status(thm)],[235,242,theory(equality)]) ).
cnf(248,negated_conjecture,
( esk7_0 = esk6_0
| sequential(esk7_0,esk6_0) ),
inference(cn,[status(thm)],[247,theory(equality)]) ).
cnf(266,negated_conjecture,
( precedes(X1,esk6_0,esk8_0)
| ~ on_path(X1,esk8_0)
| ~ sequential(X1,esk6_0) ),
inference(spm,[status(thm)],[169,237,theory(equality)]) ).
cnf(279,negated_conjecture,
( precedes(esk7_0,esk6_0,esk8_0)
| ~ sequential(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[266,217,theory(equality)]) ).
cnf(284,negated_conjecture,
~ sequential(esk7_0,esk6_0),
inference(sr,[status(thm)],[279,161,theory(equality)]) ).
cnf(285,negated_conjecture,
esk7_0 = esk6_0,
inference(sr,[status(thm)],[248,284,theory(equality)]) ).
cnf(296,negated_conjecture,
$false,
inference(rw,[status(thm)],[187,285,theory(equality)]) ).
cnf(297,negated_conjecture,
$false,
inference(cn,[status(thm)],[296,theory(equality)]) ).
cnf(298,negated_conjecture,
$false,
297,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA004+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/tmpbcCnJD/sel_GRA004+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpbcCnJD/sel_GRA004+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/tmpbcCnJD/sel_GRA004+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/tmpbcCnJD/sel_GRA004+1.p_4 with time limit 55
% -prover status ResourceOut
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmpbcCnJD/sel_GRA004+1.p_5 with time limit 54
% -prover status Theorem
% Problem GRA004+1.p solved in phase 4.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA004+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA004+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
%
%------------------------------------------------------------------------------